59.097 * [progress]: [Phase 1 of 3] Setting up. 0.001 * * * [progress]: [1/2] Preparing points 0.247 * * * [progress]: [2/2] Setting up program. 0.253 * [progress]: [Phase 2 of 3] Improving. 0.253 * * * * [progress]: [ 1 / 1 ] simplifiying candidate # 0.253 * [simplify]: Simplifying: (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 0.253 * * [simplify]: iteration 0: 13 enodes 0.256 * * [simplify]: iteration 1: 31 enodes 0.262 * * [simplify]: iteration 2: 62 enodes 0.274 * * [simplify]: iteration 3: 124 enodes 0.317 * * [simplify]: iteration 4: 328 enodes 0.560 * * [simplify]: iteration 5: 970 enodes 1.688 * * [simplify]: iteration 6: 2753 enodes 2.807 * * [simplify]: iteration complete: 5000 enodes 2.807 * * [simplify]: Extracting #0: cost 1 inf + 0 2.808 * * [simplify]: Extracting #1: cost 218 inf + 0 2.810 * * [simplify]: Extracting #2: cost 583 inf + 1 2.813 * * [simplify]: Extracting #3: cost 872 inf + 91 2.818 * * [simplify]: Extracting #4: cost 882 inf + 7092 2.838 * * [simplify]: Extracting #5: cost 661 inf + 35266 2.873 * * [simplify]: Extracting #6: cost 372 inf + 225053 3.008 * * [simplify]: Extracting #7: cost 38 inf + 563892 3.165 * * [simplify]: Extracting #8: cost 0 inf + 582786 3.361 * * [simplify]: Extracting #9: cost 0 inf + 575286 3.546 * [simplify]: Simplified to: (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) 3.550 * * [progress]: iteration 1 / 4 3.550 * * * [progress]: picking best candidate 3.556 * * * * [pick]: Picked # 3.556 * * * [progress]: localizing error 3.577 * * * [progress]: generating rewritten candidates 3.577 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1 1) 3.610 * * * * [progress]: [ 2 / 3 ] rewriting at (2) 3.625 * * * * [progress]: [ 3 / 3 ] rewriting at (2 1) 3.679 * * * [progress]: generating series expansions 3.679 * * * * [progress]: [ 1 / 3 ] generating series at (2 1 1) 3.679 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI)) 3.679 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 3.679 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 3.679 * [taylor]: Taking taylor expansion of 2 in n 3.679 * [backup-simplify]: Simplify 2 into 2 3.679 * [taylor]: Taking taylor expansion of (* n PI) in n 3.679 * [taylor]: Taking taylor expansion of n in n 3.679 * [backup-simplify]: Simplify 0 into 0 3.679 * [backup-simplify]: Simplify 1 into 1 3.679 * [taylor]: Taking taylor expansion of PI in n 3.679 * [backup-simplify]: Simplify PI into PI 3.679 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 3.679 * [taylor]: Taking taylor expansion of 2 in n 3.679 * [backup-simplify]: Simplify 2 into 2 3.679 * [taylor]: Taking taylor expansion of (* n PI) in n 3.679 * [taylor]: Taking taylor expansion of n in n 3.679 * [backup-simplify]: Simplify 0 into 0 3.679 * [backup-simplify]: Simplify 1 into 1 3.680 * [taylor]: Taking taylor expansion of PI in n 3.680 * [backup-simplify]: Simplify PI into PI 3.680 * [backup-simplify]: Simplify (* 0 PI) into 0 3.681 * [backup-simplify]: Simplify (* 2 0) into 0 3.681 * [backup-simplify]: Simplify 0 into 0 3.683 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.684 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 3.685 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 3.685 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.686 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 3.686 * [backup-simplify]: Simplify 0 into 0 3.687 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.687 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.687 * [backup-simplify]: Simplify 0 into 0 3.688 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.689 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 3.689 * [backup-simplify]: Simplify 0 into 0 3.690 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.691 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 3.691 * [backup-simplify]: Simplify 0 into 0 3.692 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.693 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 3.693 * [backup-simplify]: Simplify 0 into 0 3.694 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 3.695 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 3.695 * [backup-simplify]: Simplify 0 into 0 3.696 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 3.696 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n)) 3.696 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 3.696 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 3.696 * [taylor]: Taking taylor expansion of 2 in n 3.696 * [backup-simplify]: Simplify 2 into 2 3.696 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.696 * [taylor]: Taking taylor expansion of PI in n 3.696 * [backup-simplify]: Simplify PI into PI 3.696 * [taylor]: Taking taylor expansion of n in n 3.696 * [backup-simplify]: Simplify 0 into 0 3.696 * [backup-simplify]: Simplify 1 into 1 3.696 * [backup-simplify]: Simplify (/ PI 1) into PI 3.696 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 3.696 * [taylor]: Taking taylor expansion of 2 in n 3.696 * [backup-simplify]: Simplify 2 into 2 3.696 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.696 * [taylor]: Taking taylor expansion of PI in n 3.696 * [backup-simplify]: Simplify PI into PI 3.696 * [taylor]: Taking taylor expansion of n in n 3.696 * [backup-simplify]: Simplify 0 into 0 3.696 * [backup-simplify]: Simplify 1 into 1 3.697 * [backup-simplify]: Simplify (/ PI 1) into PI 3.697 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 3.697 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 3.698 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.698 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 3.698 * [backup-simplify]: Simplify 0 into 0 3.699 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.699 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 3.700 * [backup-simplify]: Simplify 0 into 0 3.700 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.701 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.701 * [backup-simplify]: Simplify 0 into 0 3.701 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.702 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.702 * [backup-simplify]: Simplify 0 into 0 3.703 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.704 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.704 * [backup-simplify]: Simplify 0 into 0 3.705 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.706 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.706 * [backup-simplify]: Simplify 0 into 0 3.706 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 3.706 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n)) 3.706 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 3.706 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 3.706 * [taylor]: Taking taylor expansion of -2 in n 3.706 * [backup-simplify]: Simplify -2 into -2 3.706 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.706 * [taylor]: Taking taylor expansion of PI in n 3.706 * [backup-simplify]: Simplify PI into PI 3.706 * [taylor]: Taking taylor expansion of n in n 3.706 * [backup-simplify]: Simplify 0 into 0 3.706 * [backup-simplify]: Simplify 1 into 1 3.707 * [backup-simplify]: Simplify (/ PI 1) into PI 3.707 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 3.707 * [taylor]: Taking taylor expansion of -2 in n 3.707 * [backup-simplify]: Simplify -2 into -2 3.707 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.707 * [taylor]: Taking taylor expansion of PI in n 3.707 * [backup-simplify]: Simplify PI into PI 3.707 * [taylor]: Taking taylor expansion of n in n 3.707 * [backup-simplify]: Simplify 0 into 0 3.707 * [backup-simplify]: Simplify 1 into 1 3.707 * [backup-simplify]: Simplify (/ PI 1) into PI 3.708 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 3.708 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 3.708 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.709 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 3.709 * [backup-simplify]: Simplify 0 into 0 3.709 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.710 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 3.710 * [backup-simplify]: Simplify 0 into 0 3.711 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.711 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.712 * [backup-simplify]: Simplify 0 into 0 3.712 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.713 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.713 * [backup-simplify]: Simplify 0 into 0 3.714 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.716 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 3.716 * [backup-simplify]: Simplify 0 into 0 3.717 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.719 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 3.719 * [backup-simplify]: Simplify 0 into 0 3.719 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 3.720 * * * * [progress]: [ 2 / 3 ] generating series at (2) 3.720 * [backup-simplify]: Simplify (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 3.720 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 3.720 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 3.720 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.720 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.720 * [taylor]: Taking taylor expansion of k in k 3.720 * [backup-simplify]: Simplify 0 into 0 3.720 * [backup-simplify]: Simplify 1 into 1 3.720 * [backup-simplify]: Simplify (/ 1 1) into 1 3.721 * [backup-simplify]: Simplify (sqrt 0) into 0 3.722 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.722 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 3.722 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 3.722 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 3.722 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 3.722 * [taylor]: Taking taylor expansion of 1/2 in k 3.722 * [backup-simplify]: Simplify 1/2 into 1/2 3.723 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 3.723 * [taylor]: Taking taylor expansion of 1/2 in k 3.723 * [backup-simplify]: Simplify 1/2 into 1/2 3.723 * [taylor]: Taking taylor expansion of k in k 3.723 * [backup-simplify]: Simplify 0 into 0 3.723 * [backup-simplify]: Simplify 1 into 1 3.723 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 3.723 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 3.723 * [taylor]: Taking taylor expansion of 2 in k 3.723 * [backup-simplify]: Simplify 2 into 2 3.723 * [taylor]: Taking taylor expansion of (* n PI) in k 3.723 * [taylor]: Taking taylor expansion of n in k 3.723 * [backup-simplify]: Simplify n into n 3.723 * [taylor]: Taking taylor expansion of PI in k 3.723 * [backup-simplify]: Simplify PI into PI 3.723 * [backup-simplify]: Simplify (* n PI) into (* n PI) 3.723 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 3.723 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 3.724 * [backup-simplify]: Simplify (* 1/2 0) into 0 3.724 * [backup-simplify]: Simplify (- 0) into 0 3.724 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 3.724 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 3.725 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 3.725 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 3.725 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 3.725 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.725 * [taylor]: Taking taylor expansion of k in n 3.725 * [backup-simplify]: Simplify k into k 3.725 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.725 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 3.725 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.725 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 3.725 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 3.725 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 3.725 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 3.725 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 3.725 * [taylor]: Taking taylor expansion of 1/2 in n 3.725 * [backup-simplify]: Simplify 1/2 into 1/2 3.725 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 3.725 * [taylor]: Taking taylor expansion of 1/2 in n 3.725 * [backup-simplify]: Simplify 1/2 into 1/2 3.725 * [taylor]: Taking taylor expansion of k in n 3.725 * [backup-simplify]: Simplify k into k 3.725 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 3.725 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 3.725 * [taylor]: Taking taylor expansion of 2 in n 3.725 * [backup-simplify]: Simplify 2 into 2 3.725 * [taylor]: Taking taylor expansion of (* n PI) in n 3.726 * [taylor]: Taking taylor expansion of n in n 3.726 * [backup-simplify]: Simplify 0 into 0 3.726 * [backup-simplify]: Simplify 1 into 1 3.726 * [taylor]: Taking taylor expansion of PI in n 3.726 * [backup-simplify]: Simplify PI into PI 3.726 * [backup-simplify]: Simplify (* 0 PI) into 0 3.727 * [backup-simplify]: Simplify (* 2 0) into 0 3.728 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.730 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 3.731 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 3.731 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 3.731 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 3.731 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 3.733 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 3.734 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 3.735 * [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))))) 3.735 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 3.735 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 3.735 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.735 * [taylor]: Taking taylor expansion of k in n 3.735 * [backup-simplify]: Simplify k into k 3.735 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.735 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 3.735 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.736 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 3.736 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 3.736 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 3.736 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 3.736 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 3.736 * [taylor]: Taking taylor expansion of 1/2 in n 3.736 * [backup-simplify]: Simplify 1/2 into 1/2 3.736 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 3.736 * [taylor]: Taking taylor expansion of 1/2 in n 3.736 * [backup-simplify]: Simplify 1/2 into 1/2 3.736 * [taylor]: Taking taylor expansion of k in n 3.736 * [backup-simplify]: Simplify k into k 3.736 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 3.736 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 3.736 * [taylor]: Taking taylor expansion of 2 in n 3.736 * [backup-simplify]: Simplify 2 into 2 3.736 * [taylor]: Taking taylor expansion of (* n PI) in n 3.736 * [taylor]: Taking taylor expansion of n in n 3.736 * [backup-simplify]: Simplify 0 into 0 3.736 * [backup-simplify]: Simplify 1 into 1 3.736 * [taylor]: Taking taylor expansion of PI in n 3.736 * [backup-simplify]: Simplify PI into PI 3.737 * [backup-simplify]: Simplify (* 0 PI) into 0 3.737 * [backup-simplify]: Simplify (* 2 0) into 0 3.739 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 3.740 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 3.741 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 3.742 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 3.742 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 3.742 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 3.743 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 3.744 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 3.746 * [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))))) 3.747 * [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))) 3.747 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k 3.747 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 3.747 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 3.747 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 3.747 * [taylor]: Taking taylor expansion of 1/2 in k 3.747 * [backup-simplify]: Simplify 1/2 into 1/2 3.747 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 3.747 * [taylor]: Taking taylor expansion of 1/2 in k 3.747 * [backup-simplify]: Simplify 1/2 into 1/2 3.747 * [taylor]: Taking taylor expansion of k in k 3.747 * [backup-simplify]: Simplify 0 into 0 3.747 * [backup-simplify]: Simplify 1 into 1 3.747 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 3.747 * [taylor]: Taking taylor expansion of (log n) in k 3.747 * [taylor]: Taking taylor expansion of n in k 3.747 * [backup-simplify]: Simplify n into n 3.747 * [backup-simplify]: Simplify (log n) into (log n) 3.747 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 3.747 * [taylor]: Taking taylor expansion of (* 2 PI) in k 3.747 * [taylor]: Taking taylor expansion of 2 in k 3.748 * [backup-simplify]: Simplify 2 into 2 3.748 * [taylor]: Taking taylor expansion of PI in k 3.748 * [backup-simplify]: Simplify PI into PI 3.748 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 3.749 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 3.750 * [backup-simplify]: Simplify (* 1/2 0) into 0 3.750 * [backup-simplify]: Simplify (- 0) into 0 3.751 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 3.752 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 3.753 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 3.754 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 3.754 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 3.754 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.754 * [taylor]: Taking taylor expansion of k in k 3.754 * [backup-simplify]: Simplify 0 into 0 3.754 * [backup-simplify]: Simplify 1 into 1 3.755 * [backup-simplify]: Simplify (/ 1 1) into 1 3.755 * [backup-simplify]: Simplify (sqrt 0) into 0 3.757 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.757 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0 3.757 * [backup-simplify]: Simplify 0 into 0 3.758 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 3.759 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 3.760 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 3.760 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 3.760 * [backup-simplify]: Simplify (- 0) into 0 3.760 * [backup-simplify]: Simplify (+ 0 0) into 0 3.761 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 3.762 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 3.763 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 3.764 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0 3.764 * [taylor]: Taking taylor expansion of 0 in k 3.764 * [backup-simplify]: Simplify 0 into 0 3.764 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 3.765 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 3.766 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 3.766 * [backup-simplify]: Simplify (+ 0 0) into 0 3.767 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 3.767 * [backup-simplify]: Simplify (- 1/2) into -1/2 3.767 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 3.768 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3.770 * [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))))))) 3.772 * [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))))))) 3.773 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 3.774 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 3.775 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 3.776 * [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 3.777 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 3.778 * [backup-simplify]: Simplify (- 0) into 0 3.778 * [backup-simplify]: Simplify (+ 0 0) into 0 3.779 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 3.781 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 3.783 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 3.784 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.784 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 3.786 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0 3.786 * [taylor]: Taking taylor expansion of 0 in k 3.786 * [backup-simplify]: Simplify 0 into 0 3.786 * [backup-simplify]: Simplify 0 into 0 3.787 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 3.797 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.798 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 3.799 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 3.803 * [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 3.804 * [backup-simplify]: Simplify (+ 0 0) into 0 3.805 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 3.805 * [backup-simplify]: Simplify (- 0) into 0 3.806 * [backup-simplify]: Simplify (+ 0 0) into 0 3.808 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 3.812 * [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))))) 3.821 * [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)))))))) 3.824 * [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)))))))) 3.825 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 3.825 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 3.829 * [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 3.829 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0 3.830 * [backup-simplify]: Simplify (- 0) into 0 3.830 * [backup-simplify]: Simplify (+ 0 0) into 0 3.831 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 3.832 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 3.833 * [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 3.834 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.834 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 3.835 * [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 3.835 * [taylor]: Taking taylor expansion of 0 in k 3.835 * [backup-simplify]: Simplify 0 into 0 3.835 * [backup-simplify]: Simplify 0 into 0 3.835 * [backup-simplify]: Simplify 0 into 0 3.836 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.838 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.840 * [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 3.841 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.844 * [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 3.844 * [backup-simplify]: Simplify (+ 0 0) into 0 3.845 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 3.845 * [backup-simplify]: Simplify (- 0) into 0 3.846 * [backup-simplify]: Simplify (+ 0 0) into 0 3.847 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0 3.852 * [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))))))) 3.868 * [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)))))))))))))) 3.875 * [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)))))))))))))) 3.886 * [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)))))))))))))))))))))) 3.887 * [backup-simplify]: Simplify (/ (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 3.887 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 3.887 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 3.887 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.887 * [taylor]: Taking taylor expansion of k in k 3.887 * [backup-simplify]: Simplify 0 into 0 3.887 * [backup-simplify]: Simplify 1 into 1 3.887 * [backup-simplify]: Simplify (sqrt 0) into 0 3.888 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.888 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 3.888 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 3.888 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 3.888 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 3.888 * [taylor]: Taking taylor expansion of 1/2 in k 3.888 * [backup-simplify]: Simplify 1/2 into 1/2 3.888 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 3.888 * [taylor]: Taking taylor expansion of 1/2 in k 3.888 * [backup-simplify]: Simplify 1/2 into 1/2 3.888 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.888 * [taylor]: Taking taylor expansion of k in k 3.888 * [backup-simplify]: Simplify 0 into 0 3.888 * [backup-simplify]: Simplify 1 into 1 3.888 * [backup-simplify]: Simplify (/ 1 1) into 1 3.889 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 3.889 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 3.889 * [taylor]: Taking taylor expansion of 2 in k 3.889 * [backup-simplify]: Simplify 2 into 2 3.889 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.889 * [taylor]: Taking taylor expansion of PI in k 3.889 * [backup-simplify]: Simplify PI into PI 3.889 * [taylor]: Taking taylor expansion of n in k 3.889 * [backup-simplify]: Simplify n into n 3.889 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.889 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 3.889 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 3.889 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 3.889 * [backup-simplify]: Simplify (- 1/2) into -1/2 3.890 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 3.890 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 3.890 * [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)))) 3.890 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 3.890 * [taylor]: Taking taylor expansion of (sqrt k) in n 3.890 * [taylor]: Taking taylor expansion of k in n 3.890 * [backup-simplify]: Simplify k into k 3.890 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 3.890 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 3.890 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 3.890 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 3.890 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 3.890 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 3.890 * [taylor]: Taking taylor expansion of 1/2 in n 3.890 * [backup-simplify]: Simplify 1/2 into 1/2 3.890 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 3.890 * [taylor]: Taking taylor expansion of 1/2 in n 3.890 * [backup-simplify]: Simplify 1/2 into 1/2 3.890 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.890 * [taylor]: Taking taylor expansion of k in n 3.890 * [backup-simplify]: Simplify k into k 3.890 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.890 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 3.890 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 3.890 * [taylor]: Taking taylor expansion of 2 in n 3.890 * [backup-simplify]: Simplify 2 into 2 3.890 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.890 * [taylor]: Taking taylor expansion of PI in n 3.890 * [backup-simplify]: Simplify PI into PI 3.890 * [taylor]: Taking taylor expansion of n in n 3.890 * [backup-simplify]: Simplify 0 into 0 3.890 * [backup-simplify]: Simplify 1 into 1 3.891 * [backup-simplify]: Simplify (/ PI 1) into PI 3.891 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 3.897 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 3.897 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 3.897 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 3.897 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 3.899 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 3.900 * [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))) 3.901 * [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)))) 3.901 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 3.901 * [taylor]: Taking taylor expansion of (sqrt k) in n 3.901 * [taylor]: Taking taylor expansion of k in n 3.901 * [backup-simplify]: Simplify k into k 3.901 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 3.901 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 3.901 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 3.901 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 3.902 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 3.902 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 3.902 * [taylor]: Taking taylor expansion of 1/2 in n 3.902 * [backup-simplify]: Simplify 1/2 into 1/2 3.902 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 3.902 * [taylor]: Taking taylor expansion of 1/2 in n 3.902 * [backup-simplify]: Simplify 1/2 into 1/2 3.902 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.902 * [taylor]: Taking taylor expansion of k in n 3.902 * [backup-simplify]: Simplify k into k 3.902 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.902 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 3.902 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 3.902 * [taylor]: Taking taylor expansion of 2 in n 3.902 * [backup-simplify]: Simplify 2 into 2 3.902 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.902 * [taylor]: Taking taylor expansion of PI in n 3.902 * [backup-simplify]: Simplify PI into PI 3.902 * [taylor]: Taking taylor expansion of n in n 3.902 * [backup-simplify]: Simplify 0 into 0 3.902 * [backup-simplify]: Simplify 1 into 1 3.903 * [backup-simplify]: Simplify (/ PI 1) into PI 3.903 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 3.904 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 3.904 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 3.904 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 3.904 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 3.906 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 3.907 * [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))) 3.908 * [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)))) 3.909 * [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)) 3.909 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k 3.909 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 3.909 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 3.909 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 3.909 * [taylor]: Taking taylor expansion of 1/2 in k 3.909 * [backup-simplify]: Simplify 1/2 into 1/2 3.909 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 3.909 * [taylor]: Taking taylor expansion of 1/2 in k 3.909 * [backup-simplify]: Simplify 1/2 into 1/2 3.909 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.910 * [taylor]: Taking taylor expansion of k in k 3.910 * [backup-simplify]: Simplify 0 into 0 3.910 * [backup-simplify]: Simplify 1 into 1 3.910 * [backup-simplify]: Simplify (/ 1 1) into 1 3.910 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 3.910 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 3.910 * [taylor]: Taking taylor expansion of (* 2 PI) in k 3.910 * [taylor]: Taking taylor expansion of 2 in k 3.910 * [backup-simplify]: Simplify 2 into 2 3.910 * [taylor]: Taking taylor expansion of PI in k 3.910 * [backup-simplify]: Simplify PI into PI 3.910 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 3.911 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 3.911 * [taylor]: Taking taylor expansion of (log n) in k 3.911 * [taylor]: Taking taylor expansion of n in k 3.911 * [backup-simplify]: Simplify n into n 3.911 * [backup-simplify]: Simplify (log n) into (log n) 3.911 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 3.911 * [backup-simplify]: Simplify (- 1/2) into -1/2 3.912 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 3.912 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.912 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 3.913 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 3.914 * [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)))) 3.914 * [taylor]: Taking taylor expansion of (sqrt k) in k 3.914 * [taylor]: Taking taylor expansion of k in k 3.914 * [backup-simplify]: Simplify 0 into 0 3.914 * [backup-simplify]: Simplify 1 into 1 3.914 * [backup-simplify]: Simplify (sqrt 0) into 0 3.915 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 3.916 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0 3.916 * [backup-simplify]: Simplify 0 into 0 3.917 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.917 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 3.918 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 3.918 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.918 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 3.919 * [backup-simplify]: Simplify (- 0) into 0 3.919 * [backup-simplify]: Simplify (+ 0 0) into 0 3.920 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 3.921 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 3.922 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 3.922 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 3.922 * [taylor]: Taking taylor expansion of 0 in k 3.922 * [backup-simplify]: Simplify 0 into 0 3.923 * [backup-simplify]: Simplify 0 into 0 3.923 * [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)))))) 3.924 * [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)))))) 3.925 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.925 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 3.927 * [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 3.927 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.928 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 3.928 * [backup-simplify]: Simplify (- 0) into 0 3.928 * [backup-simplify]: Simplify (+ 0 0) into 0 3.929 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 3.930 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 3.932 * [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 3.932 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 3.933 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 3.933 * [taylor]: Taking taylor expansion of 0 in k 3.933 * [backup-simplify]: Simplify 0 into 0 3.933 * [backup-simplify]: Simplify 0 into 0 3.933 * [backup-simplify]: Simplify 0 into 0 3.935 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 3.937 * [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)))))) 3.938 * [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)))))) 3.939 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 3.940 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 3.946 * [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 3.947 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 3.948 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 3.948 * [backup-simplify]: Simplify (- 0) into 0 3.949 * [backup-simplify]: Simplify (+ 0 0) into 0 3.950 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 3.952 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 3.955 * [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 3.956 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 3.958 * [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 3.958 * [taylor]: Taking taylor expansion of 0 in k 3.958 * [backup-simplify]: Simplify 0 into 0 3.958 * [backup-simplify]: Simplify 0 into 0 3.958 * [backup-simplify]: Simplify 0 into 0 3.958 * [backup-simplify]: Simplify 0 into 0 3.962 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 3.964 * [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)))))) 3.965 * [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)))))) 3.970 * [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)))))))) 3.970 * [backup-simplify]: Simplify (/ (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 3.970 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0 3.970 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 3.970 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 3.970 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 3.970 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 3.970 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 3.970 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 3.970 * [taylor]: Taking taylor expansion of 1/2 in k 3.970 * [backup-simplify]: Simplify 1/2 into 1/2 3.970 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.970 * [taylor]: Taking taylor expansion of k in k 3.970 * [backup-simplify]: Simplify 0 into 0 3.971 * [backup-simplify]: Simplify 1 into 1 3.971 * [backup-simplify]: Simplify (/ 1 1) into 1 3.971 * [taylor]: Taking taylor expansion of 1/2 in k 3.971 * [backup-simplify]: Simplify 1/2 into 1/2 3.971 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 3.971 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 3.971 * [taylor]: Taking taylor expansion of -2 in k 3.971 * [backup-simplify]: Simplify -2 into -2 3.971 * [taylor]: Taking taylor expansion of (/ PI n) in k 3.971 * [taylor]: Taking taylor expansion of PI in k 3.971 * [backup-simplify]: Simplify PI into PI 3.971 * [taylor]: Taking taylor expansion of n in k 3.971 * [backup-simplify]: Simplify n into n 3.971 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 3.971 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 3.972 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 3.972 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 3.972 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 3.973 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 3.973 * [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))) 3.973 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.973 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.973 * [taylor]: Taking taylor expansion of -1 in k 3.973 * [backup-simplify]: Simplify -1 into -1 3.973 * [taylor]: Taking taylor expansion of k in k 3.973 * [backup-simplify]: Simplify 0 into 0 3.973 * [backup-simplify]: Simplify 1 into 1 3.973 * [backup-simplify]: Simplify (/ -1 1) into -1 3.974 * [backup-simplify]: Simplify (sqrt 0) into 0 3.975 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.975 * [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)))) 3.975 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 3.975 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 3.976 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 3.976 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 3.976 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 3.976 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 3.976 * [taylor]: Taking taylor expansion of 1/2 in n 3.976 * [backup-simplify]: Simplify 1/2 into 1/2 3.976 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.976 * [taylor]: Taking taylor expansion of k in n 3.976 * [backup-simplify]: Simplify k into k 3.976 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.976 * [taylor]: Taking taylor expansion of 1/2 in n 3.976 * [backup-simplify]: Simplify 1/2 into 1/2 3.976 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 3.976 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 3.976 * [taylor]: Taking taylor expansion of -2 in n 3.976 * [backup-simplify]: Simplify -2 into -2 3.976 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.976 * [taylor]: Taking taylor expansion of PI in n 3.976 * [backup-simplify]: Simplify PI into PI 3.976 * [taylor]: Taking taylor expansion of n in n 3.976 * [backup-simplify]: Simplify 0 into 0 3.976 * [backup-simplify]: Simplify 1 into 1 3.977 * [backup-simplify]: Simplify (/ PI 1) into PI 3.977 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 3.978 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 3.978 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 3.978 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 3.980 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 3.981 * [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))) 3.982 * [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)))) 3.982 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 3.982 * [taylor]: Taking taylor expansion of (/ -1 k) in n 3.982 * [taylor]: Taking taylor expansion of -1 in n 3.982 * [backup-simplify]: Simplify -1 into -1 3.982 * [taylor]: Taking taylor expansion of k in n 3.982 * [backup-simplify]: Simplify k into k 3.982 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 3.982 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 3.982 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 3.982 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 3.983 * [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))) 3.983 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 3.983 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 3.983 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 3.983 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 3.983 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 3.983 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 3.983 * [taylor]: Taking taylor expansion of 1/2 in n 3.983 * [backup-simplify]: Simplify 1/2 into 1/2 3.983 * [taylor]: Taking taylor expansion of (/ 1 k) in n 3.983 * [taylor]: Taking taylor expansion of k in n 3.983 * [backup-simplify]: Simplify k into k 3.983 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 3.983 * [taylor]: Taking taylor expansion of 1/2 in n 3.983 * [backup-simplify]: Simplify 1/2 into 1/2 3.983 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 3.983 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 3.983 * [taylor]: Taking taylor expansion of -2 in n 3.983 * [backup-simplify]: Simplify -2 into -2 3.983 * [taylor]: Taking taylor expansion of (/ PI n) in n 3.983 * [taylor]: Taking taylor expansion of PI in n 3.983 * [backup-simplify]: Simplify PI into PI 3.983 * [taylor]: Taking taylor expansion of n in n 3.983 * [backup-simplify]: Simplify 0 into 0 3.983 * [backup-simplify]: Simplify 1 into 1 3.983 * [backup-simplify]: Simplify (/ PI 1) into PI 3.984 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 3.985 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 3.985 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 3.985 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 3.986 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 3.986 * [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))) 3.987 * [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)))) 3.987 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 3.987 * [taylor]: Taking taylor expansion of (/ -1 k) in n 3.987 * [taylor]: Taking taylor expansion of -1 in n 3.987 * [backup-simplify]: Simplify -1 into -1 3.987 * [taylor]: Taking taylor expansion of k in n 3.987 * [backup-simplify]: Simplify k into k 3.987 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 3.987 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 3.987 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 3.987 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 3.988 * [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))) 3.988 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k 3.988 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 3.988 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 3.988 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 3.988 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 3.988 * [taylor]: Taking taylor expansion of 1/2 in k 3.988 * [backup-simplify]: Simplify 1/2 into 1/2 3.988 * [taylor]: Taking taylor expansion of (/ 1 k) in k 3.988 * [taylor]: Taking taylor expansion of k in k 3.988 * [backup-simplify]: Simplify 0 into 0 3.988 * [backup-simplify]: Simplify 1 into 1 3.989 * [backup-simplify]: Simplify (/ 1 1) into 1 3.989 * [taylor]: Taking taylor expansion of 1/2 in k 3.989 * [backup-simplify]: Simplify 1/2 into 1/2 3.989 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 3.989 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 3.989 * [taylor]: Taking taylor expansion of (* -2 PI) in k 3.989 * [taylor]: Taking taylor expansion of -2 in k 3.989 * [backup-simplify]: Simplify -2 into -2 3.989 * [taylor]: Taking taylor expansion of PI in k 3.989 * [backup-simplify]: Simplify PI into PI 3.989 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 3.990 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 3.990 * [taylor]: Taking taylor expansion of (log n) in k 3.990 * [taylor]: Taking taylor expansion of n in k 3.990 * [backup-simplify]: Simplify n into n 3.990 * [backup-simplify]: Simplify (log n) into (log n) 3.990 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 3.990 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 3.990 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 3.991 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 3.992 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 3.992 * [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)))) 3.993 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 3.993 * [taylor]: Taking taylor expansion of (/ -1 k) in k 3.993 * [taylor]: Taking taylor expansion of -1 in k 3.993 * [backup-simplify]: Simplify -1 into -1 3.993 * [taylor]: Taking taylor expansion of k in k 3.993 * [backup-simplify]: Simplify 0 into 0 3.993 * [backup-simplify]: Simplify 1 into 1 3.993 * [backup-simplify]: Simplify (/ -1 1) into -1 3.993 * [backup-simplify]: Simplify (sqrt 0) into 0 3.994 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 3.995 * [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))))) 3.995 * [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))))) 3.996 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 3.996 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 3.997 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 3.998 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 3.998 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 3.998 * [backup-simplify]: Simplify (+ 0 0) into 0 3.999 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.000 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 4.001 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 4.002 * [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 4.002 * [taylor]: Taking taylor expansion of 0 in k 4.002 * [backup-simplify]: Simplify 0 into 0 4.002 * [backup-simplify]: Simplify 0 into 0 4.002 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 4.004 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 4.011 * [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)))))) 4.013 * [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)))))) 4.014 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.015 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 4.019 * [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 4.019 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.020 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 4.021 * [backup-simplify]: Simplify (+ 0 0) into 0 4.022 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.023 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 4.024 * [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 4.024 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.024 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 4.025 * [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 4.025 * [taylor]: Taking taylor expansion of 0 in k 4.025 * [backup-simplify]: Simplify 0 into 0 4.025 * [backup-simplify]: Simplify 0 into 0 4.025 * [backup-simplify]: Simplify 0 into 0 4.026 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.028 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 4.031 * [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)))))) 4.031 * [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)))))) 4.034 * [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))))))))))) 4.034 * * * * [progress]: [ 3 / 3 ] generating series at (2 1) 4.034 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 4.034 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 4.034 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 4.034 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 4.034 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 4.034 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 4.034 * [taylor]: Taking taylor expansion of 1/2 in k 4.034 * [backup-simplify]: Simplify 1/2 into 1/2 4.034 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 4.034 * [taylor]: Taking taylor expansion of 1/2 in k 4.035 * [backup-simplify]: Simplify 1/2 into 1/2 4.035 * [taylor]: Taking taylor expansion of k in k 4.035 * [backup-simplify]: Simplify 0 into 0 4.035 * [backup-simplify]: Simplify 1 into 1 4.035 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 4.035 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 4.035 * [taylor]: Taking taylor expansion of 2 in k 4.035 * [backup-simplify]: Simplify 2 into 2 4.035 * [taylor]: Taking taylor expansion of (* n PI) in k 4.035 * [taylor]: Taking taylor expansion of n in k 4.035 * [backup-simplify]: Simplify n into n 4.035 * [taylor]: Taking taylor expansion of PI in k 4.035 * [backup-simplify]: Simplify PI into PI 4.035 * [backup-simplify]: Simplify (* n PI) into (* n PI) 4.035 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 4.035 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 4.035 * [backup-simplify]: Simplify (* 1/2 0) into 0 4.035 * [backup-simplify]: Simplify (- 0) into 0 4.036 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 4.036 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 4.036 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 4.036 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 4.036 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 4.036 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 4.036 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 4.036 * [taylor]: Taking taylor expansion of 1/2 in n 4.036 * [backup-simplify]: Simplify 1/2 into 1/2 4.036 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 4.036 * [taylor]: Taking taylor expansion of 1/2 in n 4.036 * [backup-simplify]: Simplify 1/2 into 1/2 4.036 * [taylor]: Taking taylor expansion of k in n 4.036 * [backup-simplify]: Simplify k into k 4.036 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 4.036 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 4.036 * [taylor]: Taking taylor expansion of 2 in n 4.036 * [backup-simplify]: Simplify 2 into 2 4.036 * [taylor]: Taking taylor expansion of (* n PI) in n 4.036 * [taylor]: Taking taylor expansion of n in n 4.036 * [backup-simplify]: Simplify 0 into 0 4.036 * [backup-simplify]: Simplify 1 into 1 4.036 * [taylor]: Taking taylor expansion of PI in n 4.036 * [backup-simplify]: Simplify PI into PI 4.036 * [backup-simplify]: Simplify (* 0 PI) into 0 4.037 * [backup-simplify]: Simplify (* 2 0) into 0 4.038 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.039 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 4.039 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.039 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 4.039 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 4.039 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 4.040 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.041 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 4.042 * [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))))) 4.042 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 4.042 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 4.042 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 4.042 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 4.042 * [taylor]: Taking taylor expansion of 1/2 in n 4.042 * [backup-simplify]: Simplify 1/2 into 1/2 4.042 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 4.042 * [taylor]: Taking taylor expansion of 1/2 in n 4.042 * [backup-simplify]: Simplify 1/2 into 1/2 4.042 * [taylor]: Taking taylor expansion of k in n 4.042 * [backup-simplify]: Simplify k into k 4.042 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 4.042 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 4.042 * [taylor]: Taking taylor expansion of 2 in n 4.042 * [backup-simplify]: Simplify 2 into 2 4.042 * [taylor]: Taking taylor expansion of (* n PI) in n 4.042 * [taylor]: Taking taylor expansion of n in n 4.042 * [backup-simplify]: Simplify 0 into 0 4.042 * [backup-simplify]: Simplify 1 into 1 4.042 * [taylor]: Taking taylor expansion of PI in n 4.042 * [backup-simplify]: Simplify PI into PI 4.042 * [backup-simplify]: Simplify (* 0 PI) into 0 4.043 * [backup-simplify]: Simplify (* 2 0) into 0 4.044 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 4.044 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 4.045 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.045 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 4.045 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 4.045 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 4.046 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.047 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 4.048 * [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))))) 4.048 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 4.048 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 4.048 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 4.048 * [taylor]: Taking taylor expansion of 1/2 in k 4.048 * [backup-simplify]: Simplify 1/2 into 1/2 4.048 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 4.048 * [taylor]: Taking taylor expansion of 1/2 in k 4.048 * [backup-simplify]: Simplify 1/2 into 1/2 4.048 * [taylor]: Taking taylor expansion of k in k 4.048 * [backup-simplify]: Simplify 0 into 0 4.048 * [backup-simplify]: Simplify 1 into 1 4.048 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 4.048 * [taylor]: Taking taylor expansion of (log n) in k 4.048 * [taylor]: Taking taylor expansion of n in k 4.048 * [backup-simplify]: Simplify n into n 4.048 * [backup-simplify]: Simplify (log n) into (log n) 4.048 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 4.048 * [taylor]: Taking taylor expansion of (* 2 PI) in k 4.048 * [taylor]: Taking taylor expansion of 2 in k 4.048 * [backup-simplify]: Simplify 2 into 2 4.048 * [taylor]: Taking taylor expansion of PI in k 4.048 * [backup-simplify]: Simplify PI into PI 4.048 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.049 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.050 * [backup-simplify]: Simplify (* 1/2 0) into 0 4.050 * [backup-simplify]: Simplify (- 0) into 0 4.050 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 4.052 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.053 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 4.054 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 4.055 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 4.056 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 4.057 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 4.059 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 4.060 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 4.060 * [backup-simplify]: Simplify (- 0) into 0 4.060 * [backup-simplify]: Simplify (+ 0 0) into 0 4.062 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.063 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 4.065 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 4.065 * [taylor]: Taking taylor expansion of 0 in k 4.065 * [backup-simplify]: Simplify 0 into 0 4.065 * [backup-simplify]: Simplify 0 into 0 4.065 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 4.066 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 4.067 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 4.067 * [backup-simplify]: Simplify (+ 0 0) into 0 4.068 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 4.068 * [backup-simplify]: Simplify (- 1/2) into -1/2 4.068 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 4.069 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 4.071 * [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))))))) 4.073 * [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))))))) 4.074 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 4.074 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 4.076 * [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 4.077 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 4.077 * [backup-simplify]: Simplify (- 0) into 0 4.077 * [backup-simplify]: Simplify (+ 0 0) into 0 4.078 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 4.079 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 4.080 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 4.081 * [taylor]: Taking taylor expansion of 0 in k 4.081 * [backup-simplify]: Simplify 0 into 0 4.081 * [backup-simplify]: Simplify 0 into 0 4.081 * [backup-simplify]: Simplify 0 into 0 4.082 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 4.082 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 4.084 * [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 4.084 * [backup-simplify]: Simplify (+ 0 0) into 0 4.085 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 4.085 * [backup-simplify]: Simplify (- 0) into 0 4.085 * [backup-simplify]: Simplify (+ 0 0) into 0 4.087 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 4.089 * [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))))) 4.094 * [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))))) 4.104 * [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))))) 4.104 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 4.104 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 4.104 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 4.104 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 4.104 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 4.104 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 4.104 * [taylor]: Taking taylor expansion of 1/2 in k 4.104 * [backup-simplify]: Simplify 1/2 into 1/2 4.104 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 4.104 * [taylor]: Taking taylor expansion of 1/2 in k 4.104 * [backup-simplify]: Simplify 1/2 into 1/2 4.104 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.104 * [taylor]: Taking taylor expansion of k in k 4.104 * [backup-simplify]: Simplify 0 into 0 4.104 * [backup-simplify]: Simplify 1 into 1 4.105 * [backup-simplify]: Simplify (/ 1 1) into 1 4.105 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 4.105 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 4.105 * [taylor]: Taking taylor expansion of 2 in k 4.105 * [backup-simplify]: Simplify 2 into 2 4.105 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.105 * [taylor]: Taking taylor expansion of PI in k 4.105 * [backup-simplify]: Simplify PI into PI 4.105 * [taylor]: Taking taylor expansion of n in k 4.105 * [backup-simplify]: Simplify n into n 4.105 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.105 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 4.105 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 4.106 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 4.106 * [backup-simplify]: Simplify (- 1/2) into -1/2 4.107 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 4.107 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 4.107 * [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)))) 4.107 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 4.107 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 4.107 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 4.107 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 4.107 * [taylor]: Taking taylor expansion of 1/2 in n 4.107 * [backup-simplify]: Simplify 1/2 into 1/2 4.107 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 4.107 * [taylor]: Taking taylor expansion of 1/2 in n 4.107 * [backup-simplify]: Simplify 1/2 into 1/2 4.107 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.107 * [taylor]: Taking taylor expansion of k in n 4.107 * [backup-simplify]: Simplify k into k 4.107 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.107 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 4.107 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 4.107 * [taylor]: Taking taylor expansion of 2 in n 4.107 * [backup-simplify]: Simplify 2 into 2 4.107 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.108 * [taylor]: Taking taylor expansion of PI in n 4.108 * [backup-simplify]: Simplify PI into PI 4.108 * [taylor]: Taking taylor expansion of n in n 4.108 * [backup-simplify]: Simplify 0 into 0 4.108 * [backup-simplify]: Simplify 1 into 1 4.108 * [backup-simplify]: Simplify (/ PI 1) into PI 4.109 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.109 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.109 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 4.109 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 4.109 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 4.110 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.111 * [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))) 4.112 * [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)))) 4.112 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 4.112 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 4.112 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 4.112 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 4.112 * [taylor]: Taking taylor expansion of 1/2 in n 4.112 * [backup-simplify]: Simplify 1/2 into 1/2 4.112 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 4.112 * [taylor]: Taking taylor expansion of 1/2 in n 4.112 * [backup-simplify]: Simplify 1/2 into 1/2 4.112 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.112 * [taylor]: Taking taylor expansion of k in n 4.112 * [backup-simplify]: Simplify k into k 4.112 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.112 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 4.112 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 4.112 * [taylor]: Taking taylor expansion of 2 in n 4.112 * [backup-simplify]: Simplify 2 into 2 4.112 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.112 * [taylor]: Taking taylor expansion of PI in n 4.112 * [backup-simplify]: Simplify PI into PI 4.112 * [taylor]: Taking taylor expansion of n in n 4.112 * [backup-simplify]: Simplify 0 into 0 4.112 * [backup-simplify]: Simplify 1 into 1 4.113 * [backup-simplify]: Simplify (/ PI 1) into PI 4.113 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.118 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.118 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 4.118 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 4.118 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 4.119 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.120 * [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))) 4.120 * [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)))) 4.120 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 4.120 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 4.120 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 4.120 * [taylor]: Taking taylor expansion of 1/2 in k 4.120 * [backup-simplify]: Simplify 1/2 into 1/2 4.120 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 4.120 * [taylor]: Taking taylor expansion of 1/2 in k 4.121 * [backup-simplify]: Simplify 1/2 into 1/2 4.121 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.121 * [taylor]: Taking taylor expansion of k in k 4.121 * [backup-simplify]: Simplify 0 into 0 4.121 * [backup-simplify]: Simplify 1 into 1 4.121 * [backup-simplify]: Simplify (/ 1 1) into 1 4.121 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 4.121 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 4.121 * [taylor]: Taking taylor expansion of (* 2 PI) in k 4.121 * [taylor]: Taking taylor expansion of 2 in k 4.121 * [backup-simplify]: Simplify 2 into 2 4.121 * [taylor]: Taking taylor expansion of PI in k 4.121 * [backup-simplify]: Simplify PI into PI 4.121 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 4.122 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 4.122 * [taylor]: Taking taylor expansion of (log n) in k 4.122 * [taylor]: Taking taylor expansion of n in k 4.122 * [backup-simplify]: Simplify n into n 4.122 * [backup-simplify]: Simplify (log n) into (log n) 4.122 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 4.123 * [backup-simplify]: Simplify (- 1/2) into -1/2 4.123 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 4.123 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.123 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 4.124 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 4.125 * [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)))) 4.126 * [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)))) 4.127 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.127 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 4.128 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 4.128 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.128 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 4.129 * [backup-simplify]: Simplify (- 0) into 0 4.129 * [backup-simplify]: Simplify (+ 0 0) into 0 4.130 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.131 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 4.132 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 4.132 * [taylor]: Taking taylor expansion of 0 in k 4.132 * [backup-simplify]: Simplify 0 into 0 4.132 * [backup-simplify]: Simplify 0 into 0 4.132 * [backup-simplify]: Simplify 0 into 0 4.132 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.133 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 4.135 * [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 4.135 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.136 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 4.136 * [backup-simplify]: Simplify (- 0) into 0 4.136 * [backup-simplify]: Simplify (+ 0 0) into 0 4.137 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.139 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 4.141 * [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 4.141 * [taylor]: Taking taylor expansion of 0 in k 4.141 * [backup-simplify]: Simplify 0 into 0 4.141 * [backup-simplify]: Simplify 0 into 0 4.141 * [backup-simplify]: Simplify 0 into 0 4.141 * [backup-simplify]: Simplify 0 into 0 4.143 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.144 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.150 * [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 4.150 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.151 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 4.152 * [backup-simplify]: Simplify (- 0) into 0 4.152 * [backup-simplify]: Simplify (+ 0 0) into 0 4.153 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 4.155 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 4.158 * [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 4.158 * [taylor]: Taking taylor expansion of 0 in k 4.158 * [backup-simplify]: Simplify 0 into 0 4.158 * [backup-simplify]: Simplify 0 into 0 4.160 * [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))))) 4.160 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 4.160 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 4.160 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 4.160 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 4.160 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 4.160 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 4.160 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 4.160 * [taylor]: Taking taylor expansion of 1/2 in k 4.160 * [backup-simplify]: Simplify 1/2 into 1/2 4.160 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.160 * [taylor]: Taking taylor expansion of k in k 4.160 * [backup-simplify]: Simplify 0 into 0 4.160 * [backup-simplify]: Simplify 1 into 1 4.161 * [backup-simplify]: Simplify (/ 1 1) into 1 4.161 * [taylor]: Taking taylor expansion of 1/2 in k 4.161 * [backup-simplify]: Simplify 1/2 into 1/2 4.161 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 4.161 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 4.161 * [taylor]: Taking taylor expansion of -2 in k 4.161 * [backup-simplify]: Simplify -2 into -2 4.161 * [taylor]: Taking taylor expansion of (/ PI n) in k 4.161 * [taylor]: Taking taylor expansion of PI in k 4.161 * [backup-simplify]: Simplify PI into PI 4.161 * [taylor]: Taking taylor expansion of n in k 4.161 * [backup-simplify]: Simplify n into n 4.161 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 4.161 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 4.161 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 4.162 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 4.162 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 4.162 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 4.163 * [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))) 4.163 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 4.163 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 4.163 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 4.163 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 4.163 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 4.163 * [taylor]: Taking taylor expansion of 1/2 in n 4.163 * [backup-simplify]: Simplify 1/2 into 1/2 4.163 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.163 * [taylor]: Taking taylor expansion of k in n 4.163 * [backup-simplify]: Simplify k into k 4.163 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.163 * [taylor]: Taking taylor expansion of 1/2 in n 4.163 * [backup-simplify]: Simplify 1/2 into 1/2 4.163 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 4.163 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 4.163 * [taylor]: Taking taylor expansion of -2 in n 4.163 * [backup-simplify]: Simplify -2 into -2 4.163 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.163 * [taylor]: Taking taylor expansion of PI in n 4.163 * [backup-simplify]: Simplify PI into PI 4.163 * [taylor]: Taking taylor expansion of n in n 4.163 * [backup-simplify]: Simplify 0 into 0 4.163 * [backup-simplify]: Simplify 1 into 1 4.164 * [backup-simplify]: Simplify (/ PI 1) into PI 4.164 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 4.165 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 4.165 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 4.166 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 4.167 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.168 * [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))) 4.170 * [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)))) 4.170 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 4.170 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 4.170 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 4.170 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 4.170 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 4.170 * [taylor]: Taking taylor expansion of 1/2 in n 4.170 * [backup-simplify]: Simplify 1/2 into 1/2 4.170 * [taylor]: Taking taylor expansion of (/ 1 k) in n 4.170 * [taylor]: Taking taylor expansion of k in n 4.170 * [backup-simplify]: Simplify k into k 4.170 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 4.170 * [taylor]: Taking taylor expansion of 1/2 in n 4.170 * [backup-simplify]: Simplify 1/2 into 1/2 4.170 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 4.170 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 4.170 * [taylor]: Taking taylor expansion of -2 in n 4.170 * [backup-simplify]: Simplify -2 into -2 4.170 * [taylor]: Taking taylor expansion of (/ PI n) in n 4.170 * [taylor]: Taking taylor expansion of PI in n 4.170 * [backup-simplify]: Simplify PI into PI 4.170 * [taylor]: Taking taylor expansion of n in n 4.170 * [backup-simplify]: Simplify 0 into 0 4.170 * [backup-simplify]: Simplify 1 into 1 4.171 * [backup-simplify]: Simplify (/ PI 1) into PI 4.171 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 4.172 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 4.172 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 4.173 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 4.174 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.176 * [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))) 4.177 * [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)))) 4.177 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 4.177 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 4.177 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 4.177 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 4.177 * [taylor]: Taking taylor expansion of 1/2 in k 4.177 * [backup-simplify]: Simplify 1/2 into 1/2 4.177 * [taylor]: Taking taylor expansion of (/ 1 k) in k 4.177 * [taylor]: Taking taylor expansion of k in k 4.177 * [backup-simplify]: Simplify 0 into 0 4.177 * [backup-simplify]: Simplify 1 into 1 4.178 * [backup-simplify]: Simplify (/ 1 1) into 1 4.178 * [taylor]: Taking taylor expansion of 1/2 in k 4.178 * [backup-simplify]: Simplify 1/2 into 1/2 4.178 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 4.178 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 4.178 * [taylor]: Taking taylor expansion of (* -2 PI) in k 4.178 * [taylor]: Taking taylor expansion of -2 in k 4.178 * [backup-simplify]: Simplify -2 into -2 4.178 * [taylor]: Taking taylor expansion of PI in k 4.178 * [backup-simplify]: Simplify PI into PI 4.178 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 4.180 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 4.180 * [taylor]: Taking taylor expansion of (log n) in k 4.180 * [taylor]: Taking taylor expansion of n in k 4.180 * [backup-simplify]: Simplify n into n 4.180 * [backup-simplify]: Simplify (log n) into (log n) 4.180 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 4.181 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 4.181 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 4.182 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 4.183 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 4.184 * [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)))) 4.186 * [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)))) 4.187 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 4.187 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 4.189 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 4.190 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 4.190 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 4.190 * [backup-simplify]: Simplify (+ 0 0) into 0 4.192 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.193 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 4.195 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 4.195 * [taylor]: Taking taylor expansion of 0 in k 4.195 * [backup-simplify]: Simplify 0 into 0 4.195 * [backup-simplify]: Simplify 0 into 0 4.195 * [backup-simplify]: Simplify 0 into 0 4.197 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.198 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 4.201 * [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 4.202 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.203 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 4.203 * [backup-simplify]: Simplify (+ 0 0) into 0 4.204 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.206 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 4.209 * [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 4.209 * [taylor]: Taking taylor expansion of 0 in k 4.209 * [backup-simplify]: Simplify 0 into 0 4.209 * [backup-simplify]: Simplify 0 into 0 4.209 * [backup-simplify]: Simplify 0 into 0 4.209 * [backup-simplify]: Simplify 0 into 0 4.210 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 4.211 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 4.218 * [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 4.218 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 4.219 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 4.220 * [backup-simplify]: Simplify (+ 0 0) into 0 4.221 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 4.223 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 4.227 * [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 4.227 * [taylor]: Taking taylor expansion of 0 in k 4.227 * [backup-simplify]: Simplify 0 into 0 4.227 * [backup-simplify]: Simplify 0 into 0 4.228 * [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))))) 4.229 * * * [progress]: simplifying candidates 4.229 * * * * [progress]: [ 1 / 445 ] simplifiying candidate # 4.229 * * * * [progress]: [ 2 / 445 ] simplifiying candidate # 4.229 * * * * [progress]: [ 3 / 445 ] simplifiying candidate # 4.229 * * * * [progress]: [ 4 / 445 ] simplifiying candidate # 4.229 * * * * [progress]: [ 5 / 445 ] simplifiying candidate # 4.229 * * * * [progress]: [ 6 / 445 ] simplifiying candidate # 4.229 * * * * [progress]: [ 7 / 445 ] simplifiying candidate # 4.229 * * * * [progress]: [ 8 / 445 ] simplifiying candidate # 4.229 * * * * [progress]: [ 9 / 445 ] simplifiying candidate # 4.229 * * * * [progress]: [ 10 / 445 ] simplifiying candidate # 4.229 * * * * [progress]: [ 11 / 445 ] simplifiying candidate # 4.229 * * * * [progress]: [ 12 / 445 ] simplifiying candidate # 4.229 * * * * [progress]: [ 13 / 445 ] simplifiying candidate # 4.229 * * * * [progress]: [ 14 / 445 ] simplifiying candidate # 4.230 * * * * [progress]: [ 15 / 445 ] simplifiying candidate # 4.230 * * * * [progress]: [ 16 / 445 ] simplifiying candidate # 4.230 * * * * [progress]: [ 17 / 445 ] simplifiying candidate # 4.230 * * * * [progress]: [ 18 / 445 ] simplifiying candidate # 4.230 * * * * [progress]: [ 19 / 445 ] simplifiying candidate # 4.230 * * * * [progress]: [ 20 / 445 ] simplifiying candidate #real (real->posit16 (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))> 4.230 * * * * [progress]: [ 21 / 445 ] simplifiying candidate # 4.230 * * * * [progress]: [ 22 / 445 ] simplifiying candidate # 4.230 * * * * [progress]: [ 23 / 445 ] simplifiying candidate # 4.230 * * * * [progress]: [ 24 / 445 ] simplifiying candidate # 4.230 * * * * [progress]: [ 25 / 445 ] simplifiying candidate # 4.230 * * * * [progress]: [ 26 / 445 ] simplifiying candidate # 4.230 * * * * [progress]: [ 27 / 445 ] simplifiying 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(pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (- (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))) (- (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k))) (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k))) (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k))) (- (log (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (log (sqrt k))) (log (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (exp (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (* (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (- (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (- (sqrt k)) (/ (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (cbrt (sqrt k))) (/ (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt (cbrt k))) (/ (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt 1)) (/ (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt k)) (/ (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) 1) (/ (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))) (sqrt k)) (/ (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 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(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))))))))))) (- (+ (* 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))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 4.305 * * [simplify]: iteration 0: 699 enodes 4.565 * * [simplify]: iteration 1: 1539 enodes 5.183 * * [simplify]: iteration 2: 4186 enodes 6.201 * * [simplify]: iteration complete: 5000 enodes 6.202 * * [simplify]: Extracting #0: cost 219 inf + 0 6.203 * * [simplify]: Extracting #1: cost 794 inf + 1 6.208 * * [simplify]: Extracting #2: cost 1267 inf + 987 6.223 * * [simplify]: Extracting #3: cost 1372 inf + 41391 6.283 * * [simplify]: Extracting #4: cost 863 inf + 209716 6.369 * * [simplify]: Extracting #5: cost 537 inf + 364654 6.487 * * [simplify]: Extracting #6: cost 256 inf + 521341 6.718 * * [simplify]: Extracting #7: cost 42 inf + 672570 6.924 * * [simplify]: Extracting #8: cost 1 inf + 697089 7.111 * * [simplify]: Extracting #9: cost 0 inf + 696533 7.307 * * [simplify]: Extracting #10: cost 0 inf + 696518 7.541 * [simplify]: Simplified to: (expm1 (* n (* PI 2))) (log1p (* n (* PI 2))) (* n (* PI 2)) (* n (* PI 2)) (log (* n (* PI 2))) (log (* n (* PI 2))) (log (* n (* PI 2))) (* (exp (* PI n)) (exp (* PI n))) (* (* (* (* n (* n n)) 8) (* PI PI)) PI) (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2))) (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2))) (* (* (* n (* PI 2)) (* n (* PI 2))) (* n (* PI 2))) (sqrt (* n (* PI 2))) (sqrt (* n (* PI 2))) (* (* (* (cbrt PI) (cbrt PI)) 2) n) (* (sqrt PI) (* n 2)) (* n 2) (* PI 2) (real->posit16 (* n (* PI 2))) (expm1 (/ (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (sqrt k))) (log1p (/ (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (sqrt k))) (- (* (log (* n (* PI 2))) (- 1/2 (* k 1/2))) (log (sqrt k))) (- (* (log (* n (* PI 2))) (- 1/2 (* k 1/2))) (log (sqrt k))) (- (* (log (* n (* PI 2))) (- 1/2 (* k 1/2))) (log (sqrt k))) (- (* (log (* n (* PI 2))) (- 1/2 (* k 1/2))) (log (sqrt k))) (- (* (log (* n (* PI 2))) (- 1/2 (* k 1/2))) (log 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(* n (* PI 2)) (- 1/2 (/ (/ (cbrt k) (sqrt 2)) (/ (sqrt 2) (* (cbrt k) (cbrt k)))))) (pow (* n (* PI 2)) (* (/ (cbrt k) (sqrt 2)) (+ (- (/ (* (cbrt k) (cbrt k)) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* n (* PI 2)) (- 1/2 (/ (* (cbrt k) (* (cbrt k) (cbrt k))) 2))) (pow (* n (* PI 2)) (* (* (cbrt k) (cbrt k)) (+ (- (/ (cbrt k) 2)) (/ (cbrt k) 2)))) (pow (* n (* PI 2)) (- 1/2 (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2))))) (pow (* n (* PI 2)) (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (+ (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (cbrt 2))))) (pow (* n (* PI 2)) (- 1/2 (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* n (* PI 2)) (+ (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2)))) (pow (* n (* PI 2)) (+ (- (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2))) (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2)))) (pow (* n (* PI 2)) (- 1/2 (/ (/ k (sqrt 2)) (sqrt 2)))) (pow (* n (* PI 2)) (fma (/ k (sqrt 2)) (/ -1 (sqrt 2)) (/ (/ k (sqrt 2)) (sqrt 2)))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (* (/ (cbrt k) (cbrt 2)) (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2)))))) (pow (* n (* PI 2)) (* (* (/ (cbrt k) (cbrt 2)) (/ (cbrt k) (cbrt 2))) (+ (- (/ (cbrt k) (cbrt 2))) (/ (cbrt k) (cbrt 2))))) (pow (* n (* PI 2)) (- 1/2 (/ (/ (cbrt k) (sqrt 2)) (/ (sqrt 2) (* (cbrt k) (cbrt k)))))) (pow (* n (* PI 2)) (* (/ (cbrt k) (sqrt 2)) (+ (- (/ (* (cbrt k) (cbrt k)) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))) (pow (* n (* PI 2)) (- 1/2 (/ (* (cbrt k) (* (cbrt k) (cbrt k))) 2))) (pow (* n (* PI 2)) (* (* (cbrt k) (cbrt k)) (+ (- (/ (cbrt k) 2)) (/ (cbrt k) 2)))) (pow (* n (* PI 2)) (- 1/2 (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (/ (sqrt k) (cbrt 2))))) (pow (* n (* PI 2)) (* (/ (/ (sqrt k) (cbrt 2)) (cbrt 2)) (+ (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (cbrt 2))))) (pow (* n (* PI 2)) (- 1/2 (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* n (* PI 2)) (+ (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2)))) (pow (* n (* PI 2)) (+ (- (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2))) (/ (/ (/ k (cbrt 2)) (cbrt 2)) (cbrt 2)))) (pow (* n (* PI 2)) (- 1/2 (/ (/ k (sqrt 2)) (sqrt 2)))) (pow (* n (* PI 2)) (fma (/ k (sqrt 2)) (/ -1 (sqrt 2)) (/ (/ k (sqrt 2)) (sqrt 2)))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (fma -1/2 k (* k 1/2))) (sqrt (* n (* PI 2))) (pow (* n (* PI 2)) (* -1/2 k)) (sqrt (* n (* PI 2))) (pow (* n (* PI 2)) (* -1/2 k)) (pow (* n 2) (- 1/2 (* k 1/2))) (pow PI (- 1/2 (* k 1/2))) (* (log (* n (* PI 2))) (- 1/2 (* k 1/2))) (exp (pow (* n (* PI 2)) (- 1/2 (* k 1/2)))) (* (cbrt (pow (* n (* PI 2)) (- 1/2 (* k 1/2)))) (cbrt (pow (* n (* PI 2)) (- 1/2 (* k 1/2))))) (cbrt (pow (* n (* PI 2)) (- 1/2 (* k 1/2)))) (* (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (* (pow (* n (* PI 2)) (- 1/2 (* k 1/2))) (pow (* n (* PI 2)) (- 1/2 (* k 1/2))))) (sqrt (pow (* n (* PI 2)) (- 1/2 (* k 1/2)))) (sqrt (pow (* n (* PI 2)) (- 1/2 (* k 1/2)))) (pow (* n (* PI 2)) (/ (- 1/2 (* k 1/2)) 2)) (pow (* n (* PI 2)) (/ (- 1/2 (* k 1/2)) 2)) (real->posit16 (pow (* n (* PI 2)) (- 1/2 (* k 1/2)))) (* n (* PI 2)) (* n (* PI 2)) (* n (* PI 2)) (- (fma (* (* +nan.0 (log (* PI 2))) (exp (* (log (* n (* PI 2))) 1/2))) (* (log n) (* k k)) (fma (- (* +nan.0 (log (* PI 2)))) (* (* k k) (exp (* (log (* n (* PI 2))) 1/2))) (fma (* +nan.0 (exp (* (log (* n (* PI 2))) 1/2))) (* (* k k) (* (log n) (log n))) (fma (- (* (exp (* (log (* n (* PI 2))) 1/2)) k)) +nan.0 (- (- (* +nan.0 (exp (* (log (* n (* PI 2))) 1/2))) (* (* (* k k) (exp (* (log (* n (* PI 2))) 1/2))) (* (* +nan.0 (log (* PI 2))) (log (* PI 2))))) (fma (* +nan.0 (exp (* (log (* n (* PI 2))) 1/2))) (- (* (log n) (* k k))) (fma (* k k) (* +nan.0 (exp (* (log (* n (* PI 2))) 1/2))) (fma (- (* +nan.0 (log (* PI 2)))) (* (exp (* (log (* n (* PI 2))) 1/2)) k) (* +nan.0 (* (log n) (* (exp (* (log (* n (* PI 2))) 1/2)) k)))))))))))) (fma (- (/ (exp (* (log (* n (* PI 2))) (- 1/2 (* k 1/2)))) (* (* k k) k))) +nan.0 (* +nan.0 (- (/ (exp (* (log (* n (* PI 2))) (- 1/2 (* k 1/2)))) k) (/ (exp (* (log (* n (* PI 2))) (- 1/2 (* k 1/2)))) (* k k))))) (fma (- +nan.0) (/ (exp (* (- 1/2 (* k 1/2)) (- (log (* -2 PI)) (log (/ -1 n))))) k) (- (/ (* +nan.0 (exp (* (- 1/2 (* k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))))) (* k k)) (* +nan.0 (exp (* (- 1/2 (* k 1/2)) (- (log (* -2 PI)) (log (/ -1 n)))))))) (fma -1/2 (* k (fma (log n) (pow (* n (* PI 2)) 1/2) (* (log (* PI 2)) (pow (* n (* PI 2)) 1/2)))) (fma (* (* (pow (* n (* PI 2)) 1/2) (* (* k k) (log (* PI 2)))) (log n)) 1/4 (fma (* (log (* PI 2)) (* (pow (* n (* PI 2)) 1/2) (* (* k k) (log (* PI 2))))) 1/8 (fma (* (* k k) (* (log n) (log n))) (* (pow (* n (* PI 2)) 1/2) 1/8) (pow (* n (* PI 2)) 1/2))))) (exp (* (log (* n (* PI 2))) (- 1/2 (* k 1/2)))) (exp (* (- 1/2 (* k 1/2)) (- (log (* -2 PI)) (log (/ -1 n))))) 7.643 * * * [progress]: adding candidates to table 10.708 * * [progress]: iteration 2 / 4 10.708 * * * [progress]: picking best candidate 10.753 * * * * [pick]: Picked # 10.754 * * * [progress]: localizing error 10.810 * * * [progress]: generating rewritten candidates 10.810 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 1) 10.839 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2) 10.865 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2) 10.905 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 11.044 * * * [progress]: generating series expansions 11.044 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 1) 11.045 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI)) 11.045 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 11.045 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.045 * [taylor]: Taking taylor expansion of 2 in n 11.045 * [backup-simplify]: Simplify 2 into 2 11.045 * [taylor]: Taking taylor expansion of (* n PI) in n 11.045 * [taylor]: Taking taylor expansion of n in n 11.045 * [backup-simplify]: Simplify 0 into 0 11.045 * [backup-simplify]: Simplify 1 into 1 11.045 * [taylor]: Taking taylor expansion of PI in n 11.045 * [backup-simplify]: Simplify PI into PI 11.045 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.045 * [taylor]: Taking taylor expansion of 2 in n 11.045 * [backup-simplify]: Simplify 2 into 2 11.045 * [taylor]: Taking taylor expansion of (* n PI) in n 11.045 * [taylor]: Taking taylor expansion of n in n 11.045 * [backup-simplify]: Simplify 0 into 0 11.045 * [backup-simplify]: Simplify 1 into 1 11.045 * [taylor]: Taking taylor expansion of PI in n 11.045 * [backup-simplify]: Simplify PI into PI 11.046 * [backup-simplify]: Simplify (* 0 PI) into 0 11.047 * [backup-simplify]: Simplify (* 2 0) into 0 11.047 * [backup-simplify]: Simplify 0 into 0 11.049 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.050 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.051 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.052 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.053 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 11.053 * [backup-simplify]: Simplify 0 into 0 11.054 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.055 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.055 * [backup-simplify]: Simplify 0 into 0 11.057 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.080 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 11.080 * [backup-simplify]: Simplify 0 into 0 11.082 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.083 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 11.083 * [backup-simplify]: Simplify 0 into 0 11.085 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.086 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 11.086 * [backup-simplify]: Simplify 0 into 0 11.087 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 11.088 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 11.088 * [backup-simplify]: Simplify 0 into 0 11.089 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 11.089 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n)) 11.089 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 11.089 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.089 * [taylor]: Taking taylor expansion of 2 in n 11.089 * [backup-simplify]: Simplify 2 into 2 11.089 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.089 * [taylor]: Taking taylor expansion of PI in n 11.089 * [backup-simplify]: Simplify PI into PI 11.089 * [taylor]: Taking taylor expansion of n in n 11.089 * [backup-simplify]: Simplify 0 into 0 11.089 * [backup-simplify]: Simplify 1 into 1 11.089 * [backup-simplify]: Simplify (/ PI 1) into PI 11.089 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.089 * [taylor]: Taking taylor expansion of 2 in n 11.089 * [backup-simplify]: Simplify 2 into 2 11.089 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.089 * [taylor]: Taking taylor expansion of PI in n 11.089 * [backup-simplify]: Simplify PI into PI 11.089 * [taylor]: Taking taylor expansion of n in n 11.089 * [backup-simplify]: Simplify 0 into 0 11.089 * [backup-simplify]: Simplify 1 into 1 11.090 * [backup-simplify]: Simplify (/ PI 1) into PI 11.090 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.090 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.091 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.091 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.091 * [backup-simplify]: Simplify 0 into 0 11.092 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.093 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 11.093 * [backup-simplify]: Simplify 0 into 0 11.093 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.094 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.094 * [backup-simplify]: Simplify 0 into 0 11.095 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.095 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.095 * [backup-simplify]: Simplify 0 into 0 11.096 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.097 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.097 * [backup-simplify]: Simplify 0 into 0 11.098 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.099 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.099 * [backup-simplify]: Simplify 0 into 0 11.099 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 11.099 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n)) 11.099 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 11.099 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.099 * [taylor]: Taking taylor expansion of -2 in n 11.099 * [backup-simplify]: Simplify -2 into -2 11.099 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.099 * [taylor]: Taking taylor expansion of PI in n 11.099 * [backup-simplify]: Simplify PI into PI 11.099 * [taylor]: Taking taylor expansion of n in n 11.099 * [backup-simplify]: Simplify 0 into 0 11.099 * [backup-simplify]: Simplify 1 into 1 11.100 * [backup-simplify]: Simplify (/ PI 1) into PI 11.100 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.100 * [taylor]: Taking taylor expansion of -2 in n 11.100 * [backup-simplify]: Simplify -2 into -2 11.100 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.100 * [taylor]: Taking taylor expansion of PI in n 11.100 * [backup-simplify]: Simplify PI into PI 11.100 * [taylor]: Taking taylor expansion of n in n 11.100 * [backup-simplify]: Simplify 0 into 0 11.100 * [backup-simplify]: Simplify 1 into 1 11.100 * [backup-simplify]: Simplify (/ PI 1) into PI 11.100 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.101 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.101 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.102 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 11.102 * [backup-simplify]: Simplify 0 into 0 11.102 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.103 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 11.103 * [backup-simplify]: Simplify 0 into 0 11.104 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.105 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 11.105 * [backup-simplify]: Simplify 0 into 0 11.105 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.106 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 11.106 * [backup-simplify]: Simplify 0 into 0 11.107 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.108 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 11.108 * [backup-simplify]: Simplify 0 into 0 11.108 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.109 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 11.109 * [backup-simplify]: Simplify 0 into 0 11.110 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 11.110 * * * * [progress]: [ 2 / 4 ] generating series at (2 2) 11.110 * [backup-simplify]: Simplify (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) into (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) 11.110 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in (k n) around 0 11.110 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in n 11.110 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 11.110 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 11.110 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 11.110 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 11.110 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 11.110 * [taylor]: Taking taylor expansion of 1/2 in n 11.110 * [backup-simplify]: Simplify 1/2 into 1/2 11.110 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 11.110 * [taylor]: Taking taylor expansion of 1/2 in n 11.110 * [backup-simplify]: Simplify 1/2 into 1/2 11.110 * [taylor]: Taking taylor expansion of k in n 11.110 * [backup-simplify]: Simplify k into k 11.110 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.110 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.110 * [taylor]: Taking taylor expansion of 2 in n 11.110 * [backup-simplify]: Simplify 2 into 2 11.111 * [taylor]: Taking taylor expansion of (* n PI) in n 11.111 * [taylor]: Taking taylor expansion of n in n 11.111 * [backup-simplify]: Simplify 0 into 0 11.111 * [backup-simplify]: Simplify 1 into 1 11.111 * [taylor]: Taking taylor expansion of PI in n 11.111 * [backup-simplify]: Simplify PI into PI 11.111 * [backup-simplify]: Simplify (* 0 PI) into 0 11.111 * [backup-simplify]: Simplify (* 2 0) into 0 11.112 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.113 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.114 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.114 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 11.114 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 11.114 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 11.115 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.116 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 11.116 * [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))))) 11.117 * [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)))))) 11.117 * [taylor]: Taking taylor expansion of (sqrt k) in n 11.117 * [taylor]: Taking taylor expansion of k in n 11.117 * [backup-simplify]: Simplify k into k 11.117 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 11.117 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 11.117 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 11.117 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 11.117 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 11.117 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 11.117 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 11.118 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.118 * [taylor]: Taking taylor expansion of 1/2 in k 11.118 * [backup-simplify]: Simplify 1/2 into 1/2 11.118 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.118 * [taylor]: Taking taylor expansion of 1/2 in k 11.118 * [backup-simplify]: Simplify 1/2 into 1/2 11.118 * [taylor]: Taking taylor expansion of k in k 11.118 * [backup-simplify]: Simplify 0 into 0 11.118 * [backup-simplify]: Simplify 1 into 1 11.118 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.118 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.118 * [taylor]: Taking taylor expansion of 2 in k 11.118 * [backup-simplify]: Simplify 2 into 2 11.118 * [taylor]: Taking taylor expansion of (* n PI) in k 11.118 * [taylor]: Taking taylor expansion of n in k 11.118 * [backup-simplify]: Simplify n into n 11.118 * [taylor]: Taking taylor expansion of PI in k 11.118 * [backup-simplify]: Simplify PI into PI 11.118 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.118 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.118 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.118 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.118 * [backup-simplify]: Simplify (- 0) into 0 11.119 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.119 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.119 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.119 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 11.119 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.119 * [taylor]: Taking taylor expansion of k in k 11.119 * [backup-simplify]: Simplify 0 into 0 11.119 * [backup-simplify]: Simplify 1 into 1 11.119 * [backup-simplify]: Simplify (sqrt 0) into 0 11.120 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.120 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) (sqrt k)) in k 11.120 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 11.120 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 11.120 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 11.120 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 11.120 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.120 * [taylor]: Taking taylor expansion of 1/2 in k 11.120 * [backup-simplify]: Simplify 1/2 into 1/2 11.120 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.120 * [taylor]: Taking taylor expansion of 1/2 in k 11.120 * [backup-simplify]: Simplify 1/2 into 1/2 11.120 * [taylor]: Taking taylor expansion of k in k 11.120 * [backup-simplify]: Simplify 0 into 0 11.120 * [backup-simplify]: Simplify 1 into 1 11.120 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.120 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.120 * [taylor]: Taking taylor expansion of 2 in k 11.121 * [backup-simplify]: Simplify 2 into 2 11.121 * [taylor]: Taking taylor expansion of (* n PI) in k 11.121 * [taylor]: Taking taylor expansion of n in k 11.121 * [backup-simplify]: Simplify n into n 11.121 * [taylor]: Taking taylor expansion of PI in k 11.121 * [backup-simplify]: Simplify PI into PI 11.121 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.121 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.121 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.121 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.122 * [backup-simplify]: Simplify (- 0) into 0 11.122 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.122 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.122 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.122 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 11.122 * [taylor]: Taking taylor expansion of (sqrt k) in k 11.122 * [taylor]: Taking taylor expansion of k in k 11.123 * [backup-simplify]: Simplify 0 into 0 11.123 * [backup-simplify]: Simplify 1 into 1 11.123 * [backup-simplify]: Simplify (sqrt 0) into 0 11.125 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.125 * [backup-simplify]: Simplify (* (sqrt (/ 1 (* PI (* n 2)))) 0) into 0 11.125 * [taylor]: Taking taylor expansion of 0 in n 11.125 * [backup-simplify]: Simplify 0 into 0 11.125 * [backup-simplify]: Simplify 0 into 0 11.126 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 11.126 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 11.127 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 11.128 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 11.128 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.129 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.129 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 11.130 * [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))))) 11.130 * [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))))) 11.132 * [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)))) 11.132 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 11.132 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 11.132 * [taylor]: Taking taylor expansion of +nan.0 in n 11.132 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.132 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 11.132 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 11.132 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 11.132 * [taylor]: Taking taylor expansion of (* n PI) in n 11.132 * [taylor]: Taking taylor expansion of n in n 11.132 * [backup-simplify]: Simplify 0 into 0 11.133 * [backup-simplify]: Simplify 1 into 1 11.133 * [taylor]: Taking taylor expansion of PI in n 11.133 * [backup-simplify]: Simplify PI into PI 11.133 * [backup-simplify]: Simplify (* 0 PI) into 0 11.135 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.135 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 11.136 * [backup-simplify]: Simplify (sqrt 0) into 0 11.138 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 11.138 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 11.138 * [taylor]: Taking taylor expansion of 1/2 in n 11.138 * [backup-simplify]: Simplify 1/2 into 1/2 11.139 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 11.140 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 11.143 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.143 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0 11.149 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.151 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.153 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) PI))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.153 * [backup-simplify]: Simplify 0 into 0 11.155 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.155 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 11.156 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 11.157 * [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 11.157 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 11.158 * [backup-simplify]: Simplify (- 0) into 0 11.158 * [backup-simplify]: Simplify (+ 0 0) into 0 11.158 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 11.159 * [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))) 11.161 * [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)))))) 11.165 * [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)))))) 11.165 * [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 11.165 * [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 11.165 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI))))) in n 11.165 * [taylor]: Taking taylor expansion of +nan.0 in n 11.165 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.165 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) (sqrt (/ 1 (* n PI)))) in n 11.165 * [taylor]: Taking taylor expansion of (* (sqrt 2) (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2))) in n 11.165 * [taylor]: Taking taylor expansion of (sqrt 2) in n 11.165 * [taylor]: Taking taylor expansion of 2 in n 11.165 * [backup-simplify]: Simplify 2 into 2 11.165 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 11.166 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 11.166 * [taylor]: Taking taylor expansion of (* (log (* 2 (* n PI))) (pow (sqrt 1/2) 2)) in n 11.166 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.166 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.166 * [taylor]: Taking taylor expansion of 2 in n 11.166 * [backup-simplify]: Simplify 2 into 2 11.166 * [taylor]: Taking taylor expansion of (* n PI) in n 11.166 * [taylor]: Taking taylor expansion of n in n 11.166 * [backup-simplify]: Simplify 0 into 0 11.166 * [backup-simplify]: Simplify 1 into 1 11.166 * [taylor]: Taking taylor expansion of PI in n 11.166 * [backup-simplify]: Simplify PI into PI 11.166 * [backup-simplify]: Simplify (* 0 PI) into 0 11.167 * [backup-simplify]: Simplify (* 2 0) into 0 11.167 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.169 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.169 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.169 * [taylor]: Taking taylor expansion of (pow (sqrt 1/2) 2) in n 11.169 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 11.169 * [taylor]: Taking taylor expansion of 1/2 in n 11.169 * [backup-simplify]: Simplify 1/2 into 1/2 11.170 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 11.170 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 11.170 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 11.170 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 11.170 * [taylor]: Taking taylor expansion of (* n PI) in n 11.170 * [taylor]: Taking taylor expansion of n in n 11.170 * [backup-simplify]: Simplify 0 into 0 11.170 * [backup-simplify]: Simplify 1 into 1 11.170 * [taylor]: Taking taylor expansion of PI in n 11.170 * [backup-simplify]: Simplify PI into PI 11.170 * [backup-simplify]: Simplify (* 0 PI) into 0 11.171 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.172 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 11.172 * [backup-simplify]: Simplify (sqrt 0) into 0 11.173 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 11.174 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)))) in n 11.174 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt (/ 1 (* n PI))) (sqrt 1/2))) in n 11.174 * [taylor]: Taking taylor expansion of +nan.0 in n 11.174 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.174 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 (* n PI))) (sqrt 1/2)) in n 11.174 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (* n PI))) in n 11.174 * [taylor]: Taking taylor expansion of (/ 1 (* n PI)) in n 11.174 * [taylor]: Taking taylor expansion of (* n PI) in n 11.174 * [taylor]: Taking taylor expansion of n in n 11.174 * [backup-simplify]: Simplify 0 into 0 11.174 * [backup-simplify]: Simplify 1 into 1 11.174 * [taylor]: Taking taylor expansion of PI in n 11.174 * [backup-simplify]: Simplify PI into PI 11.174 * [backup-simplify]: Simplify (* 0 PI) into 0 11.175 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.176 * [backup-simplify]: Simplify (/ 1 PI) into (/ 1 PI) 11.176 * [backup-simplify]: Simplify (sqrt 0) into 0 11.177 * [backup-simplify]: Simplify (/ (/ 1 PI) (* 2 (sqrt 0))) into (/ +nan.0 PI) 11.177 * [taylor]: Taking taylor expansion of (sqrt 1/2) in n 11.177 * [taylor]: Taking taylor expansion of 1/2 in n 11.177 * [backup-simplify]: Simplify 1/2 into 1/2 11.177 * [backup-simplify]: Simplify (sqrt 1/2) into (sqrt 1/2) 11.178 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1/2))) into 0 11.179 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.180 * [backup-simplify]: Simplify (* (sqrt 1/2) (sqrt 1/2)) into (pow (sqrt 1/2) 2) 11.181 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (pow (sqrt 1/2) 2)) into (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))) 11.580 * [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))))) 11.581 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.582 * [backup-simplify]: Simplify (+ (* (sqrt 1/2) 0) (* 0 (sqrt 1/2))) into 0 11.583 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.584 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 11.586 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.589 * [backup-simplify]: Simplify (+ (* (+ (log n) (log (* 2 PI))) 0) (* 0 (pow (sqrt 1/2) 2))) into 0 11.592 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI)))))) into 0 11.596 * [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))))) 11.599 * [backup-simplify]: Simplify (* (* (sqrt 2) (* (pow (sqrt 1/2) 2) (+ (log n) (log (* 2 PI))))) 0) into 0 11.611 * [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))))) 11.614 * [backup-simplify]: Simplify (+ (* 0 0) (* (/ +nan.0 PI) (sqrt 1/2))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.615 * [backup-simplify]: Simplify (* 0 (sqrt 1/2)) into 0 11.621 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (/ (sqrt 1/2) PI)))) (* 0 0)) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.624 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) PI)))) into (- (* +nan.0 (/ (sqrt 1/2) PI))) 11.640 * [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))))))) 11.660 * [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))))))) 11.681 * [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))))))) 11.683 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1/2))) into 0 11.684 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.685 * [backup-simplify]: Simplify (- (+ (* (/ 1 PI) (/ 0 PI)))) into 0 11.690 * [backup-simplify]: Simplify (/ (- 0 (pow (/ +nan.0 PI) 2) (+)) (* 2 0)) into (/ +nan.0 (pow PI 2)) 11.698 * [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)))) 11.707 * [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)))) 11.712 * [backup-simplify]: Simplify (- (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2))))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 11.715 * [backup-simplify]: Simplify (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) into (- (* +nan.0 (/ (sqrt 1/2) (pow PI 2)))) 11.749 * [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))))))))))) 11.750 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2)))) into (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) 11.750 * [approximate]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in (k n) around 0 11.750 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in n 11.750 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 11.750 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.750 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.750 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.750 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.750 * [taylor]: Taking taylor expansion of 1/2 in n 11.750 * [backup-simplify]: Simplify 1/2 into 1/2 11.750 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.750 * [taylor]: Taking taylor expansion of 1/2 in n 11.750 * [backup-simplify]: Simplify 1/2 into 1/2 11.750 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.750 * [taylor]: Taking taylor expansion of k in n 11.750 * [backup-simplify]: Simplify k into k 11.750 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.750 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.750 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.750 * [taylor]: Taking taylor expansion of 2 in n 11.751 * [backup-simplify]: Simplify 2 into 2 11.751 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.751 * [taylor]: Taking taylor expansion of PI in n 11.751 * [backup-simplify]: Simplify PI into PI 11.751 * [taylor]: Taking taylor expansion of n in n 11.751 * [backup-simplify]: Simplify 0 into 0 11.751 * [backup-simplify]: Simplify 1 into 1 11.751 * [backup-simplify]: Simplify (/ PI 1) into PI 11.752 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.753 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.753 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.753 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.753 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.755 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.756 * [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))) 11.757 * [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)))) 11.759 * [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))))) 11.759 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 11.759 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.759 * [taylor]: Taking taylor expansion of k in n 11.759 * [backup-simplify]: Simplify k into k 11.759 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.759 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 11.759 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.759 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 11.759 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 11.759 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 11.759 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 11.759 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 11.759 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 11.759 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.759 * [taylor]: Taking taylor expansion of 1/2 in k 11.759 * [backup-simplify]: Simplify 1/2 into 1/2 11.759 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.759 * [taylor]: Taking taylor expansion of 1/2 in k 11.760 * [backup-simplify]: Simplify 1/2 into 1/2 11.760 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.760 * [taylor]: Taking taylor expansion of k in k 11.760 * [backup-simplify]: Simplify 0 into 0 11.760 * [backup-simplify]: Simplify 1 into 1 11.760 * [backup-simplify]: Simplify (/ 1 1) into 1 11.760 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 11.760 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 11.760 * [taylor]: Taking taylor expansion of 2 in k 11.760 * [backup-simplify]: Simplify 2 into 2 11.760 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.760 * [taylor]: Taking taylor expansion of PI in k 11.760 * [backup-simplify]: Simplify PI into PI 11.760 * [taylor]: Taking taylor expansion of n in k 11.760 * [backup-simplify]: Simplify n into n 11.760 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.760 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 11.761 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 11.761 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.762 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.762 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.762 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 11.762 * [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)))) 11.763 * [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))))) 11.763 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.763 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.763 * [taylor]: Taking taylor expansion of k in k 11.763 * [backup-simplify]: Simplify 0 into 0 11.763 * [backup-simplify]: Simplify 1 into 1 11.763 * [backup-simplify]: Simplify (/ 1 1) into 1 11.763 * [backup-simplify]: Simplify (sqrt 0) into 0 11.765 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.765 * [taylor]: Taking taylor expansion of (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) (sqrt (/ 1 k))) in k 11.765 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 11.765 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 11.765 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 11.765 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 11.765 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 11.765 * [taylor]: Taking taylor expansion of 1/2 in k 11.765 * [backup-simplify]: Simplify 1/2 into 1/2 11.765 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.765 * [taylor]: Taking taylor expansion of 1/2 in k 11.765 * [backup-simplify]: Simplify 1/2 into 1/2 11.765 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.765 * [taylor]: Taking taylor expansion of k in k 11.765 * [backup-simplify]: Simplify 0 into 0 11.765 * [backup-simplify]: Simplify 1 into 1 11.766 * [backup-simplify]: Simplify (/ 1 1) into 1 11.766 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 11.766 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 11.766 * [taylor]: Taking taylor expansion of 2 in k 11.766 * [backup-simplify]: Simplify 2 into 2 11.766 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.766 * [taylor]: Taking taylor expansion of PI in k 11.766 * [backup-simplify]: Simplify PI into PI 11.766 * [taylor]: Taking taylor expansion of n in k 11.766 * [backup-simplify]: Simplify n into n 11.766 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.766 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 11.766 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 11.766 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.767 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.767 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.767 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 11.767 * [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)))) 11.768 * [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))))) 11.768 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 11.768 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.768 * [taylor]: Taking taylor expansion of k in k 11.768 * [backup-simplify]: Simplify 0 into 0 11.768 * [backup-simplify]: Simplify 1 into 1 11.768 * [backup-simplify]: Simplify (/ 1 1) into 1 11.769 * [backup-simplify]: Simplify (sqrt 0) into 0 11.770 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 11.770 * [backup-simplify]: Simplify (* (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 0) into 0 11.770 * [taylor]: Taking taylor expansion of 0 in n 11.770 * [backup-simplify]: Simplify 0 into 0 11.770 * [backup-simplify]: Simplify 0 into 0 11.771 * [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 11.771 * [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))))))) 11.771 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 11.771 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 11.771 * [taylor]: Taking taylor expansion of +nan.0 in n 11.771 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.771 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 11.771 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.771 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.771 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.771 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.772 * [taylor]: Taking taylor expansion of 1/2 in n 11.772 * [backup-simplify]: Simplify 1/2 into 1/2 11.772 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.772 * [taylor]: Taking taylor expansion of 1/2 in n 11.772 * [backup-simplify]: Simplify 1/2 into 1/2 11.772 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.772 * [taylor]: Taking taylor expansion of k in n 11.772 * [backup-simplify]: Simplify k into k 11.772 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.772 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.772 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.772 * [taylor]: Taking taylor expansion of 2 in n 11.772 * [backup-simplify]: Simplify 2 into 2 11.772 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.772 * [taylor]: Taking taylor expansion of PI in n 11.772 * [backup-simplify]: Simplify PI into PI 11.772 * [taylor]: Taking taylor expansion of n in n 11.772 * [backup-simplify]: Simplify 0 into 0 11.772 * [backup-simplify]: Simplify 1 into 1 11.773 * [backup-simplify]: Simplify (/ PI 1) into PI 11.773 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.774 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.774 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.774 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.774 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.776 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.777 * [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))) 11.778 * [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)))) 11.779 * [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))))) 11.780 * [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))))) 11.781 * [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))))))) 11.783 * [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))))))) 11.783 * [backup-simplify]: Simplify 0 into 0 11.783 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 11.786 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.787 * [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 11.787 * [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))))))) 11.787 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 11.787 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 11.787 * [taylor]: Taking taylor expansion of +nan.0 in n 11.788 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.788 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 11.788 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.788 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.788 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.788 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.788 * [taylor]: Taking taylor expansion of 1/2 in n 11.788 * [backup-simplify]: Simplify 1/2 into 1/2 11.788 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.788 * [taylor]: Taking taylor expansion of 1/2 in n 11.788 * [backup-simplify]: Simplify 1/2 into 1/2 11.788 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.788 * [taylor]: Taking taylor expansion of k in n 11.788 * [backup-simplify]: Simplify k into k 11.788 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.788 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.788 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.788 * [taylor]: Taking taylor expansion of 2 in n 11.788 * [backup-simplify]: Simplify 2 into 2 11.788 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.788 * [taylor]: Taking taylor expansion of PI in n 11.788 * [backup-simplify]: Simplify PI into PI 11.788 * [taylor]: Taking taylor expansion of n in n 11.788 * [backup-simplify]: Simplify 0 into 0 11.788 * [backup-simplify]: Simplify 1 into 1 11.789 * [backup-simplify]: Simplify (/ PI 1) into PI 11.789 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.790 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.790 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.790 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.790 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.792 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.793 * [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))) 11.794 * [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)))) 11.795 * [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))))) 11.796 * [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))))) 11.798 * [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))))))) 11.799 * [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))))))) 11.800 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.801 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.802 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.803 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.803 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 11.803 * [backup-simplify]: Simplify (- 0) into 0 11.804 * [backup-simplify]: Simplify (+ 0 0) into 0 11.805 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.806 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 11.808 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 11.811 * [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 11.812 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0 11.813 * [backup-simplify]: Simplify (- 0) into 0 11.813 * [backup-simplify]: Simplify 0 into 0 11.813 * [backup-simplify]: Simplify 0 into 0 11.814 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.818 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.818 * [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 11.820 * [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))))))) 11.820 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))))) in n 11.820 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 11.820 * [taylor]: Taking taylor expansion of +nan.0 in n 11.820 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.820 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 11.820 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 11.820 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 11.820 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 11.820 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 11.820 * [taylor]: Taking taylor expansion of 1/2 in n 11.820 * [backup-simplify]: Simplify 1/2 into 1/2 11.820 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.820 * [taylor]: Taking taylor expansion of 1/2 in n 11.820 * [backup-simplify]: Simplify 1/2 into 1/2 11.820 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.820 * [taylor]: Taking taylor expansion of k in n 11.820 * [backup-simplify]: Simplify k into k 11.820 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.820 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 11.820 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 11.820 * [taylor]: Taking taylor expansion of 2 in n 11.820 * [backup-simplify]: Simplify 2 into 2 11.820 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.820 * [taylor]: Taking taylor expansion of PI in n 11.820 * [backup-simplify]: Simplify PI into PI 11.820 * [taylor]: Taking taylor expansion of n in n 11.820 * [backup-simplify]: Simplify 0 into 0 11.820 * [backup-simplify]: Simplify 1 into 1 11.821 * [backup-simplify]: Simplify (/ PI 1) into PI 11.822 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.823 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.823 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.823 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 11.823 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 11.825 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 11.826 * [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))) 11.827 * [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)))) 11.828 * [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))))) 11.830 * [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))))) 11.831 * [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))))))) 11.832 * [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))))))) 11.836 * [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)))))))))))) 11.837 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 11.837 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 11.837 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 11.837 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 11.837 * [taylor]: Taking taylor expansion of (/ -1 k) in n 11.837 * [taylor]: Taking taylor expansion of -1 in n 11.837 * [backup-simplify]: Simplify -1 into -1 11.837 * [taylor]: Taking taylor expansion of k in n 11.837 * [backup-simplify]: Simplify k into k 11.837 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 11.837 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 11.837 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 11.837 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 11.837 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.837 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 11.837 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 11.837 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.838 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.838 * [taylor]: Taking taylor expansion of 1/2 in n 11.838 * [backup-simplify]: Simplify 1/2 into 1/2 11.838 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.838 * [taylor]: Taking taylor expansion of k in n 11.838 * [backup-simplify]: Simplify k into k 11.838 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.838 * [taylor]: Taking taylor expansion of 1/2 in n 11.838 * [backup-simplify]: Simplify 1/2 into 1/2 11.838 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.838 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.838 * [taylor]: Taking taylor expansion of -2 in n 11.838 * [backup-simplify]: Simplify -2 into -2 11.838 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.838 * [taylor]: Taking taylor expansion of PI in n 11.838 * [backup-simplify]: Simplify PI into PI 11.838 * [taylor]: Taking taylor expansion of n in n 11.838 * [backup-simplify]: Simplify 0 into 0 11.838 * [backup-simplify]: Simplify 1 into 1 11.839 * [backup-simplify]: Simplify (/ PI 1) into PI 11.839 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.840 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.840 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.840 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.842 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.843 * [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))) 11.844 * [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)))) 11.846 * [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))))) 11.846 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 11.846 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.846 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.846 * [taylor]: Taking taylor expansion of -1 in k 11.846 * [backup-simplify]: Simplify -1 into -1 11.846 * [taylor]: Taking taylor expansion of k in k 11.846 * [backup-simplify]: Simplify 0 into 0 11.846 * [backup-simplify]: Simplify 1 into 1 11.846 * [backup-simplify]: Simplify (/ -1 1) into -1 11.847 * [backup-simplify]: Simplify (sqrt 0) into 0 11.848 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.848 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 11.848 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 11.848 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 11.849 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 11.849 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.849 * [taylor]: Taking taylor expansion of 1/2 in k 11.849 * [backup-simplify]: Simplify 1/2 into 1/2 11.849 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.849 * [taylor]: Taking taylor expansion of k in k 11.849 * [backup-simplify]: Simplify 0 into 0 11.849 * [backup-simplify]: Simplify 1 into 1 11.849 * [backup-simplify]: Simplify (/ 1 1) into 1 11.849 * [taylor]: Taking taylor expansion of 1/2 in k 11.849 * [backup-simplify]: Simplify 1/2 into 1/2 11.849 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 11.849 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 11.849 * [taylor]: Taking taylor expansion of -2 in k 11.850 * [backup-simplify]: Simplify -2 into -2 11.850 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.850 * [taylor]: Taking taylor expansion of PI in k 11.850 * [backup-simplify]: Simplify PI into PI 11.850 * [taylor]: Taking taylor expansion of n in k 11.850 * [backup-simplify]: Simplify n into n 11.850 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.850 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 11.850 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 11.851 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.851 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.851 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 11.852 * [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))) 11.852 * [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)))) 11.852 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 11.852 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 11.852 * [taylor]: Taking taylor expansion of (/ -1 k) in k 11.852 * [taylor]: Taking taylor expansion of -1 in k 11.852 * [backup-simplify]: Simplify -1 into -1 11.852 * [taylor]: Taking taylor expansion of k in k 11.852 * [backup-simplify]: Simplify 0 into 0 11.852 * [backup-simplify]: Simplify 1 into 1 11.852 * [backup-simplify]: Simplify (/ -1 1) into -1 11.853 * [backup-simplify]: Simplify (sqrt 0) into 0 11.854 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 11.854 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 11.854 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 11.854 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 11.855 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 11.855 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 11.855 * [taylor]: Taking taylor expansion of 1/2 in k 11.855 * [backup-simplify]: Simplify 1/2 into 1/2 11.855 * [taylor]: Taking taylor expansion of (/ 1 k) in k 11.855 * [taylor]: Taking taylor expansion of k in k 11.855 * [backup-simplify]: Simplify 0 into 0 11.855 * [backup-simplify]: Simplify 1 into 1 11.855 * [backup-simplify]: Simplify (/ 1 1) into 1 11.855 * [taylor]: Taking taylor expansion of 1/2 in k 11.855 * [backup-simplify]: Simplify 1/2 into 1/2 11.855 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 11.855 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 11.855 * [taylor]: Taking taylor expansion of -2 in k 11.855 * [backup-simplify]: Simplify -2 into -2 11.855 * [taylor]: Taking taylor expansion of (/ PI n) in k 11.855 * [taylor]: Taking taylor expansion of PI in k 11.855 * [backup-simplify]: Simplify PI into PI 11.855 * [taylor]: Taking taylor expansion of n in k 11.855 * [backup-simplify]: Simplify n into n 11.855 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 11.856 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 11.856 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 11.856 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 11.856 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.857 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 11.857 * [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))) 11.857 * [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)))) 11.857 * [taylor]: Taking taylor expansion of (/ +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 11.857 * [taylor]: Taking taylor expansion of +nan.0 in n 11.857 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.857 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 11.857 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.857 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.857 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.857 * [taylor]: Taking taylor expansion of -2 in n 11.857 * [backup-simplify]: Simplify -2 into -2 11.857 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.857 * [taylor]: Taking taylor expansion of PI in n 11.857 * [backup-simplify]: Simplify PI into PI 11.857 * [taylor]: Taking taylor expansion of n in n 11.857 * [backup-simplify]: Simplify 0 into 0 11.857 * [backup-simplify]: Simplify 1 into 1 11.858 * [backup-simplify]: Simplify (/ PI 1) into PI 11.858 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.859 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.859 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.859 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.859 * [taylor]: Taking taylor expansion of 1/2 in n 11.859 * [backup-simplify]: Simplify 1/2 into 1/2 11.859 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.859 * [taylor]: Taking taylor expansion of k in n 11.859 * [backup-simplify]: Simplify k into k 11.859 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.859 * [taylor]: Taking taylor expansion of 1/2 in n 11.859 * [backup-simplify]: Simplify 1/2 into 1/2 11.860 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.860 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.860 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.861 * [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))) 11.861 * [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)))) 11.862 * [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))))) 11.863 * [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))))) 11.864 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 11.865 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 11.866 * [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)))))) 11.866 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 11.866 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 11.866 * [taylor]: Taking taylor expansion of +nan.0 in n 11.866 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.866 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 11.866 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 11.866 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.866 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.866 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.866 * [taylor]: Taking taylor expansion of -2 in n 11.866 * [backup-simplify]: Simplify -2 into -2 11.866 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.866 * [taylor]: Taking taylor expansion of PI in n 11.866 * [backup-simplify]: Simplify PI into PI 11.866 * [taylor]: Taking taylor expansion of n in n 11.866 * [backup-simplify]: Simplify 0 into 0 11.866 * [backup-simplify]: Simplify 1 into 1 11.869 * [backup-simplify]: Simplify (/ PI 1) into PI 11.869 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.870 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.870 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.870 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.870 * [taylor]: Taking taylor expansion of 1/2 in n 11.870 * [backup-simplify]: Simplify 1/2 into 1/2 11.870 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.870 * [taylor]: Taking taylor expansion of k in n 11.870 * [backup-simplify]: Simplify k into k 11.870 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.870 * [taylor]: Taking taylor expansion of 1/2 in n 11.870 * [backup-simplify]: Simplify 1/2 into 1/2 11.871 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.871 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.871 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.872 * [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))) 11.872 * [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)))) 11.873 * [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))))) 11.874 * [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))))) 11.875 * [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))))))) 11.876 * [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))))))) 11.877 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.877 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 11.877 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 11.877 * [backup-simplify]: Simplify (+ 0 0) into 0 11.878 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 11.878 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 11.879 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 11.880 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 11.881 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 11.884 * [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 11.884 * [backup-simplify]: Simplify 0 into 0 11.884 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 11.888 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 11.889 * [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)))))) 11.889 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))) in n 11.889 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 11.889 * [taylor]: Taking taylor expansion of +nan.0 in n 11.889 * [backup-simplify]: Simplify +nan.0 into +nan.0 11.889 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 11.889 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 11.890 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 11.890 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 11.890 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 11.890 * [taylor]: Taking taylor expansion of -2 in n 11.890 * [backup-simplify]: Simplify -2 into -2 11.890 * [taylor]: Taking taylor expansion of (/ PI n) in n 11.890 * [taylor]: Taking taylor expansion of PI in n 11.890 * [backup-simplify]: Simplify PI into PI 11.890 * [taylor]: Taking taylor expansion of n in n 11.890 * [backup-simplify]: Simplify 0 into 0 11.890 * [backup-simplify]: Simplify 1 into 1 11.891 * [backup-simplify]: Simplify (/ PI 1) into PI 11.891 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 11.893 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 11.893 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 11.893 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 11.893 * [taylor]: Taking taylor expansion of 1/2 in n 11.893 * [backup-simplify]: Simplify 1/2 into 1/2 11.893 * [taylor]: Taking taylor expansion of (/ 1 k) in n 11.893 * [taylor]: Taking taylor expansion of k in n 11.893 * [backup-simplify]: Simplify k into k 11.893 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 11.893 * [taylor]: Taking taylor expansion of 1/2 in n 11.893 * [backup-simplify]: Simplify 1/2 into 1/2 11.895 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 11.895 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 11.895 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 11.896 * [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))) 11.898 * [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)))) 11.899 * [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))))) 11.901 * [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))))) 11.902 * [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))))))) 11.903 * [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))))))) 11.908 * [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)))))))))))) 11.908 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2) 11.908 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 11.908 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 11.908 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 11.908 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 11.908 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 11.908 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.909 * [taylor]: Taking taylor expansion of 1/2 in k 11.909 * [backup-simplify]: Simplify 1/2 into 1/2 11.909 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.909 * [taylor]: Taking taylor expansion of 1/2 in k 11.909 * [backup-simplify]: Simplify 1/2 into 1/2 11.909 * [taylor]: Taking taylor expansion of k in k 11.909 * [backup-simplify]: Simplify 0 into 0 11.909 * [backup-simplify]: Simplify 1 into 1 11.909 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 11.909 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 11.909 * [taylor]: Taking taylor expansion of 2 in k 11.909 * [backup-simplify]: Simplify 2 into 2 11.909 * [taylor]: Taking taylor expansion of (* n PI) in k 11.909 * [taylor]: Taking taylor expansion of n in k 11.909 * [backup-simplify]: Simplify n into n 11.909 * [taylor]: Taking taylor expansion of PI in k 11.909 * [backup-simplify]: Simplify PI into PI 11.909 * [backup-simplify]: Simplify (* n PI) into (* n PI) 11.909 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 11.909 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 11.910 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.910 * [backup-simplify]: Simplify (- 0) into 0 11.910 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.911 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 11.911 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 11.911 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 11.911 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 11.911 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 11.911 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 11.911 * [taylor]: Taking taylor expansion of 1/2 in n 11.911 * [backup-simplify]: Simplify 1/2 into 1/2 11.911 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 11.911 * [taylor]: Taking taylor expansion of 1/2 in n 11.911 * [backup-simplify]: Simplify 1/2 into 1/2 11.911 * [taylor]: Taking taylor expansion of k in n 11.911 * [backup-simplify]: Simplify k into k 11.911 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.911 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.911 * [taylor]: Taking taylor expansion of 2 in n 11.911 * [backup-simplify]: Simplify 2 into 2 11.911 * [taylor]: Taking taylor expansion of (* n PI) in n 11.911 * [taylor]: Taking taylor expansion of n in n 11.911 * [backup-simplify]: Simplify 0 into 0 11.911 * [backup-simplify]: Simplify 1 into 1 11.911 * [taylor]: Taking taylor expansion of PI in n 11.911 * [backup-simplify]: Simplify PI into PI 11.912 * [backup-simplify]: Simplify (* 0 PI) into 0 11.913 * [backup-simplify]: Simplify (* 2 0) into 0 11.914 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.916 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.917 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.917 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 11.917 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 11.917 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 11.919 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.920 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 11.921 * [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))))) 11.921 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 11.921 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 11.921 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 11.921 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 11.921 * [taylor]: Taking taylor expansion of 1/2 in n 11.921 * [backup-simplify]: Simplify 1/2 into 1/2 11.921 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 11.921 * [taylor]: Taking taylor expansion of 1/2 in n 11.921 * [backup-simplify]: Simplify 1/2 into 1/2 11.921 * [taylor]: Taking taylor expansion of k in n 11.921 * [backup-simplify]: Simplify k into k 11.921 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 11.921 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 11.922 * [taylor]: Taking taylor expansion of 2 in n 11.922 * [backup-simplify]: Simplify 2 into 2 11.922 * [taylor]: Taking taylor expansion of (* n PI) in n 11.922 * [taylor]: Taking taylor expansion of n in n 11.922 * [backup-simplify]: Simplify 0 into 0 11.922 * [backup-simplify]: Simplify 1 into 1 11.922 * [taylor]: Taking taylor expansion of PI in n 11.922 * [backup-simplify]: Simplify PI into PI 11.922 * [backup-simplify]: Simplify (* 0 PI) into 0 11.923 * [backup-simplify]: Simplify (* 2 0) into 0 11.924 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 11.926 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 11.927 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.927 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 11.927 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 11.927 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 11.928 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.930 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 11.931 * [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))))) 11.931 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 11.931 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 11.931 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 11.931 * [taylor]: Taking taylor expansion of 1/2 in k 11.931 * [backup-simplify]: Simplify 1/2 into 1/2 11.931 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 11.931 * [taylor]: Taking taylor expansion of 1/2 in k 11.931 * [backup-simplify]: Simplify 1/2 into 1/2 11.931 * [taylor]: Taking taylor expansion of k in k 11.931 * [backup-simplify]: Simplify 0 into 0 11.931 * [backup-simplify]: Simplify 1 into 1 11.931 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 11.931 * [taylor]: Taking taylor expansion of (log n) in k 11.931 * [taylor]: Taking taylor expansion of n in k 11.931 * [backup-simplify]: Simplify n into n 11.931 * [backup-simplify]: Simplify (log n) into (log n) 11.931 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 11.931 * [taylor]: Taking taylor expansion of (* 2 PI) in k 11.931 * [taylor]: Taking taylor expansion of 2 in k 11.931 * [backup-simplify]: Simplify 2 into 2 11.931 * [taylor]: Taking taylor expansion of PI in k 11.931 * [backup-simplify]: Simplify PI into PI 11.932 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 11.933 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 11.933 * [backup-simplify]: Simplify (* 1/2 0) into 0 11.934 * [backup-simplify]: Simplify (- 0) into 0 11.934 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 11.935 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.936 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 11.938 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 11.939 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 11.940 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 11.941 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 11.943 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.943 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 11.944 * [backup-simplify]: Simplify (- 0) into 0 11.944 * [backup-simplify]: Simplify (+ 0 0) into 0 11.945 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.947 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 11.948 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 11.949 * [taylor]: Taking taylor expansion of 0 in k 11.949 * [backup-simplify]: Simplify 0 into 0 11.949 * [backup-simplify]: Simplify 0 into 0 11.949 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 11.951 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 11.953 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 11.953 * [backup-simplify]: Simplify (+ 0 0) into 0 11.954 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 11.954 * [backup-simplify]: Simplify (- 1/2) into -1/2 11.955 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 11.956 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 11.959 * [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))))))) 11.963 * [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))))))) 11.964 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 11.966 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 11.969 * [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 11.970 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 11.971 * [backup-simplify]: Simplify (- 0) into 0 11.971 * [backup-simplify]: Simplify (+ 0 0) into 0 11.973 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 11.975 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 11.977 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 11.977 * [taylor]: Taking taylor expansion of 0 in k 11.977 * [backup-simplify]: Simplify 0 into 0 11.978 * [backup-simplify]: Simplify 0 into 0 11.978 * [backup-simplify]: Simplify 0 into 0 11.979 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 11.980 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 11.984 * [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 11.984 * [backup-simplify]: Simplify (+ 0 0) into 0 11.985 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 11.985 * [backup-simplify]: Simplify (- 0) into 0 11.985 * [backup-simplify]: Simplify (+ 0 0) into 0 11.987 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 11.989 * [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))))) 11.992 * [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))))) 12.001 * [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))))) 12.001 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 12.001 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 12.001 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 12.001 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 12.001 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 12.001 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 12.001 * [taylor]: Taking taylor expansion of 1/2 in k 12.001 * [backup-simplify]: Simplify 1/2 into 1/2 12.001 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.001 * [taylor]: Taking taylor expansion of 1/2 in k 12.001 * [backup-simplify]: Simplify 1/2 into 1/2 12.001 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.001 * [taylor]: Taking taylor expansion of k in k 12.001 * [backup-simplify]: Simplify 0 into 0 12.001 * [backup-simplify]: Simplify 1 into 1 12.001 * [backup-simplify]: Simplify (/ 1 1) into 1 12.001 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 12.002 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 12.002 * [taylor]: Taking taylor expansion of 2 in k 12.002 * [backup-simplify]: Simplify 2 into 2 12.002 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.002 * [taylor]: Taking taylor expansion of PI in k 12.002 * [backup-simplify]: Simplify PI into PI 12.002 * [taylor]: Taking taylor expansion of n in k 12.002 * [backup-simplify]: Simplify n into n 12.002 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.002 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 12.002 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 12.002 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.002 * [backup-simplify]: Simplify (- 1/2) into -1/2 12.003 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 12.003 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 12.003 * [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)))) 12.003 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 12.003 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 12.003 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 12.003 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 12.003 * [taylor]: Taking taylor expansion of 1/2 in n 12.003 * [backup-simplify]: Simplify 1/2 into 1/2 12.003 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.003 * [taylor]: Taking taylor expansion of 1/2 in n 12.003 * [backup-simplify]: Simplify 1/2 into 1/2 12.003 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.003 * [taylor]: Taking taylor expansion of k in n 12.003 * [backup-simplify]: Simplify k into k 12.003 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.003 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.003 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.003 * [taylor]: Taking taylor expansion of 2 in n 12.003 * [backup-simplify]: Simplify 2 into 2 12.003 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.003 * [taylor]: Taking taylor expansion of PI in n 12.003 * [backup-simplify]: Simplify PI into PI 12.003 * [taylor]: Taking taylor expansion of n in n 12.003 * [backup-simplify]: Simplify 0 into 0 12.003 * [backup-simplify]: Simplify 1 into 1 12.003 * [backup-simplify]: Simplify (/ PI 1) into PI 12.004 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.004 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.004 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.004 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 12.005 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 12.005 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.006 * [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))) 12.007 * [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)))) 12.007 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 12.007 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 12.007 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 12.007 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 12.007 * [taylor]: Taking taylor expansion of 1/2 in n 12.007 * [backup-simplify]: Simplify 1/2 into 1/2 12.007 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.007 * [taylor]: Taking taylor expansion of 1/2 in n 12.007 * [backup-simplify]: Simplify 1/2 into 1/2 12.007 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.007 * [taylor]: Taking taylor expansion of k in n 12.007 * [backup-simplify]: Simplify k into k 12.007 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.007 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.007 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.007 * [taylor]: Taking taylor expansion of 2 in n 12.007 * [backup-simplify]: Simplify 2 into 2 12.007 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.007 * [taylor]: Taking taylor expansion of PI in n 12.007 * [backup-simplify]: Simplify PI into PI 12.007 * [taylor]: Taking taylor expansion of n in n 12.007 * [backup-simplify]: Simplify 0 into 0 12.007 * [backup-simplify]: Simplify 1 into 1 12.008 * [backup-simplify]: Simplify (/ PI 1) into PI 12.008 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.009 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.009 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.009 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 12.009 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 12.010 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.011 * [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))) 12.011 * [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)))) 12.011 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 12.011 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 12.011 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 12.011 * [taylor]: Taking taylor expansion of 1/2 in k 12.011 * [backup-simplify]: Simplify 1/2 into 1/2 12.011 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.012 * [taylor]: Taking taylor expansion of 1/2 in k 12.012 * [backup-simplify]: Simplify 1/2 into 1/2 12.012 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.012 * [taylor]: Taking taylor expansion of k in k 12.012 * [backup-simplify]: Simplify 0 into 0 12.012 * [backup-simplify]: Simplify 1 into 1 12.012 * [backup-simplify]: Simplify (/ 1 1) into 1 12.012 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 12.012 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 12.012 * [taylor]: Taking taylor expansion of (* 2 PI) in k 12.012 * [taylor]: Taking taylor expansion of 2 in k 12.012 * [backup-simplify]: Simplify 2 into 2 12.012 * [taylor]: Taking taylor expansion of PI in k 12.012 * [backup-simplify]: Simplify PI into PI 12.012 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.013 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.013 * [taylor]: Taking taylor expansion of (log n) in k 12.013 * [taylor]: Taking taylor expansion of n in k 12.013 * [backup-simplify]: Simplify n into n 12.013 * [backup-simplify]: Simplify (log n) into (log n) 12.014 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.014 * [backup-simplify]: Simplify (- 1/2) into -1/2 12.014 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 12.014 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.016 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 12.017 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 12.018 * [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)))) 12.019 * [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)))) 12.020 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.021 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 12.023 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 12.023 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.024 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 12.024 * [backup-simplify]: Simplify (- 0) into 0 12.025 * [backup-simplify]: Simplify (+ 0 0) into 0 12.026 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.028 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 12.030 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.030 * [taylor]: Taking taylor expansion of 0 in k 12.030 * [backup-simplify]: Simplify 0 into 0 12.030 * [backup-simplify]: Simplify 0 into 0 12.030 * [backup-simplify]: Simplify 0 into 0 12.031 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.032 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 12.037 * [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 12.037 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.038 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 12.039 * [backup-simplify]: Simplify (- 0) into 0 12.039 * [backup-simplify]: Simplify (+ 0 0) into 0 12.041 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.042 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 12.043 * [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 12.043 * [taylor]: Taking taylor expansion of 0 in k 12.043 * [backup-simplify]: Simplify 0 into 0 12.043 * [backup-simplify]: Simplify 0 into 0 12.043 * [backup-simplify]: Simplify 0 into 0 12.043 * [backup-simplify]: Simplify 0 into 0 12.044 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.045 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.048 * [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 12.048 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.049 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 12.049 * [backup-simplify]: Simplify (- 0) into 0 12.049 * [backup-simplify]: Simplify (+ 0 0) into 0 12.050 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.051 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 12.053 * [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 12.053 * [taylor]: Taking taylor expansion of 0 in k 12.053 * [backup-simplify]: Simplify 0 into 0 12.053 * [backup-simplify]: Simplify 0 into 0 12.054 * [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))))) 12.054 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 12.054 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 12.054 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 12.054 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 12.054 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 12.054 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 12.054 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.054 * [taylor]: Taking taylor expansion of 1/2 in k 12.054 * [backup-simplify]: Simplify 1/2 into 1/2 12.054 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.054 * [taylor]: Taking taylor expansion of k in k 12.054 * [backup-simplify]: Simplify 0 into 0 12.054 * [backup-simplify]: Simplify 1 into 1 12.055 * [backup-simplify]: Simplify (/ 1 1) into 1 12.055 * [taylor]: Taking taylor expansion of 1/2 in k 12.055 * [backup-simplify]: Simplify 1/2 into 1/2 12.055 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 12.055 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 12.055 * [taylor]: Taking taylor expansion of -2 in k 12.055 * [backup-simplify]: Simplify -2 into -2 12.055 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.055 * [taylor]: Taking taylor expansion of PI in k 12.055 * [backup-simplify]: Simplify PI into PI 12.055 * [taylor]: Taking taylor expansion of n in k 12.055 * [backup-simplify]: Simplify n into n 12.055 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.055 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 12.055 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 12.055 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.055 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.056 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 12.056 * [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))) 12.056 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.056 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 12.056 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 12.056 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.056 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.056 * [taylor]: Taking taylor expansion of 1/2 in n 12.056 * [backup-simplify]: Simplify 1/2 into 1/2 12.056 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.056 * [taylor]: Taking taylor expansion of k in n 12.056 * [backup-simplify]: Simplify k into k 12.056 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.056 * [taylor]: Taking taylor expansion of 1/2 in n 12.056 * [backup-simplify]: Simplify 1/2 into 1/2 12.056 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.056 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.056 * [taylor]: Taking taylor expansion of -2 in n 12.056 * [backup-simplify]: Simplify -2 into -2 12.056 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.056 * [taylor]: Taking taylor expansion of PI in n 12.056 * [backup-simplify]: Simplify PI into PI 12.056 * [taylor]: Taking taylor expansion of n in n 12.056 * [backup-simplify]: Simplify 0 into 0 12.056 * [backup-simplify]: Simplify 1 into 1 12.056 * [backup-simplify]: Simplify (/ PI 1) into PI 12.057 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.058 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.058 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.058 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.059 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.060 * [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))) 12.060 * [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)))) 12.061 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.061 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 12.061 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 12.061 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.061 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.061 * [taylor]: Taking taylor expansion of 1/2 in n 12.061 * [backup-simplify]: Simplify 1/2 into 1/2 12.061 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.061 * [taylor]: Taking taylor expansion of k in n 12.061 * [backup-simplify]: Simplify k into k 12.061 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.061 * [taylor]: Taking taylor expansion of 1/2 in n 12.061 * [backup-simplify]: Simplify 1/2 into 1/2 12.061 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.061 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.061 * [taylor]: Taking taylor expansion of -2 in n 12.061 * [backup-simplify]: Simplify -2 into -2 12.061 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.061 * [taylor]: Taking taylor expansion of PI in n 12.061 * [backup-simplify]: Simplify PI into PI 12.061 * [taylor]: Taking taylor expansion of n in n 12.061 * [backup-simplify]: Simplify 0 into 0 12.061 * [backup-simplify]: Simplify 1 into 1 12.062 * [backup-simplify]: Simplify (/ PI 1) into PI 12.062 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.063 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.064 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.064 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.065 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.067 * [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))) 12.068 * [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)))) 12.068 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 12.068 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 12.068 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 12.068 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.068 * [taylor]: Taking taylor expansion of 1/2 in k 12.068 * [backup-simplify]: Simplify 1/2 into 1/2 12.068 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.068 * [taylor]: Taking taylor expansion of k in k 12.068 * [backup-simplify]: Simplify 0 into 0 12.068 * [backup-simplify]: Simplify 1 into 1 12.069 * [backup-simplify]: Simplify (/ 1 1) into 1 12.069 * [taylor]: Taking taylor expansion of 1/2 in k 12.069 * [backup-simplify]: Simplify 1/2 into 1/2 12.069 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 12.069 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 12.069 * [taylor]: Taking taylor expansion of (* -2 PI) in k 12.069 * [taylor]: Taking taylor expansion of -2 in k 12.069 * [backup-simplify]: Simplify -2 into -2 12.069 * [taylor]: Taking taylor expansion of PI in k 12.069 * [backup-simplify]: Simplify PI into PI 12.070 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.071 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.071 * [taylor]: Taking taylor expansion of (log n) in k 12.071 * [taylor]: Taking taylor expansion of n in k 12.071 * [backup-simplify]: Simplify n into n 12.071 * [backup-simplify]: Simplify (log n) into (log n) 12.071 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.072 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.072 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.073 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 12.074 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 12.075 * [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)))) 12.076 * [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)))) 12.077 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.078 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 12.080 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 12.080 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.081 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 12.081 * [backup-simplify]: Simplify (+ 0 0) into 0 12.083 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.084 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 12.086 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.086 * [taylor]: Taking taylor expansion of 0 in k 12.086 * [backup-simplify]: Simplify 0 into 0 12.086 * [backup-simplify]: Simplify 0 into 0 12.086 * [backup-simplify]: Simplify 0 into 0 12.088 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.089 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 12.092 * [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 12.093 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.094 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 12.094 * [backup-simplify]: Simplify (+ 0 0) into 0 12.095 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.097 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 12.100 * [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 12.100 * [taylor]: Taking taylor expansion of 0 in k 12.100 * [backup-simplify]: Simplify 0 into 0 12.100 * [backup-simplify]: Simplify 0 into 0 12.100 * [backup-simplify]: Simplify 0 into 0 12.100 * [backup-simplify]: Simplify 0 into 0 12.101 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.102 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.109 * [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 12.109 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.110 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 12.110 * [backup-simplify]: Simplify (+ 0 0) into 0 12.111 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.112 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 12.114 * [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 12.114 * [taylor]: Taking taylor expansion of 0 in k 12.114 * [backup-simplify]: Simplify 0 into 0 12.114 * [backup-simplify]: Simplify 0 into 0 12.115 * [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))))) 12.115 * * * * [progress]: [ 4 / 4 ] generating series at (2) 12.115 * [backup-simplify]: Simplify (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 12.115 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (k n) around 0 12.115 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 12.115 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 12.115 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.115 * [taylor]: Taking taylor expansion of k in n 12.115 * [backup-simplify]: Simplify k into k 12.115 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.115 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 12.115 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.115 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 12.115 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 12.115 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 12.115 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 12.115 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 12.115 * [taylor]: Taking taylor expansion of 1/2 in n 12.115 * [backup-simplify]: Simplify 1/2 into 1/2 12.115 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 12.116 * [taylor]: Taking taylor expansion of 1/2 in n 12.116 * [backup-simplify]: Simplify 1/2 into 1/2 12.116 * [taylor]: Taking taylor expansion of k in n 12.116 * [backup-simplify]: Simplify k into k 12.116 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 12.116 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.116 * [taylor]: Taking taylor expansion of 2 in n 12.116 * [backup-simplify]: Simplify 2 into 2 12.116 * [taylor]: Taking taylor expansion of (* n PI) in n 12.116 * [taylor]: Taking taylor expansion of n in n 12.116 * [backup-simplify]: Simplify 0 into 0 12.116 * [backup-simplify]: Simplify 1 into 1 12.116 * [taylor]: Taking taylor expansion of PI in n 12.116 * [backup-simplify]: Simplify PI into PI 12.116 * [backup-simplify]: Simplify (* 0 PI) into 0 12.116 * [backup-simplify]: Simplify (* 2 0) into 0 12.117 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.118 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.121 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.121 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 12.121 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 12.121 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 12.122 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.123 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 12.124 * [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))))) 12.124 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 12.124 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.124 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.124 * [taylor]: Taking taylor expansion of k in k 12.124 * [backup-simplify]: Simplify 0 into 0 12.124 * [backup-simplify]: Simplify 1 into 1 12.124 * [backup-simplify]: Simplify (/ 1 1) into 1 12.124 * [backup-simplify]: Simplify (sqrt 0) into 0 12.125 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.125 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 12.125 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 12.125 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 12.125 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 12.125 * [taylor]: Taking taylor expansion of 1/2 in k 12.125 * [backup-simplify]: Simplify 1/2 into 1/2 12.125 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 12.125 * [taylor]: Taking taylor expansion of 1/2 in k 12.125 * [backup-simplify]: Simplify 1/2 into 1/2 12.125 * [taylor]: Taking taylor expansion of k in k 12.125 * [backup-simplify]: Simplify 0 into 0 12.126 * [backup-simplify]: Simplify 1 into 1 12.126 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 12.126 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 12.126 * [taylor]: Taking taylor expansion of 2 in k 12.126 * [backup-simplify]: Simplify 2 into 2 12.126 * [taylor]: Taking taylor expansion of (* n PI) in k 12.126 * [taylor]: Taking taylor expansion of n in k 12.126 * [backup-simplify]: Simplify n into n 12.126 * [taylor]: Taking taylor expansion of PI in k 12.126 * [backup-simplify]: Simplify PI into PI 12.126 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.126 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 12.126 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 12.126 * [backup-simplify]: Simplify (* 1/2 0) into 0 12.126 * [backup-simplify]: Simplify (- 0) into 0 12.127 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.127 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 12.127 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 12.127 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 12.127 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 12.127 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.127 * [taylor]: Taking taylor expansion of k in k 12.127 * [backup-simplify]: Simplify 0 into 0 12.127 * [backup-simplify]: Simplify 1 into 1 12.127 * [backup-simplify]: Simplify (/ 1 1) into 1 12.127 * [backup-simplify]: Simplify (sqrt 0) into 0 12.128 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.128 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 12.128 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 12.128 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 12.128 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 12.128 * [taylor]: Taking taylor expansion of 1/2 in k 12.128 * [backup-simplify]: Simplify 1/2 into 1/2 12.128 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 12.128 * [taylor]: Taking taylor expansion of 1/2 in k 12.128 * [backup-simplify]: Simplify 1/2 into 1/2 12.128 * [taylor]: Taking taylor expansion of k in k 12.128 * [backup-simplify]: Simplify 0 into 0 12.128 * [backup-simplify]: Simplify 1 into 1 12.128 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 12.128 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 12.128 * [taylor]: Taking taylor expansion of 2 in k 12.128 * [backup-simplify]: Simplify 2 into 2 12.128 * [taylor]: Taking taylor expansion of (* n PI) in k 12.128 * [taylor]: Taking taylor expansion of n in k 12.128 * [backup-simplify]: Simplify n into n 12.128 * [taylor]: Taking taylor expansion of PI in k 12.128 * [backup-simplify]: Simplify PI into PI 12.128 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.128 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 12.129 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 12.129 * [backup-simplify]: Simplify (* 1/2 0) into 0 12.129 * [backup-simplify]: Simplify (- 0) into 0 12.129 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.129 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 12.129 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 12.130 * [backup-simplify]: Simplify (* 0 (pow (* 2 (* n PI)) 1/2)) into 0 12.130 * [taylor]: Taking taylor expansion of 0 in n 12.130 * [backup-simplify]: Simplify 0 into 0 12.130 * [backup-simplify]: Simplify 0 into 0 12.130 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 12.130 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 12.131 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 12.131 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 12.131 * [backup-simplify]: Simplify (- 1/2) into -1/2 12.132 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 12.132 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 12.132 * [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))))) 12.132 * [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))))) 12.132 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 12.133 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 12.133 * [taylor]: Taking taylor expansion of +nan.0 in n 12.133 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.133 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 12.133 * [taylor]: Taking taylor expansion of (sqrt 2) in n 12.133 * [taylor]: Taking taylor expansion of 2 in n 12.133 * [backup-simplify]: Simplify 2 into 2 12.133 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 12.133 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 12.133 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 12.133 * [taylor]: Taking taylor expansion of (* n PI) in n 12.133 * [taylor]: Taking taylor expansion of n in n 12.133 * [backup-simplify]: Simplify 0 into 0 12.133 * [backup-simplify]: Simplify 1 into 1 12.133 * [taylor]: Taking taylor expansion of PI in n 12.133 * [backup-simplify]: Simplify PI into PI 12.134 * [backup-simplify]: Simplify (* 0 PI) into 0 12.135 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.135 * [backup-simplify]: Simplify (sqrt 0) into 0 12.136 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 12.136 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 12.136 * [backup-simplify]: Simplify (* +nan.0 0) into 0 12.137 * [backup-simplify]: Simplify (- 0) into 0 12.137 * [backup-simplify]: Simplify 0 into 0 12.137 * [backup-simplify]: Simplify 0 into 0 12.137 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 12.138 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 12.139 * [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 12.139 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 12.140 * [backup-simplify]: Simplify (- 0) into 0 12.140 * [backup-simplify]: Simplify (+ 0 0) into 0 12.140 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 12.141 * [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))) 12.142 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 12.143 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.144 * [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))))))) 12.144 * [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 12.144 * [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 12.144 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 12.144 * [taylor]: Taking taylor expansion of +nan.0 in n 12.144 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.144 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 12.144 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 12.144 * [taylor]: Taking taylor expansion of (sqrt 2) in n 12.144 * [taylor]: Taking taylor expansion of 2 in n 12.144 * [backup-simplify]: Simplify 2 into 2 12.144 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 12.145 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 12.145 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 12.145 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.145 * [taylor]: Taking taylor expansion of 2 in n 12.145 * [backup-simplify]: Simplify 2 into 2 12.145 * [taylor]: Taking taylor expansion of (* n PI) in n 12.145 * [taylor]: Taking taylor expansion of n in n 12.145 * [backup-simplify]: Simplify 0 into 0 12.145 * [backup-simplify]: Simplify 1 into 1 12.145 * [taylor]: Taking taylor expansion of PI in n 12.145 * [backup-simplify]: Simplify PI into PI 12.145 * [backup-simplify]: Simplify (* 0 PI) into 0 12.146 * [backup-simplify]: Simplify (* 2 0) into 0 12.147 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.148 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.148 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.148 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 12.148 * [taylor]: Taking taylor expansion of (* n PI) in n 12.148 * [taylor]: Taking taylor expansion of n in n 12.148 * [backup-simplify]: Simplify 0 into 0 12.148 * [backup-simplify]: Simplify 1 into 1 12.148 * [taylor]: Taking taylor expansion of PI in n 12.148 * [backup-simplify]: Simplify PI into PI 12.149 * [backup-simplify]: Simplify (* 0 PI) into 0 12.150 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.150 * [backup-simplify]: Simplify (sqrt 0) into 0 12.151 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 12.151 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 12.151 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 12.151 * [taylor]: Taking taylor expansion of +nan.0 in n 12.151 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.151 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 12.151 * [taylor]: Taking taylor expansion of (sqrt 2) in n 12.151 * [taylor]: Taking taylor expansion of 2 in n 12.151 * [backup-simplify]: Simplify 2 into 2 12.151 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 12.152 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 12.152 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 12.152 * [taylor]: Taking taylor expansion of (* n PI) in n 12.152 * [taylor]: Taking taylor expansion of n in n 12.152 * [backup-simplify]: Simplify 0 into 0 12.152 * [backup-simplify]: Simplify 1 into 1 12.152 * [taylor]: Taking taylor expansion of PI in n 12.152 * [backup-simplify]: Simplify PI into PI 12.152 * [backup-simplify]: Simplify (* 0 PI) into 0 12.153 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.154 * [backup-simplify]: Simplify (sqrt 0) into 0 12.154 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 12.155 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.156 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 12.157 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 12.158 * [backup-simplify]: Simplify (* +nan.0 0) into 0 12.158 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 12.158 * [backup-simplify]: Simplify (* +nan.0 0) into 0 12.158 * [backup-simplify]: Simplify (- 0) into 0 12.159 * [backup-simplify]: Simplify (+ 0 0) into 0 12.159 * [backup-simplify]: Simplify (- 0) into 0 12.159 * [backup-simplify]: Simplify 0 into 0 12.162 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 12.165 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 12.168 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 12.169 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 12.169 * [backup-simplify]: Simplify 0 into 0 12.170 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.171 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 12.173 * [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 12.173 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 12.173 * [backup-simplify]: Simplify (- 0) into 0 12.174 * [backup-simplify]: Simplify (+ 0 0) into 0 12.175 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 12.176 * [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))) 12.176 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.179 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.179 * [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))))))))) 12.179 * [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 12.179 * [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 12.179 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 12.179 * [taylor]: Taking taylor expansion of +nan.0 in n 12.179 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.179 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 12.179 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 12.179 * [taylor]: Taking taylor expansion of (sqrt 2) in n 12.179 * [taylor]: Taking taylor expansion of 2 in n 12.180 * [backup-simplify]: Simplify 2 into 2 12.180 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 12.180 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 12.180 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 12.180 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.180 * [taylor]: Taking taylor expansion of 2 in n 12.180 * [backup-simplify]: Simplify 2 into 2 12.180 * [taylor]: Taking taylor expansion of (* n PI) in n 12.180 * [taylor]: Taking taylor expansion of n in n 12.180 * [backup-simplify]: Simplify 0 into 0 12.180 * [backup-simplify]: Simplify 1 into 1 12.180 * [taylor]: Taking taylor expansion of PI in n 12.180 * [backup-simplify]: Simplify PI into PI 12.181 * [backup-simplify]: Simplify (* 0 PI) into 0 12.181 * [backup-simplify]: Simplify (* 2 0) into 0 12.182 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.183 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.184 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.184 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 12.184 * [taylor]: Taking taylor expansion of (* n PI) in n 12.184 * [taylor]: Taking taylor expansion of n in n 12.184 * [backup-simplify]: Simplify 0 into 0 12.184 * [backup-simplify]: Simplify 1 into 1 12.184 * [taylor]: Taking taylor expansion of PI in n 12.184 * [backup-simplify]: Simplify PI into PI 12.184 * [backup-simplify]: Simplify (* 0 PI) into 0 12.186 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.186 * [backup-simplify]: Simplify (sqrt 0) into 0 12.187 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 12.187 * [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 12.187 * [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 12.187 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 12.187 * [taylor]: Taking taylor expansion of +nan.0 in n 12.187 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.187 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 12.187 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 12.188 * [taylor]: Taking taylor expansion of (sqrt 2) in n 12.188 * [taylor]: Taking taylor expansion of 2 in n 12.188 * [backup-simplify]: Simplify 2 into 2 12.188 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 12.188 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 12.188 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 12.188 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 12.188 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 12.188 * [taylor]: Taking taylor expansion of 2 in n 12.188 * [backup-simplify]: Simplify 2 into 2 12.188 * [taylor]: Taking taylor expansion of (* n PI) in n 12.188 * [taylor]: Taking taylor expansion of n in n 12.188 * [backup-simplify]: Simplify 0 into 0 12.188 * [backup-simplify]: Simplify 1 into 1 12.188 * [taylor]: Taking taylor expansion of PI in n 12.188 * [backup-simplify]: Simplify PI into PI 12.189 * [backup-simplify]: Simplify (* 0 PI) into 0 12.189 * [backup-simplify]: Simplify (* 2 0) into 0 12.190 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.191 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 12.192 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.193 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.193 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 12.193 * [taylor]: Taking taylor expansion of (* n PI) in n 12.193 * [taylor]: Taking taylor expansion of n in n 12.193 * [backup-simplify]: Simplify 0 into 0 12.193 * [backup-simplify]: Simplify 1 into 1 12.193 * [taylor]: Taking taylor expansion of PI in n 12.193 * [backup-simplify]: Simplify PI into PI 12.193 * [backup-simplify]: Simplify (* 0 PI) into 0 12.194 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.195 * [backup-simplify]: Simplify (sqrt 0) into 0 12.195 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 12.195 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 12.195 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 12.195 * [taylor]: Taking taylor expansion of +nan.0 in n 12.195 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.195 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 12.195 * [taylor]: Taking taylor expansion of (sqrt 2) in n 12.196 * [taylor]: Taking taylor expansion of 2 in n 12.196 * [backup-simplify]: Simplify 2 into 2 12.196 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 12.196 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 12.196 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 12.196 * [taylor]: Taking taylor expansion of (* n PI) in n 12.196 * [taylor]: Taking taylor expansion of n in n 12.196 * [backup-simplify]: Simplify 0 into 0 12.196 * [backup-simplify]: Simplify 1 into 1 12.196 * [taylor]: Taking taylor expansion of PI in n 12.196 * [backup-simplify]: Simplify PI into PI 12.197 * [backup-simplify]: Simplify (* 0 PI) into 0 12.198 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.198 * [backup-simplify]: Simplify (sqrt 0) into 0 12.199 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 12.200 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.200 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 12.201 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 12.202 * [backup-simplify]: Simplify (* +nan.0 0) into 0 12.203 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.204 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.205 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 12.206 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 12.207 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 12.207 * [backup-simplify]: Simplify (* +nan.0 0) into 0 12.208 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 12.208 * [backup-simplify]: Simplify (* +nan.0 0) into 0 12.208 * [backup-simplify]: Simplify (- 0) into 0 12.208 * [backup-simplify]: Simplify (+ 0 0) into 0 12.209 * [backup-simplify]: Simplify (- 0) into 0 12.209 * [backup-simplify]: Simplify (+ 0 0) into 0 12.209 * [backup-simplify]: Simplify (- 0) into 0 12.209 * [backup-simplify]: Simplify 0 into 0 12.210 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.210 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 12.216 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 12.217 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 12.218 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 12.219 * [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)))))))) 12.223 * [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)))))))) 12.225 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 12.228 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 12.230 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 12.236 * [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)))))))))) 12.243 * [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))))))) 12.251 * [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))))))) 12.252 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.257 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 12.258 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 12.263 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 12.274 * [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)))) 12.279 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 12.282 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 12.298 * [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))))))))))))) 12.299 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 k)) (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 12.299 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (k n) around 0 12.299 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 12.299 * [taylor]: Taking taylor expansion of (sqrt k) in n 12.299 * [taylor]: Taking taylor expansion of k in n 12.299 * [backup-simplify]: Simplify k into k 12.299 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 12.299 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 12.299 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 12.299 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 12.299 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 12.299 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 12.299 * [taylor]: Taking taylor expansion of 1/2 in n 12.299 * [backup-simplify]: Simplify 1/2 into 1/2 12.299 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.299 * [taylor]: Taking taylor expansion of 1/2 in n 12.299 * [backup-simplify]: Simplify 1/2 into 1/2 12.299 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.299 * [taylor]: Taking taylor expansion of k in n 12.299 * [backup-simplify]: Simplify k into k 12.299 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.299 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.299 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.299 * [taylor]: Taking taylor expansion of 2 in n 12.300 * [backup-simplify]: Simplify 2 into 2 12.300 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.300 * [taylor]: Taking taylor expansion of PI in n 12.300 * [backup-simplify]: Simplify PI into PI 12.300 * [taylor]: Taking taylor expansion of n in n 12.300 * [backup-simplify]: Simplify 0 into 0 12.300 * [backup-simplify]: Simplify 1 into 1 12.300 * [backup-simplify]: Simplify (/ PI 1) into PI 12.301 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.302 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.302 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.302 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 12.302 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 12.304 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.305 * [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))) 12.306 * [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)))) 12.306 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 12.306 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.306 * [taylor]: Taking taylor expansion of k in k 12.307 * [backup-simplify]: Simplify 0 into 0 12.307 * [backup-simplify]: Simplify 1 into 1 12.307 * [backup-simplify]: Simplify (sqrt 0) into 0 12.309 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.309 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 12.309 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 12.309 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 12.309 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 12.309 * [taylor]: Taking taylor expansion of 1/2 in k 12.309 * [backup-simplify]: Simplify 1/2 into 1/2 12.309 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.309 * [taylor]: Taking taylor expansion of 1/2 in k 12.309 * [backup-simplify]: Simplify 1/2 into 1/2 12.309 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.309 * [taylor]: Taking taylor expansion of k in k 12.309 * [backup-simplify]: Simplify 0 into 0 12.309 * [backup-simplify]: Simplify 1 into 1 12.309 * [backup-simplify]: Simplify (/ 1 1) into 1 12.309 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 12.310 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 12.310 * [taylor]: Taking taylor expansion of 2 in k 12.310 * [backup-simplify]: Simplify 2 into 2 12.310 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.310 * [taylor]: Taking taylor expansion of PI in k 12.310 * [backup-simplify]: Simplify PI into PI 12.310 * [taylor]: Taking taylor expansion of n in k 12.310 * [backup-simplify]: Simplify n into n 12.310 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.310 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 12.310 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 12.310 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.311 * [backup-simplify]: Simplify (- 1/2) into -1/2 12.311 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 12.311 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 12.312 * [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)))) 12.312 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 12.312 * [taylor]: Taking taylor expansion of (sqrt k) in k 12.312 * [taylor]: Taking taylor expansion of k in k 12.312 * [backup-simplify]: Simplify 0 into 0 12.312 * [backup-simplify]: Simplify 1 into 1 12.312 * [backup-simplify]: Simplify (sqrt 0) into 0 12.314 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 12.314 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 12.314 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 12.314 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 12.314 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 12.314 * [taylor]: Taking taylor expansion of 1/2 in k 12.314 * [backup-simplify]: Simplify 1/2 into 1/2 12.314 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.314 * [taylor]: Taking taylor expansion of 1/2 in k 12.314 * [backup-simplify]: Simplify 1/2 into 1/2 12.314 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.314 * [taylor]: Taking taylor expansion of k in k 12.314 * [backup-simplify]: Simplify 0 into 0 12.314 * [backup-simplify]: Simplify 1 into 1 12.314 * [backup-simplify]: Simplify (/ 1 1) into 1 12.314 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 12.314 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 12.314 * [taylor]: Taking taylor expansion of 2 in k 12.315 * [backup-simplify]: Simplify 2 into 2 12.315 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.315 * [taylor]: Taking taylor expansion of PI in k 12.315 * [backup-simplify]: Simplify PI into PI 12.315 * [taylor]: Taking taylor expansion of n in k 12.315 * [backup-simplify]: Simplify n into n 12.315 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.315 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 12.315 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 12.315 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.316 * [backup-simplify]: Simplify (- 1/2) into -1/2 12.316 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 12.316 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 12.317 * [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)))) 12.317 * [backup-simplify]: Simplify (* 0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) into 0 12.317 * [taylor]: Taking taylor expansion of 0 in n 12.317 * [backup-simplify]: Simplify 0 into 0 12.317 * [backup-simplify]: Simplify 0 into 0 12.317 * [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)))))) 12.317 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 12.317 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 12.317 * [taylor]: Taking taylor expansion of +nan.0 in n 12.317 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.317 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 12.317 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 12.317 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 12.317 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 12.317 * [taylor]: Taking taylor expansion of 1/2 in n 12.317 * [backup-simplify]: Simplify 1/2 into 1/2 12.317 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.317 * [taylor]: Taking taylor expansion of 1/2 in n 12.317 * [backup-simplify]: Simplify 1/2 into 1/2 12.317 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.318 * [taylor]: Taking taylor expansion of k in n 12.318 * [backup-simplify]: Simplify k into k 12.318 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.318 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.318 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) 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 (/ PI n) in n 12.318 * [taylor]: Taking taylor expansion of PI in n 12.318 * [backup-simplify]: Simplify PI into PI 12.318 * [taylor]: Taking taylor expansion of n in n 12.318 * [backup-simplify]: Simplify 0 into 0 12.318 * [backup-simplify]: Simplify 1 into 1 12.318 * [backup-simplify]: Simplify (/ PI 1) into PI 12.318 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.319 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.319 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.319 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 12.319 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 12.320 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.321 * [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))) 12.322 * [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)))) 12.322 * [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))))) 12.323 * [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)))))) 12.324 * [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)))))) 12.324 * [backup-simplify]: Simplify 0 into 0 12.326 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.326 * [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)))))) 12.326 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 12.326 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 12.327 * [taylor]: Taking taylor expansion of +nan.0 in n 12.327 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.327 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 12.327 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 12.327 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 12.327 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 12.327 * [taylor]: Taking taylor expansion of 1/2 in n 12.327 * [backup-simplify]: Simplify 1/2 into 1/2 12.327 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.327 * [taylor]: Taking taylor expansion of 1/2 in n 12.327 * [backup-simplify]: Simplify 1/2 into 1/2 12.327 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.327 * [taylor]: Taking taylor expansion of k in n 12.327 * [backup-simplify]: Simplify k into k 12.327 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.327 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.327 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.327 * [taylor]: Taking taylor expansion of 2 in n 12.327 * [backup-simplify]: Simplify 2 into 2 12.327 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.327 * [taylor]: Taking taylor expansion of PI in n 12.327 * [backup-simplify]: Simplify PI into PI 12.327 * [taylor]: Taking taylor expansion of n in n 12.327 * [backup-simplify]: Simplify 0 into 0 12.327 * [backup-simplify]: Simplify 1 into 1 12.327 * [backup-simplify]: Simplify (/ PI 1) into PI 12.328 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.328 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.328 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.328 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 12.328 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 12.329 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.330 * [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))) 12.331 * [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)))) 12.331 * [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))))) 12.332 * [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)))))) 12.336 * [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)))))) 12.336 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.337 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 12.338 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 12.338 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.338 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 12.339 * [backup-simplify]: Simplify (- 0) into 0 12.339 * [backup-simplify]: Simplify (+ 0 0) into 0 12.340 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.340 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 12.342 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.343 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 12.343 * [backup-simplify]: Simplify (- 0) into 0 12.343 * [backup-simplify]: Simplify 0 into 0 12.343 * [backup-simplify]: Simplify 0 into 0 12.345 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.346 * [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)))))) 12.346 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 12.346 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 12.346 * [taylor]: Taking taylor expansion of +nan.0 in n 12.346 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.346 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 12.346 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 12.346 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 12.346 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 12.346 * [taylor]: Taking taylor expansion of 1/2 in n 12.346 * [backup-simplify]: Simplify 1/2 into 1/2 12.346 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.346 * [taylor]: Taking taylor expansion of 1/2 in n 12.346 * [backup-simplify]: Simplify 1/2 into 1/2 12.346 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.347 * [taylor]: Taking taylor expansion of k in n 12.347 * [backup-simplify]: Simplify k into k 12.347 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.347 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 12.347 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 12.347 * [taylor]: Taking taylor expansion of 2 in n 12.347 * [backup-simplify]: Simplify 2 into 2 12.347 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.347 * [taylor]: Taking taylor expansion of PI in n 12.347 * [backup-simplify]: Simplify PI into PI 12.347 * [taylor]: Taking taylor expansion of n in n 12.347 * [backup-simplify]: Simplify 0 into 0 12.347 * [backup-simplify]: Simplify 1 into 1 12.347 * [backup-simplify]: Simplify (/ PI 1) into PI 12.347 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 12.348 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 12.348 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.348 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 12.348 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 12.349 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 12.350 * [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))) 12.351 * [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)))) 12.351 * [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))))) 12.352 * [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)))))) 12.353 * [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)))))) 12.357 * [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)))))))) 12.357 * [backup-simplify]: Simplify (/ 1 (/ (sqrt (/ 1 (- k))) (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 12.357 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k n) around 0 12.357 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 12.357 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.357 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 12.357 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 12.357 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.357 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.357 * [taylor]: Taking taylor expansion of 1/2 in n 12.357 * [backup-simplify]: Simplify 1/2 into 1/2 12.357 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.357 * [taylor]: Taking taylor expansion of k in n 12.357 * [backup-simplify]: Simplify k into k 12.357 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.357 * [taylor]: Taking taylor expansion of 1/2 in n 12.357 * [backup-simplify]: Simplify 1/2 into 1/2 12.357 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.357 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.358 * [taylor]: Taking taylor expansion of -2 in n 12.358 * [backup-simplify]: Simplify -2 into -2 12.358 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.358 * [taylor]: Taking taylor expansion of PI in n 12.358 * [backup-simplify]: Simplify PI into PI 12.358 * [taylor]: Taking taylor expansion of n in n 12.358 * [backup-simplify]: Simplify 0 into 0 12.358 * [backup-simplify]: Simplify 1 into 1 12.358 * [backup-simplify]: Simplify (/ PI 1) into PI 12.359 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.360 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.360 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.360 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.361 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.362 * [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))) 12.363 * [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)))) 12.363 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 12.363 * [taylor]: Taking taylor expansion of (/ -1 k) in n 12.363 * [taylor]: Taking taylor expansion of -1 in n 12.363 * [backup-simplify]: Simplify -1 into -1 12.363 * [taylor]: Taking taylor expansion of k in n 12.363 * [backup-simplify]: Simplify k into k 12.363 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 12.363 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 12.364 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 12.364 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 12.365 * [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))) 12.365 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 12.365 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 12.365 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 12.365 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 12.366 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 12.366 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.366 * [taylor]: Taking taylor expansion of 1/2 in k 12.366 * [backup-simplify]: Simplify 1/2 into 1/2 12.366 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.366 * [taylor]: Taking taylor expansion of k in k 12.366 * [backup-simplify]: Simplify 0 into 0 12.366 * [backup-simplify]: Simplify 1 into 1 12.366 * [backup-simplify]: Simplify (/ 1 1) into 1 12.366 * [taylor]: Taking taylor expansion of 1/2 in k 12.366 * [backup-simplify]: Simplify 1/2 into 1/2 12.366 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 12.366 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 12.366 * [taylor]: Taking taylor expansion of -2 in k 12.366 * [backup-simplify]: Simplify -2 into -2 12.366 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.366 * [taylor]: Taking taylor expansion of PI in k 12.366 * [backup-simplify]: Simplify PI into PI 12.366 * [taylor]: Taking taylor expansion of n in k 12.366 * [backup-simplify]: Simplify n into n 12.366 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.367 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 12.367 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 12.367 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.368 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.368 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 12.368 * [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))) 12.368 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.368 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.368 * [taylor]: Taking taylor expansion of -1 in k 12.368 * [backup-simplify]: Simplify -1 into -1 12.368 * [taylor]: Taking taylor expansion of k in k 12.368 * [backup-simplify]: Simplify 0 into 0 12.368 * [backup-simplify]: Simplify 1 into 1 12.369 * [backup-simplify]: Simplify (/ -1 1) into -1 12.369 * [backup-simplify]: Simplify (sqrt 0) into 0 12.370 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.371 * [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)))) 12.371 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 12.371 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 12.371 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 12.371 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 12.371 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 12.371 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 12.371 * [taylor]: Taking taylor expansion of 1/2 in k 12.371 * [backup-simplify]: Simplify 1/2 into 1/2 12.371 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.371 * [taylor]: Taking taylor expansion of k in k 12.371 * [backup-simplify]: Simplify 0 into 0 12.371 * [backup-simplify]: Simplify 1 into 1 12.371 * [backup-simplify]: Simplify (/ 1 1) into 1 12.371 * [taylor]: Taking taylor expansion of 1/2 in k 12.372 * [backup-simplify]: Simplify 1/2 into 1/2 12.372 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 12.372 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 12.372 * [taylor]: Taking taylor expansion of -2 in k 12.372 * [backup-simplify]: Simplify -2 into -2 12.372 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.372 * [taylor]: Taking taylor expansion of PI in k 12.372 * [backup-simplify]: Simplify PI into PI 12.372 * [taylor]: Taking taylor expansion of n in k 12.372 * [backup-simplify]: Simplify n into n 12.372 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.372 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 12.372 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 12.373 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 12.373 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 12.373 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 12.374 * [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))) 12.374 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 12.374 * [taylor]: Taking taylor expansion of (/ -1 k) in k 12.374 * [taylor]: Taking taylor expansion of -1 in k 12.374 * [backup-simplify]: Simplify -1 into -1 12.374 * [taylor]: Taking taylor expansion of k in k 12.374 * [backup-simplify]: Simplify 0 into 0 12.374 * [backup-simplify]: Simplify 1 into 1 12.374 * [backup-simplify]: Simplify (/ -1 1) into -1 12.375 * [backup-simplify]: Simplify (sqrt 0) into 0 12.376 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 12.376 * [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)))) 12.377 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 12.377 * [taylor]: Taking taylor expansion of +nan.0 in n 12.377 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.377 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 12.377 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.377 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.377 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.377 * [taylor]: Taking taylor expansion of -2 in n 12.377 * [backup-simplify]: Simplify -2 into -2 12.377 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.377 * [taylor]: Taking taylor expansion of PI in n 12.377 * [backup-simplify]: Simplify PI into PI 12.377 * [taylor]: Taking taylor expansion of n in n 12.377 * [backup-simplify]: Simplify 0 into 0 12.377 * [backup-simplify]: Simplify 1 into 1 12.378 * [backup-simplify]: Simplify (/ PI 1) into PI 12.378 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.379 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.379 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.379 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.379 * [taylor]: Taking taylor expansion of 1/2 in n 12.379 * [backup-simplify]: Simplify 1/2 into 1/2 12.379 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.379 * [taylor]: Taking taylor expansion of k in n 12.379 * [backup-simplify]: Simplify k into k 12.379 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.379 * [taylor]: Taking taylor expansion of 1/2 in n 12.379 * [backup-simplify]: Simplify 1/2 into 1/2 12.381 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.381 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.381 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.382 * [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))) 12.383 * [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)))) 12.385 * [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))))) 12.386 * [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))))) 12.387 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 12.390 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 12.391 * [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))))) 12.392 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 12.392 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 12.392 * [taylor]: Taking taylor expansion of +nan.0 in n 12.392 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.392 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 12.392 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.392 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.392 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.392 * [taylor]: Taking taylor expansion of -2 in n 12.392 * [backup-simplify]: Simplify -2 into -2 12.392 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.392 * [taylor]: Taking taylor expansion of PI in n 12.392 * [backup-simplify]: Simplify PI into PI 12.392 * [taylor]: Taking taylor expansion of n in n 12.392 * [backup-simplify]: Simplify 0 into 0 12.392 * [backup-simplify]: Simplify 1 into 1 12.393 * [backup-simplify]: Simplify (/ PI 1) into PI 12.393 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.394 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.394 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.395 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.395 * [taylor]: Taking taylor expansion of 1/2 in n 12.395 * [backup-simplify]: Simplify 1/2 into 1/2 12.395 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.395 * [taylor]: Taking taylor expansion of k in n 12.395 * [backup-simplify]: Simplify k into k 12.395 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.395 * [taylor]: Taking taylor expansion of 1/2 in n 12.395 * [backup-simplify]: Simplify 1/2 into 1/2 12.397 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.397 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.397 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.398 * [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))) 12.399 * [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)))) 12.400 * [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))))) 12.402 * [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)))))) 12.403 * [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)))))) 12.405 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.405 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.405 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 12.406 * [backup-simplify]: Simplify (+ 0 0) into 0 12.406 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.407 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 12.409 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 12.410 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 12.412 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 12.414 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 12.414 * [backup-simplify]: Simplify 0 into 0 12.415 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.419 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 12.421 * [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))))) 12.421 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 12.421 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 12.421 * [taylor]: Taking taylor expansion of +nan.0 in n 12.421 * [backup-simplify]: Simplify +nan.0 into +nan.0 12.421 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 12.421 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 12.421 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 12.421 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 12.421 * [taylor]: Taking taylor expansion of -2 in n 12.421 * [backup-simplify]: Simplify -2 into -2 12.421 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.421 * [taylor]: Taking taylor expansion of PI in n 12.421 * [backup-simplify]: Simplify PI into PI 12.421 * [taylor]: Taking taylor expansion of n in n 12.421 * [backup-simplify]: Simplify 0 into 0 12.421 * [backup-simplify]: Simplify 1 into 1 12.422 * [backup-simplify]: Simplify (/ PI 1) into PI 12.422 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 12.423 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 12.423 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 12.423 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 12.423 * [taylor]: Taking taylor expansion of 1/2 in n 12.423 * [backup-simplify]: Simplify 1/2 into 1/2 12.423 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.423 * [taylor]: Taking taylor expansion of k in n 12.423 * [backup-simplify]: Simplify k into k 12.423 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.423 * [taylor]: Taking taylor expansion of 1/2 in n 12.423 * [backup-simplify]: Simplify 1/2 into 1/2 12.425 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 12.425 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 12.425 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 12.426 * [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))) 12.427 * [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)))) 12.429 * [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))))) 12.430 * [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)))))) 12.431 * [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)))))) 12.436 * [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))))))))))) 12.436 * * * [progress]: simplifying candidates 12.436 * * * * [progress]: [ 1 / 1611 ] simplifiying candidate # 12.436 * * * * [progress]: [ 2 / 1611 ] simplifiying candidate # 12.436 * * * * [progress]: [ 3 / 1611 ] simplifiying candidate # 12.436 * * * * [progress]: [ 4 / 1611 ] simplifiying candidate # 12.436 * * * * [progress]: [ 5 / 1611 ] simplifiying candidate # 12.437 * * * * [progress]: [ 6 / 1611 ] simplifiying candidate # 12.437 * * * * [progress]: [ 7 / 1611 ] simplifiying candidate # 12.437 * * * * [progress]: [ 8 / 1611 ] simplifiying candidate # 12.437 * * * * [progress]: [ 9 / 1611 ] simplifiying candidate # 12.437 * * * * [progress]: [ 10 / 1611 ] simplifiying candidate # 12.437 * * * * [progress]: [ 11 / 1611 ] simplifiying candidate # 12.437 * * * * [progress]: [ 12 / 1611 ] simplifiying candidate # 12.437 * * * * [progress]: [ 13 / 1611 ] simplifiying candidate # 12.437 * * * * [progress]: [ 14 / 1611 ] simplifiying candidate # 12.437 * * * * [progress]: [ 15 / 1611 ] simplifiying candidate # 12.437 * * * * [progress]: [ 16 / 1611 ] simplifiying candidate # 12.437 * * * * [progress]: [ 17 / 1611 ] simplifiying candidate # 12.437 * * * * [progress]: [ 18 / 1611 ] simplifiying candidate # 12.437 * * * * [progress]: [ 19 / 1611 ] simplifiying candidate # 12.437 * * * * [progress]: [ 20 / 1611 ] simplifiying candidate #real (real->posit16 (* (* n 2) PI))) (- 1/2 (/ k 2))))))> 12.438 * * * * [progress]: [ 21 / 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2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI)) (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI)) (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI)) (* (* n 2) (* (cbrt PI) (cbrt PI))) (* (* n 2) (sqrt PI)) (* (* n 2) 1) (* 2 PI) (real->posit16 (* (* n 2) PI)) (expm1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (log1p (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (- (log (sqrt k)) (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))) (- (log (sqrt k)) (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))) (- (log (sqrt k)) (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (- (log (sqrt k)) (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (- (log (sqrt k)) (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (log (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (exp (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (cbrt (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (cbrt (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))) (cbrt (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (* (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (- (sqrt k)) (- (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))))) (/ (cbrt (sqrt k)) (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2))))))) (/ (cbrt (sqrt k)) (pow (* (* n 2) PI) (fma (- (sqrt (/ k 2))) (sqrt (/ k 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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)))))))))))) (- (+ (* 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))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (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))))))))))) 12.656 * * [simplify]: iteration 0: 1732 enodes 15.138 * * [simplify]: iteration 1: 4740 enodes 17.067 * * [simplify]: iteration complete: 5000 enodes 17.070 * * [simplify]: Extracting #0: cost 589 inf + 0 17.078 * * [simplify]: Extracting #1: cost 1720 inf + 2 17.094 * * [simplify]: Extracting #2: cost 1771 inf + 7270 17.113 * * [simplify]: Extracting #3: cost 1647 inf + 33395 17.160 * * [simplify]: Extracting #4: cost 1052 inf + 186706 17.244 * * [simplify]: Extracting #5: cost 692 inf + 370492 17.337 * * [simplify]: Extracting #6: cost 367 inf + 579831 17.465 * * [simplify]: Extracting #7: cost 140 inf + 746083 17.611 * * [simplify]: Extracting #8: cost 40 inf + 813250 17.803 * * [simplify]: Extracting #9: cost 8 inf + 836345 18.018 * * [simplify]: Extracting #10: cost 0 inf + 843681 18.196 * * [simplify]: Extracting #11: cost 0 inf + 843338 18.426 * * [simplify]: Extracting #12: cost 0 inf + 843293 18.692 * [simplify]: Simplified to: (expm1 (* n (* PI 2))) (log1p (* n (* PI 2))) (* n (* PI 2)) (* n (* PI 2)) (log (* n (* PI 2))) (log (* n (* PI 2))) (log (* n (* PI 2))) (* (exp (* PI n)) (exp (* PI n))) (* (* PI (* PI PI)) (* (* n (* n n)) 8)) (* (* (* 2 n) (* (* 2 n) (* 2 n))) (* PI (* PI PI))) (* (cbrt (* n (* PI 2))) (cbrt (* n (* PI 2)))) (cbrt (* n (* PI 2))) (* (* n (* PI 2)) (* (* n (* PI 2)) (* n (* PI 2)))) (sqrt (* n (* PI 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(- (- (* +nan.0 (/ (exp (- (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2))))) (* k k))) (- (* +nan.0 (/ (exp (- (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2))))) k)) (* +nan.0 (exp (- (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2))))))))) (- (fma (* 1/4 (log (* PI 2))) (* (* (log n) (* k k)) (exp (* (log (* n (* PI 2))) 1/2))) (fma 1/8 (* (exp (* (log (* n (* PI 2))) 1/2)) (* (* k k) (* (log n) (log n)))) (fma (* 1/8 (* (log (* PI 2)) (log (* PI 2)))) (* (exp (* (log (* n (* PI 2))) 1/2)) (* k k)) (exp (* (log (* n (* PI 2))) 1/2))))) (* 1/2 (fma (* k (log n)) (exp (* (log (* n (* PI 2))) 1/2)) (* (log (* PI 2)) (* (exp (* (log (* n (* PI 2))) 1/2)) k))))) (exp (* (- 1/2 (* k 1/2)) (- (log (* PI 2)) (- (log n))))) (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (- (fma (* (* (sqrt 2) n) (* k PI)) +nan.0 (- (fma (* +nan.0 (sqrt 2)) (* PI n) (- (- (* (* (log (* PI 2)) (* (* (sqrt 2) n) (* k PI))) +nan.0) (fma (* +nan.0 (sqrt 2)) (* (* PI n) (* k (log n))) (- (* (* +nan.0 (sqrt 2)) (* (* PI PI) (* n n))))))))))) (- (- (* +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)) (* (/ (exp (* (- 1/2 (* k 1/2)) (- (log (* PI 2)) (- (log n))))) (* k k)) +nan.0)))) (- (- (* (/ (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) k) +nan.0) (- (* +nan.0 (/ (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (* k k))) (* +nan.0 (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (- 1/2 (* k 1/2)))))))) 19.192 * * * [progress]: adding candidates to table 30.267 * * [progress]: iteration 3 / 4 30.267 * * * [progress]: picking best candidate 30.318 * * * * [pick]: Picked # 30.318 * * * [progress]: localizing error 30.349 * * * [progress]: generating rewritten candidates 30.349 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1) 30.354 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1) 30.369 * * * * [progress]: [ 3 / 4 ] rewriting at (2) 30.396 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 2) 30.714 * * * [progress]: generating series expansions 30.714 * * * * [progress]: [ 1 / 4 ] generating series at (2 1) 30.715 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k)) 30.715 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0 30.715 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 30.715 * [taylor]: Taking taylor expansion of (/ 1 k) in k 30.715 * [taylor]: Taking taylor expansion of k in k 30.715 * [backup-simplify]: Simplify 0 into 0 30.715 * [backup-simplify]: Simplify 1 into 1 30.716 * [backup-simplify]: Simplify (/ 1 1) into 1 30.716 * [backup-simplify]: Simplify (sqrt 0) into 0 30.718 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 30.718 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 30.719 * [taylor]: Taking taylor expansion of (/ 1 k) in k 30.719 * [taylor]: Taking taylor expansion of k in k 30.719 * [backup-simplify]: Simplify 0 into 0 30.719 * [backup-simplify]: Simplify 1 into 1 30.719 * [backup-simplify]: Simplify (/ 1 1) into 1 30.719 * [backup-simplify]: Simplify (sqrt 0) into 0 30.721 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 30.721 * [backup-simplify]: Simplify 0 into 0 30.721 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.722 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 30.725 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 30.725 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.726 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.729 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 30.729 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.729 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) 30.730 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k) 30.730 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0 30.730 * [taylor]: Taking taylor expansion of (sqrt k) in k 30.730 * [taylor]: Taking taylor expansion of k in k 30.730 * [backup-simplify]: Simplify 0 into 0 30.730 * [backup-simplify]: Simplify 1 into 1 30.730 * [backup-simplify]: Simplify (sqrt 0) into 0 30.731 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 30.731 * [taylor]: Taking taylor expansion of (sqrt k) in k 30.731 * [taylor]: Taking taylor expansion of k in k 30.731 * [backup-simplify]: Simplify 0 into 0 30.731 * [backup-simplify]: Simplify 1 into 1 30.731 * [backup-simplify]: Simplify (sqrt 0) into 0 30.732 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 30.732 * [backup-simplify]: Simplify 0 into 0 30.732 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.734 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 30.734 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.736 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 30.736 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.737 * [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)))))))) 30.737 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k))) 30.737 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0 30.737 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 30.737 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 30.737 * [taylor]: Taking taylor expansion of (/ -1 k) in k 30.737 * [taylor]: Taking taylor expansion of -1 in k 30.737 * [backup-simplify]: Simplify -1 into -1 30.737 * [taylor]: Taking taylor expansion of k in k 30.737 * [backup-simplify]: Simplify 0 into 0 30.737 * [backup-simplify]: Simplify 1 into 1 30.737 * [backup-simplify]: Simplify (/ -1 1) into -1 30.737 * [backup-simplify]: Simplify (sqrt 0) into 0 30.738 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 30.739 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 30.739 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k 30.739 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 30.739 * [taylor]: Taking taylor expansion of (/ -1 k) in k 30.739 * [taylor]: Taking taylor expansion of -1 in k 30.739 * [backup-simplify]: Simplify -1 into -1 30.739 * [taylor]: Taking taylor expansion of k in k 30.739 * [backup-simplify]: Simplify 0 into 0 30.739 * [backup-simplify]: Simplify 1 into 1 30.739 * [backup-simplify]: Simplify (/ -1 1) into -1 30.739 * [backup-simplify]: Simplify (sqrt 0) into 0 30.740 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 30.740 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0 30.740 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.741 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 30.743 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 30.744 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 30.744 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 30.745 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.748 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 30.752 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 30.752 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 30.753 * [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))))) 30.753 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1) 30.753 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI)) 30.753 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 30.753 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 30.753 * [taylor]: Taking taylor expansion of 2 in n 30.753 * [backup-simplify]: Simplify 2 into 2 30.753 * [taylor]: Taking taylor expansion of (* n PI) in n 30.753 * [taylor]: Taking taylor expansion of n in n 30.753 * [backup-simplify]: Simplify 0 into 0 30.754 * [backup-simplify]: Simplify 1 into 1 30.754 * [taylor]: Taking taylor expansion of PI in n 30.754 * [backup-simplify]: Simplify PI into PI 30.754 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 30.754 * [taylor]: Taking taylor expansion of 2 in n 30.754 * [backup-simplify]: Simplify 2 into 2 30.754 * [taylor]: Taking taylor expansion of (* n PI) in n 30.754 * [taylor]: Taking taylor expansion of n in n 30.754 * [backup-simplify]: Simplify 0 into 0 30.754 * [backup-simplify]: Simplify 1 into 1 30.754 * [taylor]: Taking taylor expansion of PI in n 30.754 * [backup-simplify]: Simplify PI into PI 30.754 * [backup-simplify]: Simplify (* 0 PI) into 0 30.755 * [backup-simplify]: Simplify (* 2 0) into 0 30.755 * [backup-simplify]: Simplify 0 into 0 30.757 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 30.758 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 30.759 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 30.760 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 30.761 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 30.761 * [backup-simplify]: Simplify 0 into 0 30.762 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 30.764 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 30.764 * [backup-simplify]: Simplify 0 into 0 30.765 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 30.767 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 30.767 * [backup-simplify]: Simplify 0 into 0 30.768 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 30.770 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 30.770 * [backup-simplify]: Simplify 0 into 0 30.772 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 30.774 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 30.774 * [backup-simplify]: Simplify 0 into 0 30.776 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 30.778 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 30.778 * [backup-simplify]: Simplify 0 into 0 30.779 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 30.779 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n)) 30.779 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 30.779 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 30.779 * [taylor]: Taking taylor expansion of 2 in n 30.779 * [backup-simplify]: Simplify 2 into 2 30.779 * [taylor]: Taking taylor expansion of (/ PI n) in n 30.779 * [taylor]: Taking taylor expansion of PI in n 30.779 * [backup-simplify]: Simplify PI into PI 30.779 * [taylor]: Taking taylor expansion of n in n 30.779 * [backup-simplify]: Simplify 0 into 0 30.779 * [backup-simplify]: Simplify 1 into 1 30.780 * [backup-simplify]: Simplify (/ PI 1) into PI 30.780 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 30.780 * [taylor]: Taking taylor expansion of 2 in n 30.780 * [backup-simplify]: Simplify 2 into 2 30.780 * [taylor]: Taking taylor expansion of (/ PI n) in n 30.780 * [taylor]: Taking taylor expansion of PI in n 30.780 * [backup-simplify]: Simplify PI into PI 30.780 * [taylor]: Taking taylor expansion of n in n 30.780 * [backup-simplify]: Simplify 0 into 0 30.780 * [backup-simplify]: Simplify 1 into 1 30.781 * [backup-simplify]: Simplify (/ PI 1) into PI 30.781 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 30.782 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 30.783 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 30.784 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 30.784 * [backup-simplify]: Simplify 0 into 0 30.785 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.786 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 30.786 * [backup-simplify]: Simplify 0 into 0 30.787 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.789 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 30.789 * [backup-simplify]: Simplify 0 into 0 30.790 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.791 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 30.791 * [backup-simplify]: Simplify 0 into 0 30.793 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.794 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 30.794 * [backup-simplify]: Simplify 0 into 0 30.796 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.797 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 30.797 * [backup-simplify]: Simplify 0 into 0 30.798 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 30.798 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n)) 30.798 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 30.798 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 30.798 * [taylor]: Taking taylor expansion of -2 in n 30.798 * [backup-simplify]: Simplify -2 into -2 30.798 * [taylor]: Taking taylor expansion of (/ PI n) in n 30.798 * [taylor]: Taking taylor expansion of PI in n 30.798 * [backup-simplify]: Simplify PI into PI 30.798 * [taylor]: Taking taylor expansion of n in n 30.798 * [backup-simplify]: Simplify 0 into 0 30.799 * [backup-simplify]: Simplify 1 into 1 30.799 * [backup-simplify]: Simplify (/ PI 1) into PI 30.799 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 30.799 * [taylor]: Taking taylor expansion of -2 in n 30.799 * [backup-simplify]: Simplify -2 into -2 30.799 * [taylor]: Taking taylor expansion of (/ PI n) in n 30.799 * [taylor]: Taking taylor expansion of PI in n 30.799 * [backup-simplify]: Simplify PI into PI 30.799 * [taylor]: Taking taylor expansion of n in n 30.799 * [backup-simplify]: Simplify 0 into 0 30.799 * [backup-simplify]: Simplify 1 into 1 30.800 * [backup-simplify]: Simplify (/ PI 1) into PI 30.800 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 30.801 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 30.802 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 30.803 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 30.803 * [backup-simplify]: Simplify 0 into 0 30.804 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.805 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 30.805 * [backup-simplify]: Simplify 0 into 0 30.806 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.808 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 30.808 * [backup-simplify]: Simplify 0 into 0 30.809 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.811 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 30.811 * [backup-simplify]: Simplify 0 into 0 30.822 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.824 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 30.824 * [backup-simplify]: Simplify 0 into 0 30.824 * [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 30.825 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 30.826 * [backup-simplify]: Simplify 0 into 0 30.826 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 30.826 * * * * [progress]: [ 3 / 4 ] generating series at (2) 30.826 * [backup-simplify]: Simplify (/ (/ 1 (sqrt k)) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) into (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) 30.826 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in (k n) around 0 30.826 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 30.826 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 30.826 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 30.826 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 30.826 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 30.826 * [taylor]: Taking taylor expansion of 1/2 in n 30.826 * [backup-simplify]: Simplify 1/2 into 1/2 30.826 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 30.826 * [taylor]: Taking taylor expansion of 1/2 in n 30.826 * [backup-simplify]: Simplify 1/2 into 1/2 30.826 * [taylor]: Taking taylor expansion of k in n 30.826 * [backup-simplify]: Simplify k into k 30.826 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 30.826 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 30.826 * [taylor]: Taking taylor expansion of 2 in n 30.826 * [backup-simplify]: Simplify 2 into 2 30.826 * [taylor]: Taking taylor expansion of (* n PI) in n 30.827 * [taylor]: Taking taylor expansion of n in n 30.827 * [backup-simplify]: Simplify 0 into 0 30.827 * [backup-simplify]: Simplify 1 into 1 30.827 * [taylor]: Taking taylor expansion of PI in n 30.827 * [backup-simplify]: Simplify PI into PI 30.827 * [backup-simplify]: Simplify (* 0 PI) into 0 30.827 * [backup-simplify]: Simplify (* 2 0) into 0 30.828 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 30.829 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 30.830 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 30.830 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 30.830 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 30.830 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 30.831 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 30.832 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 30.832 * [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))))) 30.832 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 30.832 * [taylor]: Taking taylor expansion of (/ 1 k) in n 30.832 * [taylor]: Taking taylor expansion of k in n 30.832 * [backup-simplify]: Simplify k into k 30.832 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 30.833 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 30.833 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 30.833 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 30.833 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 30.833 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 30.833 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 30.833 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 30.833 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 30.833 * [taylor]: Taking taylor expansion of 1/2 in k 30.833 * [backup-simplify]: Simplify 1/2 into 1/2 30.833 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 30.833 * [taylor]: Taking taylor expansion of 1/2 in k 30.833 * [backup-simplify]: Simplify 1/2 into 1/2 30.833 * [taylor]: Taking taylor expansion of k in k 30.833 * [backup-simplify]: Simplify 0 into 0 30.833 * [backup-simplify]: Simplify 1 into 1 30.833 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 30.833 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 30.833 * [taylor]: Taking taylor expansion of 2 in k 30.833 * [backup-simplify]: Simplify 2 into 2 30.833 * [taylor]: Taking taylor expansion of (* n PI) in k 30.833 * [taylor]: Taking taylor expansion of n in k 30.833 * [backup-simplify]: Simplify n into n 30.833 * [taylor]: Taking taylor expansion of PI in k 30.833 * [backup-simplify]: Simplify PI into PI 30.833 * [backup-simplify]: Simplify (* n PI) into (* n PI) 30.833 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 30.833 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 30.834 * [backup-simplify]: Simplify (* 1/2 0) into 0 30.834 * [backup-simplify]: Simplify (- 0) into 0 30.834 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 30.834 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 30.834 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 30.834 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 30.834 * [taylor]: Taking taylor expansion of (/ 1 k) in k 30.834 * [taylor]: Taking taylor expansion of k in k 30.834 * [backup-simplify]: Simplify 0 into 0 30.834 * [backup-simplify]: Simplify 1 into 1 30.835 * [backup-simplify]: Simplify (/ 1 1) into 1 30.835 * [backup-simplify]: Simplify (sqrt 0) into 0 30.836 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 30.836 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 30.836 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 30.836 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 30.836 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 30.836 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 30.836 * [taylor]: Taking taylor expansion of 1/2 in k 30.836 * [backup-simplify]: Simplify 1/2 into 1/2 30.836 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 30.836 * [taylor]: Taking taylor expansion of 1/2 in k 30.836 * [backup-simplify]: Simplify 1/2 into 1/2 30.836 * [taylor]: Taking taylor expansion of k in k 30.836 * [backup-simplify]: Simplify 0 into 0 30.836 * [backup-simplify]: Simplify 1 into 1 30.836 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 30.836 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 30.836 * [taylor]: Taking taylor expansion of 2 in k 30.836 * [backup-simplify]: Simplify 2 into 2 30.836 * [taylor]: Taking taylor expansion of (* n PI) in k 30.836 * [taylor]: Taking taylor expansion of n in k 30.836 * [backup-simplify]: Simplify n into n 30.836 * [taylor]: Taking taylor expansion of PI in k 30.836 * [backup-simplify]: Simplify PI into PI 30.836 * [backup-simplify]: Simplify (* n PI) into (* n PI) 30.836 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 30.836 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 30.836 * [backup-simplify]: Simplify (* 1/2 0) into 0 30.837 * [backup-simplify]: Simplify (- 0) into 0 30.837 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 30.837 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 30.837 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 30.837 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 30.837 * [taylor]: Taking taylor expansion of (/ 1 k) in k 30.837 * [taylor]: Taking taylor expansion of k in k 30.837 * [backup-simplify]: Simplify 0 into 0 30.837 * [backup-simplify]: Simplify 1 into 1 30.837 * [backup-simplify]: Simplify (/ 1 1) into 1 30.838 * [backup-simplify]: Simplify (sqrt 0) into 0 30.838 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 30.839 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0 30.839 * [taylor]: Taking taylor expansion of 0 in n 30.839 * [backup-simplify]: Simplify 0 into 0 30.839 * [backup-simplify]: Simplify 0 into 0 30.839 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 30.840 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 30.841 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 30.841 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 30.842 * [backup-simplify]: Simplify (- 1/2) into -1/2 30.842 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 30.843 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 30.843 * [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))))) 30.844 * [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))))) 30.844 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 30.844 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 30.844 * [taylor]: Taking taylor expansion of +nan.0 in n 30.844 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.844 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 30.844 * [taylor]: Taking taylor expansion of (sqrt 2) in n 30.844 * [taylor]: Taking taylor expansion of 2 in n 30.844 * [backup-simplify]: Simplify 2 into 2 30.844 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 30.845 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 30.845 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 30.845 * [taylor]: Taking taylor expansion of (* n PI) in n 30.845 * [taylor]: Taking taylor expansion of n in n 30.845 * [backup-simplify]: Simplify 0 into 0 30.845 * [backup-simplify]: Simplify 1 into 1 30.845 * [taylor]: Taking taylor expansion of PI in n 30.845 * [backup-simplify]: Simplify PI into PI 30.846 * [backup-simplify]: Simplify (* 0 PI) into 0 30.847 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 30.848 * [backup-simplify]: Simplify (sqrt 0) into 0 30.849 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 30.849 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 30.850 * [backup-simplify]: Simplify (* +nan.0 0) into 0 30.850 * [backup-simplify]: Simplify (- 0) into 0 30.850 * [backup-simplify]: Simplify 0 into 0 30.850 * [backup-simplify]: Simplify 0 into 0 30.851 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 30.854 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 30.855 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 30.855 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 30.857 * [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 30.858 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 30.858 * [backup-simplify]: Simplify (- 0) into 0 30.859 * [backup-simplify]: Simplify (+ 0 0) into 0 30.860 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 30.861 * [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))) 30.861 * [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))))))) 30.861 * [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 30.861 * [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 30.861 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 30.861 * [taylor]: Taking taylor expansion of +nan.0 in n 30.861 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.861 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 30.861 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 30.861 * [taylor]: Taking taylor expansion of (sqrt 2) in n 30.862 * [taylor]: Taking taylor expansion of 2 in n 30.862 * [backup-simplify]: Simplify 2 into 2 30.862 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 30.863 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 30.863 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 30.863 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 30.863 * [taylor]: Taking taylor expansion of 2 in n 30.863 * [backup-simplify]: Simplify 2 into 2 30.863 * [taylor]: Taking taylor expansion of (* n PI) in n 30.863 * [taylor]: Taking taylor expansion of n in n 30.863 * [backup-simplify]: Simplify 0 into 0 30.863 * [backup-simplify]: Simplify 1 into 1 30.863 * [taylor]: Taking taylor expansion of PI in n 30.863 * [backup-simplify]: Simplify PI into PI 30.863 * [backup-simplify]: Simplify (* 0 PI) into 0 30.864 * [backup-simplify]: Simplify (* 2 0) into 0 30.865 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 30.867 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 30.868 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 30.868 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 30.868 * [taylor]: Taking taylor expansion of (* n PI) in n 30.868 * [taylor]: Taking taylor expansion of n in n 30.868 * [backup-simplify]: Simplify 0 into 0 30.868 * [backup-simplify]: Simplify 1 into 1 30.868 * [taylor]: Taking taylor expansion of PI in n 30.868 * [backup-simplify]: Simplify PI into PI 30.868 * [backup-simplify]: Simplify (* 0 PI) into 0 30.870 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 30.870 * [backup-simplify]: Simplify (sqrt 0) into 0 30.871 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 30.871 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 30.872 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 30.872 * [taylor]: Taking taylor expansion of +nan.0 in n 30.872 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.872 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 30.872 * [taylor]: Taking taylor expansion of (sqrt 2) in n 30.872 * [taylor]: Taking taylor expansion of 2 in n 30.872 * [backup-simplify]: Simplify 2 into 2 30.872 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 30.873 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 30.873 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 30.873 * [taylor]: Taking taylor expansion of (* n PI) in n 30.873 * [taylor]: Taking taylor expansion of n in n 30.873 * [backup-simplify]: Simplify 0 into 0 30.873 * [backup-simplify]: Simplify 1 into 1 30.873 * [taylor]: Taking taylor expansion of PI in n 30.873 * [backup-simplify]: Simplify PI into PI 30.873 * [backup-simplify]: Simplify (* 0 PI) into 0 30.875 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 30.875 * [backup-simplify]: Simplify (sqrt 0) into 0 30.877 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 30.878 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 30.880 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 30.881 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 30.882 * [backup-simplify]: Simplify (* +nan.0 0) into 0 30.882 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 30.882 * [backup-simplify]: Simplify (* +nan.0 0) into 0 30.883 * [backup-simplify]: Simplify (- 0) into 0 30.883 * [backup-simplify]: Simplify (+ 0 0) into 0 30.884 * [backup-simplify]: Simplify (- 0) into 0 30.884 * [backup-simplify]: Simplify 0 into 0 30.887 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 30.893 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 30.896 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 30.899 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 30.899 * [backup-simplify]: Simplify 0 into 0 30.900 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 30.904 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 30.905 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 30.906 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 30.908 * [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 30.910 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 30.910 * [backup-simplify]: Simplify (- 0) into 0 30.910 * [backup-simplify]: Simplify (+ 0 0) into 0 30.912 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 30.913 * [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))) 30.914 * [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))))))))) 30.914 * [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 30.914 * [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 30.914 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 30.914 * [taylor]: Taking taylor expansion of +nan.0 in n 30.914 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.914 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 30.915 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 30.915 * [taylor]: Taking taylor expansion of (sqrt 2) in n 30.915 * [taylor]: Taking taylor expansion of 2 in n 30.915 * [backup-simplify]: Simplify 2 into 2 30.915 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 30.916 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 30.916 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 30.916 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 30.916 * [taylor]: Taking taylor expansion of 2 in n 30.916 * [backup-simplify]: Simplify 2 into 2 30.916 * [taylor]: Taking taylor expansion of (* n PI) in n 30.916 * [taylor]: Taking taylor expansion of n in n 30.916 * [backup-simplify]: Simplify 0 into 0 30.916 * [backup-simplify]: Simplify 1 into 1 30.916 * [taylor]: Taking taylor expansion of PI in n 30.916 * [backup-simplify]: Simplify PI into PI 30.916 * [backup-simplify]: Simplify (* 0 PI) into 0 30.917 * [backup-simplify]: Simplify (* 2 0) into 0 30.918 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 30.920 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 30.921 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 30.921 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 30.921 * [taylor]: Taking taylor expansion of (* n PI) in n 30.921 * [taylor]: Taking taylor expansion of n in n 30.921 * [backup-simplify]: Simplify 0 into 0 30.921 * [backup-simplify]: Simplify 1 into 1 30.921 * [taylor]: Taking taylor expansion of PI in n 30.921 * [backup-simplify]: Simplify PI into PI 30.921 * [backup-simplify]: Simplify (* 0 PI) into 0 30.923 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 30.923 * [backup-simplify]: Simplify (sqrt 0) into 0 30.925 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 30.925 * [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 30.925 * [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 30.925 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 30.925 * [taylor]: Taking taylor expansion of +nan.0 in n 30.925 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.925 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 30.925 * [taylor]: Taking taylor expansion of (sqrt 2) in n 30.925 * [taylor]: Taking taylor expansion of 2 in n 30.925 * [backup-simplify]: Simplify 2 into 2 30.925 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 30.926 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 30.926 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 30.926 * [taylor]: Taking taylor expansion of (* n PI) in n 30.926 * [taylor]: Taking taylor expansion of n in n 30.926 * [backup-simplify]: Simplify 0 into 0 30.926 * [backup-simplify]: Simplify 1 into 1 30.926 * [taylor]: Taking taylor expansion of PI in n 30.926 * [backup-simplify]: Simplify PI into PI 30.926 * [backup-simplify]: Simplify (* 0 PI) into 0 30.928 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 30.928 * [backup-simplify]: Simplify (sqrt 0) into 0 30.930 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 30.930 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n 30.930 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 30.930 * [taylor]: Taking taylor expansion of +nan.0 in n 30.930 * [backup-simplify]: Simplify +nan.0 into +nan.0 30.930 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 30.930 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 30.930 * [taylor]: Taking taylor expansion of (sqrt 2) in n 30.930 * [taylor]: Taking taylor expansion of 2 in n 30.930 * [backup-simplify]: Simplify 2 into 2 30.930 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 30.931 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 30.931 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 30.931 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 30.931 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 30.931 * [taylor]: Taking taylor expansion of 2 in n 30.931 * [backup-simplify]: Simplify 2 into 2 30.931 * [taylor]: Taking taylor expansion of (* n PI) in n 30.931 * [taylor]: Taking taylor expansion of n in n 30.931 * [backup-simplify]: Simplify 0 into 0 30.931 * [backup-simplify]: Simplify 1 into 1 30.931 * [taylor]: Taking taylor expansion of PI in n 30.931 * [backup-simplify]: Simplify PI into PI 30.932 * [backup-simplify]: Simplify (* 0 PI) into 0 30.932 * [backup-simplify]: Simplify (* 2 0) into 0 30.934 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 30.934 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 30.935 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 30.936 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 30.936 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 30.936 * [taylor]: Taking taylor expansion of (* n PI) in n 30.936 * [taylor]: Taking taylor expansion of n in n 30.936 * [backup-simplify]: Simplify 0 into 0 30.936 * [backup-simplify]: Simplify 1 into 1 30.936 * [taylor]: Taking taylor expansion of PI in n 30.936 * [backup-simplify]: Simplify PI into PI 30.936 * [backup-simplify]: Simplify (* 0 PI) into 0 30.937 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 30.938 * [backup-simplify]: Simplify (sqrt 0) into 0 30.939 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 30.939 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 30.940 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 30.941 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 30.941 * [backup-simplify]: Simplify (* +nan.0 0) into 0 30.942 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 30.942 * [backup-simplify]: Simplify (* +nan.0 0) into 0 30.943 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 30.949 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 30.951 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 30.952 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 30.954 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 30.954 * [backup-simplify]: Simplify (* +nan.0 0) into 0 30.955 * [backup-simplify]: Simplify (- 0) into 0 30.955 * [backup-simplify]: Simplify (+ 0 0) into 0 30.955 * [backup-simplify]: Simplify (- 0) into 0 30.956 * [backup-simplify]: Simplify (+ 0 0) into 0 30.956 * [backup-simplify]: Simplify (- 0) into 0 30.956 * [backup-simplify]: Simplify 0 into 0 30.957 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 30.958 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 30.960 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 30.961 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 30.963 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 30.965 * [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)))))))) 30.972 * [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)))))))) 30.975 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 30.980 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 30.982 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 30.990 * [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)))))))))) 30.998 * [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))))))) 31.004 * [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))))))) 31.005 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 31.008 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 31.009 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 31.012 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 31.017 * [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)))) 31.020 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 31.022 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 31.031 * [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))))))))))))) 31.031 * [backup-simplify]: Simplify (/ (/ 1 (sqrt (/ 1 k))) (/ 1 (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))))) into (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) 31.031 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (k n) around 0 31.031 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 31.031 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 31.031 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 31.031 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 31.031 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 31.031 * [taylor]: Taking taylor expansion of 1/2 in n 31.031 * [backup-simplify]: Simplify 1/2 into 1/2 31.031 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.031 * [taylor]: Taking taylor expansion of 1/2 in n 31.031 * [backup-simplify]: Simplify 1/2 into 1/2 31.031 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.031 * [taylor]: Taking taylor expansion of k in n 31.031 * [backup-simplify]: Simplify k into k 31.031 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.031 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 31.031 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 31.031 * [taylor]: Taking taylor expansion of 2 in n 31.031 * [backup-simplify]: Simplify 2 into 2 31.031 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.031 * [taylor]: Taking taylor expansion of PI in n 31.032 * [backup-simplify]: Simplify PI into PI 31.032 * [taylor]: Taking taylor expansion of n in n 31.032 * [backup-simplify]: Simplify 0 into 0 31.032 * [backup-simplify]: Simplify 1 into 1 31.032 * [backup-simplify]: Simplify (/ PI 1) into PI 31.032 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 31.033 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.033 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.033 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 31.033 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 31.035 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.036 * [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))) 31.037 * [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)))) 31.038 * [taylor]: Taking taylor expansion of (sqrt k) in n 31.038 * [taylor]: Taking taylor expansion of k in n 31.038 * [backup-simplify]: Simplify k into k 31.038 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 31.038 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 31.038 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 31.038 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 31.038 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 31.038 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 31.038 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 31.038 * [taylor]: Taking taylor expansion of 1/2 in k 31.038 * [backup-simplify]: Simplify 1/2 into 1/2 31.038 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 31.038 * [taylor]: Taking taylor expansion of 1/2 in k 31.038 * [backup-simplify]: Simplify 1/2 into 1/2 31.038 * [taylor]: Taking taylor expansion of (/ 1 k) in k 31.038 * [taylor]: Taking taylor expansion of k in k 31.038 * [backup-simplify]: Simplify 0 into 0 31.038 * [backup-simplify]: Simplify 1 into 1 31.039 * [backup-simplify]: Simplify (/ 1 1) into 1 31.039 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 31.039 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 31.039 * [taylor]: Taking taylor expansion of 2 in k 31.039 * [backup-simplify]: Simplify 2 into 2 31.039 * [taylor]: Taking taylor expansion of (/ PI n) in k 31.039 * [taylor]: Taking taylor expansion of PI in k 31.039 * [backup-simplify]: Simplify PI into PI 31.039 * [taylor]: Taking taylor expansion of n in k 31.039 * [backup-simplify]: Simplify n into n 31.039 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 31.039 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 31.039 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 31.039 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 31.040 * [backup-simplify]: Simplify (- 1/2) into -1/2 31.040 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 31.040 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 31.041 * [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)))) 31.041 * [taylor]: Taking taylor expansion of (sqrt k) in k 31.041 * [taylor]: Taking taylor expansion of k in k 31.041 * [backup-simplify]: Simplify 0 into 0 31.041 * [backup-simplify]: Simplify 1 into 1 31.041 * [backup-simplify]: Simplify (sqrt 0) into 0 31.042 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 31.043 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 31.043 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 31.043 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 31.043 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 31.043 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 31.043 * [taylor]: Taking taylor expansion of 1/2 in k 31.043 * [backup-simplify]: Simplify 1/2 into 1/2 31.043 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 31.043 * [taylor]: Taking taylor expansion of 1/2 in k 31.043 * [backup-simplify]: Simplify 1/2 into 1/2 31.043 * [taylor]: Taking taylor expansion of (/ 1 k) in k 31.043 * [taylor]: Taking taylor expansion of k in k 31.043 * [backup-simplify]: Simplify 0 into 0 31.043 * [backup-simplify]: Simplify 1 into 1 31.043 * [backup-simplify]: Simplify (/ 1 1) into 1 31.043 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 31.043 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 31.043 * [taylor]: Taking taylor expansion of 2 in k 31.043 * [backup-simplify]: Simplify 2 into 2 31.043 * [taylor]: Taking taylor expansion of (/ PI n) in k 31.043 * [taylor]: Taking taylor expansion of PI in k 31.044 * [backup-simplify]: Simplify PI into PI 31.044 * [taylor]: Taking taylor expansion of n in k 31.044 * [backup-simplify]: Simplify n into n 31.044 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 31.044 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 31.044 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 31.044 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 31.045 * [backup-simplify]: Simplify (- 1/2) into -1/2 31.046 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 31.046 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 31.046 * [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)))) 31.046 * [taylor]: Taking taylor expansion of (sqrt k) in k 31.046 * [taylor]: Taking taylor expansion of k in k 31.046 * [backup-simplify]: Simplify 0 into 0 31.046 * [backup-simplify]: Simplify 1 into 1 31.047 * [backup-simplify]: Simplify (sqrt 0) into 0 31.048 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 31.048 * [backup-simplify]: Simplify (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 0) into 0 31.049 * [taylor]: Taking taylor expansion of 0 in n 31.049 * [backup-simplify]: Simplify 0 into 0 31.049 * [backup-simplify]: Simplify 0 into 0 31.049 * [backup-simplify]: Simplify (+ (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 31.049 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 31.049 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 31.049 * [taylor]: Taking taylor expansion of +nan.0 in n 31.049 * [backup-simplify]: Simplify +nan.0 into +nan.0 31.049 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 31.050 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 31.050 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 31.050 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 31.050 * [taylor]: Taking taylor expansion of 1/2 in n 31.050 * [backup-simplify]: Simplify 1/2 into 1/2 31.050 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.050 * [taylor]: Taking taylor expansion of 1/2 in n 31.050 * [backup-simplify]: Simplify 1/2 into 1/2 31.050 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.050 * [taylor]: Taking taylor expansion of k in n 31.050 * [backup-simplify]: Simplify k into k 31.050 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.050 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 31.050 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 31.050 * [taylor]: Taking taylor expansion of 2 in n 31.050 * [backup-simplify]: Simplify 2 into 2 31.050 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.050 * [taylor]: Taking taylor expansion of PI in n 31.050 * [backup-simplify]: Simplify PI into PI 31.050 * [taylor]: Taking taylor expansion of n in n 31.050 * [backup-simplify]: Simplify 0 into 0 31.050 * [backup-simplify]: Simplify 1 into 1 31.051 * [backup-simplify]: Simplify (/ PI 1) into PI 31.051 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 31.052 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.052 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.052 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 31.053 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 31.055 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.056 * [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))) 31.057 * [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)))) 31.058 * [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))))) 31.060 * [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)))))) 31.061 * [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)))))) 31.061 * [backup-simplify]: Simplify 0 into 0 31.068 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 31.068 * [backup-simplify]: Simplify (+ (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 31.068 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 31.068 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 31.068 * [taylor]: Taking taylor expansion of +nan.0 in n 31.068 * [backup-simplify]: Simplify +nan.0 into +nan.0 31.068 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 31.068 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 31.068 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 31.068 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 31.068 * [taylor]: Taking taylor expansion of 1/2 in n 31.069 * [backup-simplify]: Simplify 1/2 into 1/2 31.069 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.069 * [taylor]: Taking taylor expansion of 1/2 in n 31.069 * [backup-simplify]: Simplify 1/2 into 1/2 31.069 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.069 * [taylor]: Taking taylor expansion of k in n 31.069 * [backup-simplify]: Simplify k into k 31.069 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.069 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 31.069 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 31.069 * [taylor]: Taking taylor expansion of 2 in n 31.069 * [backup-simplify]: Simplify 2 into 2 31.069 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.069 * [taylor]: Taking taylor expansion of PI in n 31.069 * [backup-simplify]: Simplify PI into PI 31.069 * [taylor]: Taking taylor expansion of n in n 31.069 * [backup-simplify]: Simplify 0 into 0 31.069 * [backup-simplify]: Simplify 1 into 1 31.069 * [backup-simplify]: Simplify (/ PI 1) into PI 31.069 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 31.070 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.070 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.070 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 31.070 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 31.071 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.072 * [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))) 31.073 * [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)))) 31.073 * [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))))) 31.074 * [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)))))) 31.075 * [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)))))) 31.076 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 31.076 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 31.077 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 31.077 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 31.077 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 31.078 * [backup-simplify]: Simplify (- 0) into 0 31.078 * [backup-simplify]: Simplify (+ 0 0) into 0 31.079 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.080 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 31.081 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 31.082 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 31.082 * [backup-simplify]: Simplify (- 0) into 0 31.082 * [backup-simplify]: Simplify 0 into 0 31.082 * [backup-simplify]: Simplify 0 into 0 31.085 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 31.085 * [backup-simplify]: Simplify (+ (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 31.085 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 31.085 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 31.085 * [taylor]: Taking taylor expansion of +nan.0 in n 31.085 * [backup-simplify]: Simplify +nan.0 into +nan.0 31.085 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 31.085 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 31.086 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 31.086 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 31.086 * [taylor]: Taking taylor expansion of 1/2 in n 31.086 * [backup-simplify]: Simplify 1/2 into 1/2 31.086 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.086 * [taylor]: Taking taylor expansion of 1/2 in n 31.086 * [backup-simplify]: Simplify 1/2 into 1/2 31.086 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.086 * [taylor]: Taking taylor expansion of k in n 31.086 * [backup-simplify]: Simplify k into k 31.086 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.086 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 31.086 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 31.086 * [taylor]: Taking taylor expansion of 2 in n 31.086 * [backup-simplify]: Simplify 2 into 2 31.086 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.086 * [taylor]: Taking taylor expansion of PI in n 31.086 * [backup-simplify]: Simplify PI into PI 31.086 * [taylor]: Taking taylor expansion of n in n 31.086 * [backup-simplify]: Simplify 0 into 0 31.086 * [backup-simplify]: Simplify 1 into 1 31.086 * [backup-simplify]: Simplify (/ PI 1) into PI 31.086 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 31.087 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.087 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.087 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 31.087 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 31.088 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.089 * [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))) 31.090 * [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)))) 31.091 * [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))))) 31.093 * [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)))))) 31.094 * [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)))))) 31.098 * [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)))))))) 31.098 * [backup-simplify]: Simplify (/ (/ 1 (sqrt (/ 1 (- k)))) (/ 1 (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) 31.098 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (k n) around 0 31.098 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n 31.098 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 31.098 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 31.098 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 31.098 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 31.098 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.098 * [taylor]: Taking taylor expansion of 1/2 in n 31.098 * [backup-simplify]: Simplify 1/2 into 1/2 31.098 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.098 * [taylor]: Taking taylor expansion of k in n 31.098 * [backup-simplify]: Simplify k into k 31.099 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.099 * [taylor]: Taking taylor expansion of 1/2 in n 31.099 * [backup-simplify]: Simplify 1/2 into 1/2 31.099 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 31.099 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 31.099 * [taylor]: Taking taylor expansion of -2 in n 31.099 * [backup-simplify]: Simplify -2 into -2 31.099 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.099 * [taylor]: Taking taylor expansion of PI in n 31.099 * [backup-simplify]: Simplify PI into PI 31.099 * [taylor]: Taking taylor expansion of n in n 31.099 * [backup-simplify]: Simplify 0 into 0 31.099 * [backup-simplify]: Simplify 1 into 1 31.099 * [backup-simplify]: Simplify (/ PI 1) into PI 31.100 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 31.101 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 31.101 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.101 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 31.102 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.103 * [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))) 31.105 * [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)))) 31.105 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 31.105 * [taylor]: Taking taylor expansion of (/ -1 k) in n 31.105 * [taylor]: Taking taylor expansion of -1 in n 31.105 * [backup-simplify]: Simplify -1 into -1 31.105 * [taylor]: Taking taylor expansion of k in n 31.105 * [backup-simplify]: Simplify k into k 31.105 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 31.105 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 31.105 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 31.105 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 31.106 * [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))) 31.106 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 31.106 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 31.106 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 31.106 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 31.106 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 31.107 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 31.107 * [taylor]: Taking taylor expansion of 1/2 in k 31.107 * [backup-simplify]: Simplify 1/2 into 1/2 31.107 * [taylor]: Taking taylor expansion of (/ 1 k) in k 31.107 * [taylor]: Taking taylor expansion of k in k 31.107 * [backup-simplify]: Simplify 0 into 0 31.107 * [backup-simplify]: Simplify 1 into 1 31.107 * [backup-simplify]: Simplify (/ 1 1) into 1 31.107 * [taylor]: Taking taylor expansion of 1/2 in k 31.107 * [backup-simplify]: Simplify 1/2 into 1/2 31.107 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 31.107 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 31.107 * [taylor]: Taking taylor expansion of -2 in k 31.107 * [backup-simplify]: Simplify -2 into -2 31.107 * [taylor]: Taking taylor expansion of (/ PI n) in k 31.107 * [taylor]: Taking taylor expansion of PI in k 31.107 * [backup-simplify]: Simplify PI into PI 31.107 * [taylor]: Taking taylor expansion of n in k 31.107 * [backup-simplify]: Simplify n into n 31.107 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 31.107 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 31.108 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 31.108 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 31.108 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 31.108 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 31.109 * [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))) 31.109 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 31.109 * [taylor]: Taking taylor expansion of (/ -1 k) in k 31.109 * [taylor]: Taking taylor expansion of -1 in k 31.109 * [backup-simplify]: Simplify -1 into -1 31.109 * [taylor]: Taking taylor expansion of k in k 31.109 * [backup-simplify]: Simplify 0 into 0 31.109 * [backup-simplify]: Simplify 1 into 1 31.109 * [backup-simplify]: Simplify (/ -1 1) into -1 31.110 * [backup-simplify]: Simplify (sqrt 0) into 0 31.111 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 31.111 * [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)))) 31.111 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k 31.111 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 31.111 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 31.111 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 31.111 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 31.111 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 31.111 * [taylor]: Taking taylor expansion of 1/2 in k 31.111 * [backup-simplify]: Simplify 1/2 into 1/2 31.112 * [taylor]: Taking taylor expansion of (/ 1 k) in k 31.112 * [taylor]: Taking taylor expansion of k in k 31.112 * [backup-simplify]: Simplify 0 into 0 31.112 * [backup-simplify]: Simplify 1 into 1 31.112 * [backup-simplify]: Simplify (/ 1 1) into 1 31.112 * [taylor]: Taking taylor expansion of 1/2 in k 31.112 * [backup-simplify]: Simplify 1/2 into 1/2 31.112 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 31.112 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 31.112 * [taylor]: Taking taylor expansion of -2 in k 31.112 * [backup-simplify]: Simplify -2 into -2 31.112 * [taylor]: Taking taylor expansion of (/ PI n) in k 31.112 * [taylor]: Taking taylor expansion of PI in k 31.112 * [backup-simplify]: Simplify PI into PI 31.112 * [taylor]: Taking taylor expansion of n in k 31.112 * [backup-simplify]: Simplify n into n 31.112 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 31.112 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 31.112 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 31.113 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 31.113 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 31.113 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 31.113 * [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))) 31.113 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 31.114 * [taylor]: Taking taylor expansion of (/ -1 k) in k 31.114 * [taylor]: Taking taylor expansion of -1 in k 31.114 * [backup-simplify]: Simplify -1 into -1 31.114 * [taylor]: Taking taylor expansion of k in k 31.114 * [backup-simplify]: Simplify 0 into 0 31.114 * [backup-simplify]: Simplify 1 into 1 31.114 * [backup-simplify]: Simplify (/ -1 1) into -1 31.114 * [backup-simplify]: Simplify (sqrt 0) into 0 31.115 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 31.115 * [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)))) 31.115 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 31.115 * [taylor]: Taking taylor expansion of +nan.0 in n 31.115 * [backup-simplify]: Simplify +nan.0 into +nan.0 31.115 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 31.115 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 31.115 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 31.115 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 31.115 * [taylor]: Taking taylor expansion of -2 in n 31.115 * [backup-simplify]: Simplify -2 into -2 31.115 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.115 * [taylor]: Taking taylor expansion of PI in n 31.115 * [backup-simplify]: Simplify PI into PI 31.115 * [taylor]: Taking taylor expansion of n in n 31.115 * [backup-simplify]: Simplify 0 into 0 31.115 * [backup-simplify]: Simplify 1 into 1 31.116 * [backup-simplify]: Simplify (/ PI 1) into PI 31.116 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 31.117 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 31.117 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 31.117 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.117 * [taylor]: Taking taylor expansion of 1/2 in n 31.117 * [backup-simplify]: Simplify 1/2 into 1/2 31.117 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.117 * [taylor]: Taking taylor expansion of k in n 31.117 * [backup-simplify]: Simplify k into k 31.117 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.117 * [taylor]: Taking taylor expansion of 1/2 in n 31.117 * [backup-simplify]: Simplify 1/2 into 1/2 31.118 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.118 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.118 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 31.119 * [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))) 31.119 * [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)))) 31.120 * [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))))) 31.121 * [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))))) 31.121 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 31.123 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 31.124 * [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))))) 31.124 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 31.124 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 31.124 * [taylor]: Taking taylor expansion of +nan.0 in n 31.124 * [backup-simplify]: Simplify +nan.0 into +nan.0 31.124 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 31.124 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 31.124 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 31.124 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 31.124 * [taylor]: Taking taylor expansion of -2 in n 31.124 * [backup-simplify]: Simplify -2 into -2 31.124 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.124 * [taylor]: Taking taylor expansion of PI in n 31.124 * [backup-simplify]: Simplify PI into PI 31.124 * [taylor]: Taking taylor expansion of n in n 31.124 * [backup-simplify]: Simplify 0 into 0 31.124 * [backup-simplify]: Simplify 1 into 1 31.124 * [backup-simplify]: Simplify (/ PI 1) into PI 31.125 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 31.125 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 31.125 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 31.125 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.125 * [taylor]: Taking taylor expansion of 1/2 in n 31.125 * [backup-simplify]: Simplify 1/2 into 1/2 31.125 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.125 * [taylor]: Taking taylor expansion of k in n 31.125 * [backup-simplify]: Simplify k into k 31.126 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.126 * [taylor]: Taking taylor expansion of 1/2 in n 31.126 * [backup-simplify]: Simplify 1/2 into 1/2 31.126 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.127 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.127 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 31.127 * [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))) 31.128 * [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)))) 31.129 * [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))))) 31.130 * [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)))))) 31.130 * [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)))))) 31.131 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.131 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 31.132 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 31.132 * [backup-simplify]: Simplify (+ 0 0) into 0 31.132 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 31.133 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 31.134 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 31.135 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 31.136 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 31.137 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 31.137 * [backup-simplify]: Simplify 0 into 0 31.138 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 31.142 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 31.144 * [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))))) 31.144 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 31.144 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 31.144 * [taylor]: Taking taylor expansion of +nan.0 in n 31.144 * [backup-simplify]: Simplify +nan.0 into +nan.0 31.144 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 31.144 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 31.144 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 31.144 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 31.144 * [taylor]: Taking taylor expansion of -2 in n 31.144 * [backup-simplify]: Simplify -2 into -2 31.144 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.144 * [taylor]: Taking taylor expansion of PI in n 31.144 * [backup-simplify]: Simplify PI into PI 31.144 * [taylor]: Taking taylor expansion of n in n 31.144 * [backup-simplify]: Simplify 0 into 0 31.144 * [backup-simplify]: Simplify 1 into 1 31.145 * [backup-simplify]: Simplify (/ PI 1) into PI 31.145 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 31.146 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 31.146 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 31.146 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.146 * [taylor]: Taking taylor expansion of 1/2 in n 31.146 * [backup-simplify]: Simplify 1/2 into 1/2 31.146 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.146 * [taylor]: Taking taylor expansion of k in n 31.146 * [backup-simplify]: Simplify k into k 31.147 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.147 * [taylor]: Taking taylor expansion of 1/2 in n 31.147 * [backup-simplify]: Simplify 1/2 into 1/2 31.148 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.148 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.148 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 31.149 * [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))) 31.150 * [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)))) 31.152 * [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))))) 31.153 * [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)))))) 31.154 * [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)))))) 31.158 * [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))))))))))) 31.158 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 2) 31.158 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 31.158 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 31.158 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 31.158 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 31.158 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 31.158 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 31.158 * [taylor]: Taking taylor expansion of 1/2 in k 31.158 * [backup-simplify]: Simplify 1/2 into 1/2 31.158 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 31.158 * [taylor]: Taking taylor expansion of 1/2 in k 31.158 * [backup-simplify]: Simplify 1/2 into 1/2 31.159 * [taylor]: Taking taylor expansion of k in k 31.159 * [backup-simplify]: Simplify 0 into 0 31.159 * [backup-simplify]: Simplify 1 into 1 31.159 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 31.159 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 31.159 * [taylor]: Taking taylor expansion of 2 in k 31.159 * [backup-simplify]: Simplify 2 into 2 31.159 * [taylor]: Taking taylor expansion of (* n PI) in k 31.159 * [taylor]: Taking taylor expansion of n in k 31.159 * [backup-simplify]: Simplify n into n 31.159 * [taylor]: Taking taylor expansion of PI in k 31.159 * [backup-simplify]: Simplify PI into PI 31.159 * [backup-simplify]: Simplify (* n PI) into (* n PI) 31.159 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 31.159 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 31.159 * [backup-simplify]: Simplify (* 1/2 0) into 0 31.160 * [backup-simplify]: Simplify (- 0) into 0 31.160 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 31.160 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 31.160 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 31.160 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 31.161 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 31.161 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 31.161 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 31.161 * [taylor]: Taking taylor expansion of 1/2 in n 31.161 * [backup-simplify]: Simplify 1/2 into 1/2 31.161 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 31.161 * [taylor]: Taking taylor expansion of 1/2 in n 31.161 * [backup-simplify]: Simplify 1/2 into 1/2 31.161 * [taylor]: Taking taylor expansion of k in n 31.161 * [backup-simplify]: Simplify k into k 31.161 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 31.161 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 31.161 * [taylor]: Taking taylor expansion of 2 in n 31.161 * [backup-simplify]: Simplify 2 into 2 31.161 * [taylor]: Taking taylor expansion of (* n PI) in n 31.161 * [taylor]: Taking taylor expansion of n in n 31.161 * [backup-simplify]: Simplify 0 into 0 31.161 * [backup-simplify]: Simplify 1 into 1 31.161 * [taylor]: Taking taylor expansion of PI in n 31.161 * [backup-simplify]: Simplify PI into PI 31.161 * [backup-simplify]: Simplify (* 0 PI) into 0 31.162 * [backup-simplify]: Simplify (* 2 0) into 0 31.163 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 31.165 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 31.166 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.166 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 31.166 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 31.166 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 31.167 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 31.169 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 31.169 * [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))))) 31.169 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 31.169 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 31.169 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 31.169 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 31.169 * [taylor]: Taking taylor expansion of 1/2 in n 31.169 * [backup-simplify]: Simplify 1/2 into 1/2 31.170 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 31.170 * [taylor]: Taking taylor expansion of 1/2 in n 31.170 * [backup-simplify]: Simplify 1/2 into 1/2 31.170 * [taylor]: Taking taylor expansion of k in n 31.170 * [backup-simplify]: Simplify k into k 31.170 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 31.170 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 31.170 * [taylor]: Taking taylor expansion of 2 in n 31.170 * [backup-simplify]: Simplify 2 into 2 31.170 * [taylor]: Taking taylor expansion of (* n PI) in n 31.170 * [taylor]: Taking taylor expansion of n in n 31.170 * [backup-simplify]: Simplify 0 into 0 31.170 * [backup-simplify]: Simplify 1 into 1 31.170 * [taylor]: Taking taylor expansion of PI in n 31.170 * [backup-simplify]: Simplify PI into PI 31.170 * [backup-simplify]: Simplify (* 0 PI) into 0 31.170 * [backup-simplify]: Simplify (* 2 0) into 0 31.171 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 31.172 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 31.173 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.173 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 31.173 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 31.173 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 31.174 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 31.180 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 31.181 * [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))))) 31.181 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 31.181 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 31.181 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 31.181 * [taylor]: Taking taylor expansion of 1/2 in k 31.181 * [backup-simplify]: Simplify 1/2 into 1/2 31.181 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 31.181 * [taylor]: Taking taylor expansion of 1/2 in k 31.181 * [backup-simplify]: Simplify 1/2 into 1/2 31.181 * [taylor]: Taking taylor expansion of k in k 31.181 * [backup-simplify]: Simplify 0 into 0 31.181 * [backup-simplify]: Simplify 1 into 1 31.181 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 31.181 * [taylor]: Taking taylor expansion of (log n) in k 31.181 * [taylor]: Taking taylor expansion of n in k 31.181 * [backup-simplify]: Simplify n into n 31.181 * [backup-simplify]: Simplify (log n) into (log n) 31.181 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 31.181 * [taylor]: Taking taylor expansion of (* 2 PI) in k 31.181 * [taylor]: Taking taylor expansion of 2 in k 31.181 * [backup-simplify]: Simplify 2 into 2 31.181 * [taylor]: Taking taylor expansion of PI in k 31.181 * [backup-simplify]: Simplify PI into PI 31.182 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 31.183 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.183 * [backup-simplify]: Simplify (* 1/2 0) into 0 31.183 * [backup-simplify]: Simplify (- 0) into 0 31.183 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 31.184 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 31.185 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 31.186 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 31.186 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 31.187 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 31.188 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 31.189 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 31.189 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 31.189 * [backup-simplify]: Simplify (- 0) into 0 31.189 * [backup-simplify]: Simplify (+ 0 0) into 0 31.190 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 31.191 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 31.192 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 31.192 * [taylor]: Taking taylor expansion of 0 in k 31.192 * [backup-simplify]: Simplify 0 into 0 31.192 * [backup-simplify]: Simplify 0 into 0 31.193 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 31.193 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 31.194 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 31.194 * [backup-simplify]: Simplify (+ 0 0) into 0 31.195 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 31.195 * [backup-simplify]: Simplify (- 1/2) into -1/2 31.195 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 31.196 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 31.199 * [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))))))) 31.202 * [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))))))) 31.203 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 31.204 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 31.207 * [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 31.208 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 31.209 * [backup-simplify]: Simplify (- 0) into 0 31.209 * [backup-simplify]: Simplify (+ 0 0) into 0 31.210 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 31.212 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 31.215 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 31.215 * [taylor]: Taking taylor expansion of 0 in k 31.215 * [backup-simplify]: Simplify 0 into 0 31.215 * [backup-simplify]: Simplify 0 into 0 31.215 * [backup-simplify]: Simplify 0 into 0 31.216 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 31.217 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 31.221 * [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 31.221 * [backup-simplify]: Simplify (+ 0 0) into 0 31.222 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 31.222 * [backup-simplify]: Simplify (- 0) into 0 31.223 * [backup-simplify]: Simplify (+ 0 0) into 0 31.224 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 31.228 * [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))))) 31.232 * [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))))) 31.238 * [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))))) 31.238 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 31.238 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 31.238 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 31.238 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 31.238 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 31.238 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 31.239 * [taylor]: Taking taylor expansion of 1/2 in k 31.239 * [backup-simplify]: Simplify 1/2 into 1/2 31.239 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 31.239 * [taylor]: Taking taylor expansion of 1/2 in k 31.239 * [backup-simplify]: Simplify 1/2 into 1/2 31.239 * [taylor]: Taking taylor expansion of (/ 1 k) in k 31.239 * [taylor]: Taking taylor expansion of k in k 31.239 * [backup-simplify]: Simplify 0 into 0 31.239 * [backup-simplify]: Simplify 1 into 1 31.239 * [backup-simplify]: Simplify (/ 1 1) into 1 31.239 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 31.239 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 31.239 * [taylor]: Taking taylor expansion of 2 in k 31.239 * [backup-simplify]: Simplify 2 into 2 31.239 * [taylor]: Taking taylor expansion of (/ PI n) in k 31.239 * [taylor]: Taking taylor expansion of PI in k 31.239 * [backup-simplify]: Simplify PI into PI 31.239 * [taylor]: Taking taylor expansion of n in k 31.239 * [backup-simplify]: Simplify n into n 31.239 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 31.239 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 31.239 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 31.239 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 31.240 * [backup-simplify]: Simplify (- 1/2) into -1/2 31.240 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 31.240 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 31.240 * [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)))) 31.240 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 31.240 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 31.240 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 31.240 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 31.240 * [taylor]: Taking taylor expansion of 1/2 in n 31.240 * [backup-simplify]: Simplify 1/2 into 1/2 31.240 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.240 * [taylor]: Taking taylor expansion of 1/2 in n 31.240 * [backup-simplify]: Simplify 1/2 into 1/2 31.240 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.240 * [taylor]: Taking taylor expansion of k in n 31.240 * [backup-simplify]: Simplify k into k 31.240 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.240 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 31.240 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 31.240 * [taylor]: Taking taylor expansion of 2 in n 31.240 * [backup-simplify]: Simplify 2 into 2 31.241 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.241 * [taylor]: Taking taylor expansion of PI in n 31.241 * [backup-simplify]: Simplify PI into PI 31.241 * [taylor]: Taking taylor expansion of n in n 31.241 * [backup-simplify]: Simplify 0 into 0 31.241 * [backup-simplify]: Simplify 1 into 1 31.241 * [backup-simplify]: Simplify (/ PI 1) into PI 31.241 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 31.242 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.242 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.242 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 31.242 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 31.243 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.244 * [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))) 31.245 * [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)))) 31.245 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 31.245 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 31.245 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 31.245 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 31.245 * [taylor]: Taking taylor expansion of 1/2 in n 31.245 * [backup-simplify]: Simplify 1/2 into 1/2 31.245 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.245 * [taylor]: Taking taylor expansion of 1/2 in n 31.245 * [backup-simplify]: Simplify 1/2 into 1/2 31.245 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.245 * [taylor]: Taking taylor expansion of k in n 31.245 * [backup-simplify]: Simplify k into k 31.245 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.245 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 31.245 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 31.245 * [taylor]: Taking taylor expansion of 2 in n 31.245 * [backup-simplify]: Simplify 2 into 2 31.245 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.245 * [taylor]: Taking taylor expansion of PI in n 31.245 * [backup-simplify]: Simplify PI into PI 31.245 * [taylor]: Taking taylor expansion of n in n 31.245 * [backup-simplify]: Simplify 0 into 0 31.245 * [backup-simplify]: Simplify 1 into 1 31.245 * [backup-simplify]: Simplify (/ PI 1) into PI 31.246 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 31.246 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.247 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.247 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 31.247 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 31.248 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.248 * [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))) 31.249 * [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)))) 31.249 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 31.249 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 31.249 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 31.249 * [taylor]: Taking taylor expansion of 1/2 in k 31.249 * [backup-simplify]: Simplify 1/2 into 1/2 31.249 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 31.249 * [taylor]: Taking taylor expansion of 1/2 in k 31.249 * [backup-simplify]: Simplify 1/2 into 1/2 31.249 * [taylor]: Taking taylor expansion of (/ 1 k) in k 31.249 * [taylor]: Taking taylor expansion of k in k 31.249 * [backup-simplify]: Simplify 0 into 0 31.249 * [backup-simplify]: Simplify 1 into 1 31.250 * [backup-simplify]: Simplify (/ 1 1) into 1 31.250 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 31.250 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 31.250 * [taylor]: Taking taylor expansion of (* 2 PI) in k 31.250 * [taylor]: Taking taylor expansion of 2 in k 31.250 * [backup-simplify]: Simplify 2 into 2 31.250 * [taylor]: Taking taylor expansion of PI in k 31.250 * [backup-simplify]: Simplify PI into PI 31.250 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 31.251 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 31.251 * [taylor]: Taking taylor expansion of (log n) in k 31.251 * [taylor]: Taking taylor expansion of n in k 31.251 * [backup-simplify]: Simplify n into n 31.251 * [backup-simplify]: Simplify (log n) into (log n) 31.251 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 31.251 * [backup-simplify]: Simplify (- 1/2) into -1/2 31.252 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 31.252 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 31.252 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 31.253 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 31.254 * [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)))) 31.255 * [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)))) 31.255 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 31.256 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 31.257 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 31.257 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 31.257 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 31.258 * [backup-simplify]: Simplify (- 0) into 0 31.259 * [backup-simplify]: Simplify (+ 0 0) into 0 31.260 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.262 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 31.264 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 31.264 * [taylor]: Taking taylor expansion of 0 in k 31.264 * [backup-simplify]: Simplify 0 into 0 31.264 * [backup-simplify]: Simplify 0 into 0 31.264 * [backup-simplify]: Simplify 0 into 0 31.265 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 31.266 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 31.269 * [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 31.269 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 31.270 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 31.271 * [backup-simplify]: Simplify (- 0) into 0 31.271 * [backup-simplify]: Simplify (+ 0 0) into 0 31.272 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.274 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 31.276 * [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 31.276 * [taylor]: Taking taylor expansion of 0 in k 31.276 * [backup-simplify]: Simplify 0 into 0 31.276 * [backup-simplify]: Simplify 0 into 0 31.276 * [backup-simplify]: Simplify 0 into 0 31.276 * [backup-simplify]: Simplify 0 into 0 31.278 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 31.279 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 31.283 * [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 31.283 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 31.284 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 31.284 * [backup-simplify]: Simplify (- 0) into 0 31.284 * [backup-simplify]: Simplify (+ 0 0) into 0 31.285 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 31.287 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 31.293 * [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 31.294 * [taylor]: Taking taylor expansion of 0 in k 31.294 * [backup-simplify]: Simplify 0 into 0 31.294 * [backup-simplify]: Simplify 0 into 0 31.295 * [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))))) 31.295 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 31.295 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 31.295 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 31.295 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 31.295 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 31.295 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 31.295 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 31.295 * [taylor]: Taking taylor expansion of 1/2 in k 31.295 * [backup-simplify]: Simplify 1/2 into 1/2 31.295 * [taylor]: Taking taylor expansion of (/ 1 k) in k 31.295 * [taylor]: Taking taylor expansion of k in k 31.295 * [backup-simplify]: Simplify 0 into 0 31.295 * [backup-simplify]: Simplify 1 into 1 31.296 * [backup-simplify]: Simplify (/ 1 1) into 1 31.296 * [taylor]: Taking taylor expansion of 1/2 in k 31.296 * [backup-simplify]: Simplify 1/2 into 1/2 31.296 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 31.296 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 31.296 * [taylor]: Taking taylor expansion of -2 in k 31.296 * [backup-simplify]: Simplify -2 into -2 31.296 * [taylor]: Taking taylor expansion of (/ PI n) in k 31.296 * [taylor]: Taking taylor expansion of PI in k 31.296 * [backup-simplify]: Simplify PI into PI 31.296 * [taylor]: Taking taylor expansion of n in k 31.296 * [backup-simplify]: Simplify n into n 31.296 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 31.296 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 31.296 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 31.297 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 31.297 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 31.297 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 31.297 * [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))) 31.297 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 31.298 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 31.298 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 31.298 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 31.298 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.298 * [taylor]: Taking taylor expansion of 1/2 in n 31.298 * [backup-simplify]: Simplify 1/2 into 1/2 31.298 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.298 * [taylor]: Taking taylor expansion of k in n 31.298 * [backup-simplify]: Simplify k into k 31.298 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.298 * [taylor]: Taking taylor expansion of 1/2 in n 31.298 * [backup-simplify]: Simplify 1/2 into 1/2 31.298 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 31.298 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 31.298 * [taylor]: Taking taylor expansion of -2 in n 31.298 * [backup-simplify]: Simplify -2 into -2 31.298 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.298 * [taylor]: Taking taylor expansion of PI in n 31.298 * [backup-simplify]: Simplify PI into PI 31.298 * [taylor]: Taking taylor expansion of n in n 31.298 * [backup-simplify]: Simplify 0 into 0 31.298 * [backup-simplify]: Simplify 1 into 1 31.299 * [backup-simplify]: Simplify (/ PI 1) into PI 31.299 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 31.300 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 31.300 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.300 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 31.302 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.303 * [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))) 31.304 * [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)))) 31.304 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 31.304 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 31.304 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 31.304 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 31.304 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 31.304 * [taylor]: Taking taylor expansion of 1/2 in n 31.304 * [backup-simplify]: Simplify 1/2 into 1/2 31.304 * [taylor]: Taking taylor expansion of (/ 1 k) in n 31.304 * [taylor]: Taking taylor expansion of k in n 31.304 * [backup-simplify]: Simplify k into k 31.304 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 31.304 * [taylor]: Taking taylor expansion of 1/2 in n 31.304 * [backup-simplify]: Simplify 1/2 into 1/2 31.304 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 31.304 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 31.304 * [taylor]: Taking taylor expansion of -2 in n 31.304 * [backup-simplify]: Simplify -2 into -2 31.304 * [taylor]: Taking taylor expansion of (/ PI n) in n 31.304 * [taylor]: Taking taylor expansion of PI in n 31.304 * [backup-simplify]: Simplify PI into PI 31.304 * [taylor]: Taking taylor expansion of n in n 31.304 * [backup-simplify]: Simplify 0 into 0 31.304 * [backup-simplify]: Simplify 1 into 1 31.305 * [backup-simplify]: Simplify (/ PI 1) into PI 31.305 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 31.306 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 31.306 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 31.306 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 31.307 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.308 * [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))) 31.309 * [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)))) 31.309 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 31.309 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 31.309 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 31.309 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 31.309 * [taylor]: Taking taylor expansion of 1/2 in k 31.309 * [backup-simplify]: Simplify 1/2 into 1/2 31.309 * [taylor]: Taking taylor expansion of (/ 1 k) in k 31.309 * [taylor]: Taking taylor expansion of k in k 31.309 * [backup-simplify]: Simplify 0 into 0 31.309 * [backup-simplify]: Simplify 1 into 1 31.309 * [backup-simplify]: Simplify (/ 1 1) into 1 31.309 * [taylor]: Taking taylor expansion of 1/2 in k 31.309 * [backup-simplify]: Simplify 1/2 into 1/2 31.309 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 31.309 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 31.309 * [taylor]: Taking taylor expansion of (* -2 PI) in k 31.309 * [taylor]: Taking taylor expansion of -2 in k 31.309 * [backup-simplify]: Simplify -2 into -2 31.309 * [taylor]: Taking taylor expansion of PI in k 31.309 * [backup-simplify]: Simplify PI into PI 31.310 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 31.310 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 31.310 * [taylor]: Taking taylor expansion of (log n) in k 31.310 * [taylor]: Taking taylor expansion of n in k 31.310 * [backup-simplify]: Simplify n into n 31.310 * [backup-simplify]: Simplify (log n) into (log n) 31.310 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 31.311 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 31.311 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 31.311 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 31.312 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 31.313 * [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)))) 31.314 * [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)))) 31.314 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 31.315 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 31.316 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 31.316 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 31.316 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 31.316 * [backup-simplify]: Simplify (+ 0 0) into 0 31.317 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.318 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 31.319 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 31.319 * [taylor]: Taking taylor expansion of 0 in k 31.319 * [backup-simplify]: Simplify 0 into 0 31.319 * [backup-simplify]: Simplify 0 into 0 31.319 * [backup-simplify]: Simplify 0 into 0 31.320 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 31.321 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 31.322 * [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 31.323 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 31.323 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 31.323 * [backup-simplify]: Simplify (+ 0 0) into 0 31.324 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.325 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 31.327 * [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 31.327 * [taylor]: Taking taylor expansion of 0 in k 31.327 * [backup-simplify]: Simplify 0 into 0 31.327 * [backup-simplify]: Simplify 0 into 0 31.327 * [backup-simplify]: Simplify 0 into 0 31.327 * [backup-simplify]: Simplify 0 into 0 31.327 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 31.328 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 31.331 * [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 31.332 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 31.332 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 31.333 * [backup-simplify]: Simplify (+ 0 0) into 0 31.334 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 31.335 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 31.337 * [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 31.337 * [taylor]: Taking taylor expansion of 0 in k 31.337 * [backup-simplify]: Simplify 0 into 0 31.337 * [backup-simplify]: Simplify 0 into 0 31.337 * [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))))) 31.338 * * * [progress]: simplifying candidates 31.338 * * * * [progress]: [ 1 / 3542 ] simplifiying candidate # 31.338 * * * * [progress]: [ 2 / 3542 ] simplifiying candidate # 31.338 * * * * [progress]: [ 3 / 3542 ] simplifiying candidate # 31.338 * * * * [progress]: [ 4 / 3542 ] simplifiying candidate # 31.338 * * * * [progress]: [ 5 / 3542 ] simplifiying candidate # 31.338 * * * * [progress]: [ 6 / 3542 ] simplifiying candidate # 31.338 * * * * [progress]: [ 7 / 3542 ] simplifiying candidate # 31.338 * * * * [progress]: [ 8 / 3542 ] simplifiying candidate # 31.338 * * * * [progress]: [ 9 / 3542 ] simplifiying candidate # 31.338 * * * * [progress]: [ 10 / 3542 ] simplifiying candidate # 31.338 * * * * [progress]: [ 11 / 3542 ] simplifiying candidate # 31.338 * * * * [progress]: [ 12 / 3542 ] simplifiying candidate # 31.338 * * * * [progress]: [ 13 / 3542 ] simplifiying candidate # 31.338 * * * * [progress]: [ 14 / 3542 ] simplifiying candidate # 31.338 * * * * [progress]: [ 15 / 3542 ] simplifiying candidate # 31.338 * * * * [progress]: [ 16 / 3542 ] simplifiying candidate # 31.338 * * * * [progress]: [ 17 / 3542 ] simplifiying candidate # 31.338 * * * * [progress]: [ 18 / 3542 ] simplifiying candidate # 31.339 * * * * [progress]: [ 19 / 3542 ] simplifiying candidate # 31.339 * * * * [progress]: [ 20 / 3542 ] simplifiying candidate # 31.339 * * * * [progress]: [ 21 / 3542 ] simplifiying candidate # 31.339 * * * * [progress]: [ 22 / 3542 ] simplifiying candidate # 31.339 * * * * [progress]: [ 23 / 3542 ] simplifiying candidate # 31.339 * * * * 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[progress]: [ 39 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 40 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 41 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 42 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 43 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 44 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 45 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 46 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 47 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 48 / 3542 ] simplifiying candidate #real (real->posit16 (/ 1 (sqrt k)))) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))> 31.340 * * * * [progress]: [ 49 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 50 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 51 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 52 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 53 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 54 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 55 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 56 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 57 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 58 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 59 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 60 / 3542 ] simplifiying candidate # 31.340 * * * * [progress]: [ 61 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 62 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 63 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 64 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 65 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 66 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 67 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 68 / 3542 ] simplifiying candidate #real (real->posit16 (* (* n 2) PI))) (- 1/2 (/ k 2))))))> 31.341 * * * * [progress]: [ 69 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 70 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 71 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 72 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 73 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 74 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 75 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 76 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 77 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 78 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 79 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 80 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 81 / 3542 ] simplifiying candidate # 31.341 * * * * [progress]: [ 82 / 3542 ] simplifiying candidate # 31.342 * * * * [progress]: [ 83 / 3542 ] simplifiying candidate # 31.342 * * * * [progress]: [ 84 / 3542 ] simplifiying candidate # 31.342 * * * * [progress]: [ 85 / 3542 ] simplifiying candidate # 31.342 * * * * [progress]: [ 86 / 3542 ] simplifiying candidate # 31.342 * * * * [progress]: [ 87 / 3542 ] simplifiying candidate # 31.342 * * * * [progress]: [ 88 / 3542 ] simplifiying candidate # 31.342 * * * * [progress]: [ 89 / 3542 ] simplifiying candidate # 31.342 * * * * [progress]: [ 90 / 3542 ] simplifiying candidate # 31.342 * * * * [progress]: [ 91 / 3542 ] simplifiying candidate # 31.342 * * * * [progress]: [ 92 / 3542 ] simplifiying candidate # 31.342 * * * * [progress]: [ 93 / 3542 ] simplifiying candidate # 31.342 * * * * [progress]: [ 94 / 3542 ] simplifiying candidate # 31.342 * * * * [progress]: [ 95 / 3542 ] simplifiying candidate # 31.342 * * * * [progress]: [ 96 / 3542 ] simplifiying candidate # 31.342 * * * * [progress]: [ 97 / 3542 ] 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1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 32.084 * * [simplify]: iteration 0: 4156 enodes 34.499 * * [simplify]: iteration complete: 5001 enodes 34.506 * * [simplify]: Extracting #0: cost 2908 inf + 0 34.532 * * [simplify]: Extracting #1: cost 3398 inf + 1 34.545 * * [simplify]: Extracting #2: cost 3570 inf + 1090 34.557 * * [simplify]: Extracting #3: cost 3540 inf + 18390 34.578 * * [simplify]: Extracting #4: cost 3276 inf + 120727 34.675 * * [simplify]: Extracting #5: cost 2478 inf + 632723 34.823 * * [simplify]: Extracting #6: cost 1517 inf + 1351569 35.118 * * [simplify]: Extracting #7: cost 680 inf + 2071837 35.402 * * [simplify]: Extracting #8: cost 274 inf + 2438713 35.780 * * [simplify]: Extracting #9: cost 38 inf + 2670024 36.188 * * [simplify]: Extracting #10: cost 21 inf + 2687755 36.581 * * [simplify]: Extracting #11: cost 13 inf + 2689430 37.003 * * [simplify]: Extracting #12: cost 10 inf + 2690894 37.375 * * [simplify]: Extracting #13: cost 6 inf + 2693843 37.813 * * [simplify]: Extracting #14: cost 3 inf + 2697168 38.184 * * [simplify]: Extracting #15: cost 1 inf + 2699418 38.550 * * [simplify]: Extracting #16: cost 0 inf + 2700558 38.852 * * [simplify]: Extracting #17: cost 0 inf + 2700493 39.285 * [simplify]: Simplified to: (expm1 (/ 1 (sqrt k))) (log1p (/ 1 (sqrt k))) (- 1/2) (- 1) (- (/ 1 2)) (- (log (sqrt k))) (- (log (sqrt k))) (- (log (sqrt k))) (- (log (sqrt k))) (exp (/ 1 (sqrt k))) (/ (/ 1 k) (sqrt k)) (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k))) (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))) (- 1) (- (sqrt k)) (* (/ (cbrt 1) (cbrt (sqrt k))) (/ (cbrt 1) (cbrt (sqrt k)))) (/ (cbrt 1) (cbrt (sqrt k))) (/ (* (cbrt 1) (cbrt 1)) (fabs (cbrt k))) (/ (cbrt 1) (sqrt (cbrt k))) (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k))) (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (/ (cbrt 1) (sqrt k)) (/ (* 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(* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (- (fma +nan.0 (* k k) (+ (- +nan.0) (- (* (- +nan.0) k))))) (- (fma +nan.0 (/ 1 (* k k)) (- (fma +nan.0 (/ 1 k) (* (- +nan.0) (/ 1 (* (* k k) k))))))) (- (fma +nan.0 (/ 1 (* k k)) (- (fma +nan.0 (/ 1 k) (- +nan.0))))) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (- (fma +nan.0 (* (sqrt 2) (* (* n PI) k)) (- (fma +nan.0 (* (* (sqrt 2) n) PI) (- (fma +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* (* n PI) k))) (- (fma +nan.0 (* (* (sqrt 2) n) (* PI (* (log n) k))) (* (- +nan.0) (* (* (sqrt 2) (* n n)) (* PI PI))))))))))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (* (* k k) k)) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) k) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (* k k)))))))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* k k)) (* +nan.0 (- (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))) (- (fma 1/4 (* (* (log (* 2 PI)) (exp (* 1/2 (log (* (* n 2) PI))))) (* (log n) (* k k))) (fma 1/8 (* (exp (* 1/2 (log (* (* n 2) PI)))) (* (* (log n) (log n)) (* k k))) (+ (exp (* 1/2 (log (* (* n 2) PI)))) (* (* 1/8 (* (log (* 2 PI)) (log (* 2 PI)))) (* (exp (* 1/2 (log (* (* n 2) PI)))) (* k k)))))) (* 1/2 (+ (* (exp (* 1/2 (log (* (* n 2) PI)))) (* (log n) k)) (* (* (log (* 2 PI)) (exp (* 1/2 (log (* (* n 2) PI))))) k)))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) 40.601 * * * [progress]: adding candidates to table 67.598 * * [progress]: iteration 4 / 4 67.598 * * * [progress]: picking best candidate 67.664 * * * * [pick]: Picked # 67.664 * * * [progress]: localizing error 67.716 * * * [progress]: generating rewritten candidates 67.716 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 1) 67.739 * * * * [progress]: [ 2 / 4 ] rewriting at (2) 67.783 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2) 67.819 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2) 67.917 * * * [progress]: generating series expansions 67.918 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 1) 67.918 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI)) 67.918 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0 67.918 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 67.918 * [taylor]: Taking taylor expansion of 2 in n 67.918 * [backup-simplify]: Simplify 2 into 2 67.918 * [taylor]: Taking taylor expansion of (* n PI) in n 67.918 * [taylor]: Taking taylor expansion of n in n 67.918 * [backup-simplify]: Simplify 0 into 0 67.918 * [backup-simplify]: Simplify 1 into 1 67.918 * [taylor]: Taking taylor expansion of PI in n 67.918 * [backup-simplify]: Simplify PI into PI 67.918 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 67.918 * [taylor]: Taking taylor expansion of 2 in n 67.918 * [backup-simplify]: Simplify 2 into 2 67.918 * [taylor]: Taking taylor expansion of (* n PI) in n 67.918 * [taylor]: Taking taylor expansion of n in n 67.918 * [backup-simplify]: Simplify 0 into 0 67.918 * [backup-simplify]: Simplify 1 into 1 67.918 * [taylor]: Taking taylor expansion of PI in n 67.918 * [backup-simplify]: Simplify PI into PI 67.919 * [backup-simplify]: Simplify (* 0 PI) into 0 67.919 * [backup-simplify]: Simplify (* 2 0) into 0 67.919 * [backup-simplify]: Simplify 0 into 0 67.920 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 67.921 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 67.921 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.922 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 67.923 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 67.923 * [backup-simplify]: Simplify 0 into 0 67.923 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 67.924 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 67.924 * [backup-simplify]: Simplify 0 into 0 67.925 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 67.926 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 67.926 * [backup-simplify]: Simplify 0 into 0 67.927 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 67.927 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 67.927 * [backup-simplify]: Simplify 0 into 0 67.928 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 67.929 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 67.929 * [backup-simplify]: Simplify 0 into 0 67.931 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 67.932 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 67.932 * [backup-simplify]: Simplify 0 into 0 67.932 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI)) 67.932 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n)) 67.932 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0 67.932 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 67.932 * [taylor]: Taking taylor expansion of 2 in n 67.932 * [backup-simplify]: Simplify 2 into 2 67.932 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.932 * [taylor]: Taking taylor expansion of PI in n 67.932 * [backup-simplify]: Simplify PI into PI 67.932 * [taylor]: Taking taylor expansion of n in n 67.932 * [backup-simplify]: Simplify 0 into 0 67.932 * [backup-simplify]: Simplify 1 into 1 67.933 * [backup-simplify]: Simplify (/ PI 1) into PI 67.933 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 67.933 * [taylor]: Taking taylor expansion of 2 in n 67.933 * [backup-simplify]: Simplify 2 into 2 67.933 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.933 * [taylor]: Taking taylor expansion of PI in n 67.933 * [backup-simplify]: Simplify PI into PI 67.933 * [taylor]: Taking taylor expansion of n in n 67.933 * [backup-simplify]: Simplify 0 into 0 67.933 * [backup-simplify]: Simplify 1 into 1 67.934 * [backup-simplify]: Simplify (/ PI 1) into PI 67.934 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.935 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 67.936 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 67.936 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 67.937 * [backup-simplify]: Simplify 0 into 0 67.938 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.939 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 67.939 * [backup-simplify]: Simplify 0 into 0 67.961 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.963 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 67.963 * [backup-simplify]: Simplify 0 into 0 67.964 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.966 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 67.966 * [backup-simplify]: Simplify 0 into 0 67.967 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.969 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 67.969 * [backup-simplify]: Simplify 0 into 0 67.970 * [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 67.972 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 67.972 * [backup-simplify]: Simplify 0 into 0 67.973 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI)) 67.973 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n)) 67.973 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0 67.973 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 67.973 * [taylor]: Taking taylor expansion of -2 in n 67.973 * [backup-simplify]: Simplify -2 into -2 67.973 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.974 * [taylor]: Taking taylor expansion of PI in n 67.974 * [backup-simplify]: Simplify PI into PI 67.974 * [taylor]: Taking taylor expansion of n in n 67.974 * [backup-simplify]: Simplify 0 into 0 67.974 * [backup-simplify]: Simplify 1 into 1 67.974 * [backup-simplify]: Simplify (/ PI 1) into PI 67.974 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 67.974 * [taylor]: Taking taylor expansion of -2 in n 67.974 * [backup-simplify]: Simplify -2 into -2 67.974 * [taylor]: Taking taylor expansion of (/ PI n) in n 67.974 * [taylor]: Taking taylor expansion of PI in n 67.974 * [backup-simplify]: Simplify PI into PI 67.974 * [taylor]: Taking taylor expansion of n in n 67.974 * [backup-simplify]: Simplify 0 into 0 67.974 * [backup-simplify]: Simplify 1 into 1 67.975 * [backup-simplify]: Simplify (/ PI 1) into PI 67.975 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 67.976 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 67.977 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 67.978 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 67.978 * [backup-simplify]: Simplify 0 into 0 67.979 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.980 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 67.980 * [backup-simplify]: Simplify 0 into 0 67.981 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.982 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 67.982 * [backup-simplify]: Simplify 0 into 0 67.983 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.985 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 67.985 * [backup-simplify]: Simplify 0 into 0 67.986 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 67.988 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 67.988 * [backup-simplify]: Simplify 0 into 0 67.989 * [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 67.991 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 67.991 * [backup-simplify]: Simplify 0 into 0 67.991 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI)) 67.992 * * * * [progress]: [ 2 / 4 ] generating series at (2) 67.992 * [backup-simplify]: Simplify (/ (pow k (- 1/2)) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) into (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) 67.992 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in (k n) around 0 67.992 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in n 67.992 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 67.992 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 67.992 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 67.992 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 67.992 * [taylor]: Taking taylor expansion of 1/2 in n 67.992 * [backup-simplify]: Simplify 1/2 into 1/2 67.992 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 67.993 * [taylor]: Taking taylor expansion of 1/2 in n 67.993 * [backup-simplify]: Simplify 1/2 into 1/2 67.993 * [taylor]: Taking taylor expansion of k in n 67.993 * [backup-simplify]: Simplify k into k 67.993 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 67.993 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 67.993 * [taylor]: Taking taylor expansion of 2 in n 67.993 * [backup-simplify]: Simplify 2 into 2 67.993 * [taylor]: Taking taylor expansion of (* n PI) in n 67.993 * [taylor]: Taking taylor expansion of n in n 67.993 * [backup-simplify]: Simplify 0 into 0 67.993 * [backup-simplify]: Simplify 1 into 1 67.993 * [taylor]: Taking taylor expansion of PI in n 67.993 * [backup-simplify]: Simplify PI into PI 67.993 * [backup-simplify]: Simplify (* 0 PI) into 0 67.994 * [backup-simplify]: Simplify (* 2 0) into 0 67.995 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 67.997 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 67.998 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 67.998 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 67.998 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 67.998 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 68.000 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 68.001 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 68.002 * [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))))) 68.002 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 68.002 * [taylor]: Taking taylor expansion of (/ 1 k) in n 68.002 * [taylor]: Taking taylor expansion of k in n 68.002 * [backup-simplify]: Simplify k into k 68.002 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 68.002 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 68.002 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 68.003 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 68.003 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 68.003 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 68.003 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 68.003 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 68.003 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 68.003 * [taylor]: Taking taylor expansion of 1/2 in k 68.003 * [backup-simplify]: Simplify 1/2 into 1/2 68.003 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 68.003 * [taylor]: Taking taylor expansion of 1/2 in k 68.003 * [backup-simplify]: Simplify 1/2 into 1/2 68.003 * [taylor]: Taking taylor expansion of k in k 68.003 * [backup-simplify]: Simplify 0 into 0 68.003 * [backup-simplify]: Simplify 1 into 1 68.003 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 68.003 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 68.003 * [taylor]: Taking taylor expansion of 2 in k 68.003 * [backup-simplify]: Simplify 2 into 2 68.003 * [taylor]: Taking taylor expansion of (* n PI) in k 68.003 * [taylor]: Taking taylor expansion of n in k 68.003 * [backup-simplify]: Simplify n into n 68.003 * [taylor]: Taking taylor expansion of PI in k 68.003 * [backup-simplify]: Simplify PI into PI 68.003 * [backup-simplify]: Simplify (* n PI) into (* n PI) 68.003 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 68.003 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 68.004 * [backup-simplify]: Simplify (* 1/2 0) into 0 68.004 * [backup-simplify]: Simplify (- 0) into 0 68.004 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 68.005 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 68.005 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 68.005 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 68.005 * [taylor]: Taking taylor expansion of (/ 1 k) in k 68.005 * [taylor]: Taking taylor expansion of k in k 68.005 * [backup-simplify]: Simplify 0 into 0 68.005 * [backup-simplify]: Simplify 1 into 1 68.005 * [backup-simplify]: Simplify (/ 1 1) into 1 68.006 * [backup-simplify]: Simplify (sqrt 0) into 0 68.007 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 68.007 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) (sqrt (/ 1 k))) in k 68.007 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 68.007 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 68.007 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 68.007 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 68.007 * [taylor]: Taking taylor expansion of 1/2 in k 68.007 * [backup-simplify]: Simplify 1/2 into 1/2 68.007 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 68.007 * [taylor]: Taking taylor expansion of 1/2 in k 68.007 * [backup-simplify]: Simplify 1/2 into 1/2 68.007 * [taylor]: Taking taylor expansion of k in k 68.007 * [backup-simplify]: Simplify 0 into 0 68.007 * [backup-simplify]: Simplify 1 into 1 68.007 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 68.007 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 68.007 * [taylor]: Taking taylor expansion of 2 in k 68.007 * [backup-simplify]: Simplify 2 into 2 68.007 * [taylor]: Taking taylor expansion of (* n PI) in k 68.008 * [taylor]: Taking taylor expansion of n in k 68.008 * [backup-simplify]: Simplify n into n 68.008 * [taylor]: Taking taylor expansion of PI in k 68.008 * [backup-simplify]: Simplify PI into PI 68.008 * [backup-simplify]: Simplify (* n PI) into (* n PI) 68.008 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 68.008 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 68.008 * [backup-simplify]: Simplify (* 1/2 0) into 0 68.009 * [backup-simplify]: Simplify (- 0) into 0 68.009 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 68.009 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 68.009 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 68.009 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 68.009 * [taylor]: Taking taylor expansion of (/ 1 k) in k 68.009 * [taylor]: Taking taylor expansion of k in k 68.009 * [backup-simplify]: Simplify 0 into 0 68.009 * [backup-simplify]: Simplify 1 into 1 68.010 * [backup-simplify]: Simplify (/ 1 1) into 1 68.010 * [backup-simplify]: Simplify (sqrt 0) into 0 68.011 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 68.012 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0 68.012 * [taylor]: Taking taylor expansion of 0 in n 68.012 * [backup-simplify]: Simplify 0 into 0 68.012 * [backup-simplify]: Simplify 0 into 0 68.012 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 68.013 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0 68.013 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0 68.014 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 68.014 * [backup-simplify]: Simplify (- 1/2) into -1/2 68.014 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 68.014 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI))))) 68.015 * [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))))) 68.015 * [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))))) 68.015 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 68.015 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 68.015 * [taylor]: Taking taylor expansion of +nan.0 in n 68.015 * [backup-simplify]: Simplify +nan.0 into +nan.0 68.015 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 68.015 * [taylor]: Taking taylor expansion of (sqrt 2) in n 68.015 * [taylor]: Taking taylor expansion of 2 in n 68.015 * [backup-simplify]: Simplify 2 into 2 68.015 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 68.016 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 68.016 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 68.016 * [taylor]: Taking taylor expansion of (* n PI) in n 68.016 * [taylor]: Taking taylor expansion of n in n 68.016 * [backup-simplify]: Simplify 0 into 0 68.016 * [backup-simplify]: Simplify 1 into 1 68.016 * [taylor]: Taking taylor expansion of PI in n 68.016 * [backup-simplify]: Simplify PI into PI 68.016 * [backup-simplify]: Simplify (* 0 PI) into 0 68.017 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 68.017 * [backup-simplify]: Simplify (sqrt 0) into 0 68.018 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 68.019 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 68.019 * [backup-simplify]: Simplify (* +nan.0 0) into 0 68.019 * [backup-simplify]: Simplify (- 0) into 0 68.019 * [backup-simplify]: Simplify 0 into 0 68.019 * [backup-simplify]: Simplify 0 into 0 68.020 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 68.021 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 68.022 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 68.023 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 68.024 * [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 68.024 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 68.025 * [backup-simplify]: Simplify (- 0) into 0 68.025 * [backup-simplify]: Simplify (+ 0 0) into 0 68.025 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0 68.026 * [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))) 68.026 * [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))))))) 68.026 * [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 68.026 * [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 68.026 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 68.027 * [taylor]: Taking taylor expansion of +nan.0 in n 68.027 * [backup-simplify]: Simplify +nan.0 into +nan.0 68.027 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 68.027 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 68.027 * [taylor]: Taking taylor expansion of (sqrt 2) in n 68.027 * [taylor]: Taking taylor expansion of 2 in n 68.027 * [backup-simplify]: Simplify 2 into 2 68.027 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 68.027 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 68.027 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 68.027 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 68.027 * [taylor]: Taking taylor expansion of 2 in n 68.027 * [backup-simplify]: Simplify 2 into 2 68.027 * [taylor]: Taking taylor expansion of (* n PI) in n 68.027 * [taylor]: Taking taylor expansion of n in n 68.027 * [backup-simplify]: Simplify 0 into 0 68.027 * [backup-simplify]: Simplify 1 into 1 68.027 * [taylor]: Taking taylor expansion of PI in n 68.027 * [backup-simplify]: Simplify PI into PI 68.028 * [backup-simplify]: Simplify (* 0 PI) into 0 68.028 * [backup-simplify]: Simplify (* 2 0) into 0 68.029 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 68.030 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 68.031 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.031 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 68.031 * [taylor]: Taking taylor expansion of (* n PI) in n 68.031 * [taylor]: Taking taylor expansion of n in n 68.031 * [backup-simplify]: Simplify 0 into 0 68.031 * [backup-simplify]: Simplify 1 into 1 68.031 * [taylor]: Taking taylor expansion of PI in n 68.031 * [backup-simplify]: Simplify PI into PI 68.032 * [backup-simplify]: Simplify (* 0 PI) into 0 68.033 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 68.034 * [backup-simplify]: Simplify (sqrt 0) into 0 68.034 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 68.034 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n 68.034 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 68.034 * [taylor]: Taking taylor expansion of +nan.0 in n 68.034 * [backup-simplify]: Simplify +nan.0 into +nan.0 68.034 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 68.034 * [taylor]: Taking taylor expansion of (sqrt 2) in n 68.034 * [taylor]: Taking taylor expansion of 2 in n 68.034 * [backup-simplify]: Simplify 2 into 2 68.035 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 68.035 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 68.035 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 68.035 * [taylor]: Taking taylor expansion of (* n PI) in n 68.035 * [taylor]: Taking taylor expansion of n in n 68.035 * [backup-simplify]: Simplify 0 into 0 68.035 * [backup-simplify]: Simplify 1 into 1 68.035 * [taylor]: Taking taylor expansion of PI in n 68.035 * [backup-simplify]: Simplify PI into PI 68.036 * [backup-simplify]: Simplify (* 0 PI) into 0 68.036 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 68.037 * [backup-simplify]: Simplify (sqrt 0) into 0 68.038 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 68.038 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 68.039 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 68.040 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 68.040 * [backup-simplify]: Simplify (* +nan.0 0) into 0 68.041 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 68.041 * [backup-simplify]: Simplify (* +nan.0 0) into 0 68.041 * [backup-simplify]: Simplify (- 0) into 0 68.042 * [backup-simplify]: Simplify (+ 0 0) into 0 68.042 * [backup-simplify]: Simplify (- 0) into 0 68.042 * [backup-simplify]: Simplify 0 into 0 68.044 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 68.047 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 68.049 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 68.051 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI))) 68.051 * [backup-simplify]: Simplify 0 into 0 68.051 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 68.054 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 68.054 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 68.055 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 68.057 * [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 68.058 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0 68.058 * [backup-simplify]: Simplify (- 0) into 0 68.059 * [backup-simplify]: Simplify (+ 0 0) into 0 68.060 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0 68.061 * [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))) 68.062 * [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))))))))) 68.062 * [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 68.062 * [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 68.062 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n 68.062 * [taylor]: Taking taylor expansion of +nan.0 in n 68.062 * [backup-simplify]: Simplify +nan.0 into +nan.0 68.062 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n 68.062 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n 68.062 * [taylor]: Taking taylor expansion of (sqrt 2) in n 68.062 * [taylor]: Taking taylor expansion of 2 in n 68.062 * [backup-simplify]: Simplify 2 into 2 68.063 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 68.063 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 68.063 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 68.063 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 68.063 * [taylor]: Taking taylor expansion of 2 in n 68.063 * [backup-simplify]: Simplify 2 into 2 68.063 * [taylor]: Taking taylor expansion of (* n PI) in n 68.063 * [taylor]: Taking taylor expansion of n in n 68.063 * [backup-simplify]: Simplify 0 into 0 68.063 * [backup-simplify]: Simplify 1 into 1 68.063 * [taylor]: Taking taylor expansion of PI in n 68.063 * [backup-simplify]: Simplify PI into PI 68.063 * [backup-simplify]: Simplify (* 0 PI) into 0 68.064 * [backup-simplify]: Simplify (* 2 0) into 0 68.065 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 68.066 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 68.066 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.066 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 68.066 * [taylor]: Taking taylor expansion of (* n PI) in n 68.066 * [taylor]: Taking taylor expansion of n in n 68.066 * [backup-simplify]: Simplify 0 into 0 68.066 * [backup-simplify]: Simplify 1 into 1 68.066 * [taylor]: Taking taylor expansion of PI in n 68.066 * [backup-simplify]: Simplify PI into PI 68.067 * [backup-simplify]: Simplify (* 0 PI) into 0 68.068 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 68.068 * [backup-simplify]: Simplify (sqrt 0) into 0 68.069 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 68.069 * [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 68.069 * [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 68.069 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n 68.069 * [taylor]: Taking taylor expansion of +nan.0 in n 68.069 * [backup-simplify]: Simplify +nan.0 into +nan.0 68.069 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n 68.069 * [taylor]: Taking taylor expansion of (sqrt 2) in n 68.069 * [taylor]: Taking taylor expansion of 2 in n 68.069 * [backup-simplify]: Simplify 2 into 2 68.069 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 68.070 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 68.070 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 68.070 * [taylor]: Taking taylor expansion of (* n PI) in n 68.070 * [taylor]: Taking taylor expansion of n in n 68.070 * [backup-simplify]: Simplify 0 into 0 68.070 * [backup-simplify]: Simplify 1 into 1 68.070 * [taylor]: Taking taylor expansion of PI in n 68.070 * [backup-simplify]: Simplify PI into PI 68.070 * [backup-simplify]: Simplify (* 0 PI) into 0 68.077 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 68.077 * [backup-simplify]: Simplify (sqrt 0) into 0 68.078 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 68.078 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n 68.078 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n 68.078 * [taylor]: Taking taylor expansion of +nan.0 in n 68.078 * [backup-simplify]: Simplify +nan.0 into +nan.0 68.078 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n 68.078 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n 68.078 * [taylor]: Taking taylor expansion of (sqrt 2) in n 68.078 * [taylor]: Taking taylor expansion of 2 in n 68.078 * [backup-simplify]: Simplify 2 into 2 68.079 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2) 68.079 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0 68.079 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n 68.079 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 68.079 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 68.079 * [taylor]: Taking taylor expansion of 2 in n 68.079 * [backup-simplify]: Simplify 2 into 2 68.079 * [taylor]: Taking taylor expansion of (* n PI) in n 68.079 * [taylor]: Taking taylor expansion of n in n 68.079 * [backup-simplify]: Simplify 0 into 0 68.079 * [backup-simplify]: Simplify 1 into 1 68.079 * [taylor]: Taking taylor expansion of PI in n 68.079 * [backup-simplify]: Simplify PI into PI 68.080 * [backup-simplify]: Simplify (* 0 PI) into 0 68.080 * [backup-simplify]: Simplify (* 2 0) into 0 68.081 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 68.082 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 68.082 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.083 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 68.083 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n 68.083 * [taylor]: Taking taylor expansion of (* n PI) in n 68.083 * [taylor]: Taking taylor expansion of n in n 68.083 * [backup-simplify]: Simplify 0 into 0 68.083 * [backup-simplify]: Simplify 1 into 1 68.083 * [taylor]: Taking taylor expansion of PI in n 68.083 * [backup-simplify]: Simplify PI into PI 68.084 * [backup-simplify]: Simplify (* 0 PI) into 0 68.085 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 68.085 * [backup-simplify]: Simplify (sqrt 0) into 0 68.086 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI) 68.087 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 68.088 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 68.089 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0 68.089 * [backup-simplify]: Simplify (* +nan.0 0) into 0 68.089 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0 68.089 * [backup-simplify]: Simplify (* +nan.0 0) into 0 68.090 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 68.091 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 68.093 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2) 68.094 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 68.095 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0 68.095 * [backup-simplify]: Simplify (* +nan.0 0) into 0 68.095 * [backup-simplify]: Simplify (- 0) into 0 68.096 * [backup-simplify]: Simplify (+ 0 0) into 0 68.096 * [backup-simplify]: Simplify (- 0) into 0 68.096 * [backup-simplify]: Simplify (+ 0 0) into 0 68.096 * [backup-simplify]: Simplify (- 0) into 0 68.096 * [backup-simplify]: Simplify 0 into 0 68.097 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 68.098 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 68.100 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 68.101 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 68.103 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 68.105 * [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)))))))) 68.112 * [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)))))))) 68.115 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 68.120 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI))) 68.123 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI))) 68.129 * [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)))))))))) 68.134 * [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))))))) 68.139 * [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))))))) 68.139 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 68.142 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2)) 68.143 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0 68.146 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 68.151 * [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)))) 68.155 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 68.159 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) 68.174 * [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))))))))))))) 68.174 * [backup-simplify]: Simplify (/ (pow (/ 1 k) (- 1/2)) (/ 1 (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))))) into (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) 68.174 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in (k n) around 0 68.174 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in n 68.175 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 68.175 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 68.175 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 68.175 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 68.175 * [taylor]: Taking taylor expansion of 1/2 in n 68.175 * [backup-simplify]: Simplify 1/2 into 1/2 68.175 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 68.175 * [taylor]: Taking taylor expansion of 1/2 in n 68.175 * [backup-simplify]: Simplify 1/2 into 1/2 68.175 * [taylor]: Taking taylor expansion of (/ 1 k) in n 68.175 * [taylor]: Taking taylor expansion of k in n 68.175 * [backup-simplify]: Simplify k into k 68.175 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 68.175 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 68.175 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 68.175 * [taylor]: Taking taylor expansion of 2 in n 68.175 * [backup-simplify]: Simplify 2 into 2 68.175 * [taylor]: Taking taylor expansion of (/ PI n) in n 68.175 * [taylor]: Taking taylor expansion of PI in n 68.175 * [backup-simplify]: Simplify PI into PI 68.175 * [taylor]: Taking taylor expansion of n in n 68.175 * [backup-simplify]: Simplify 0 into 0 68.175 * [backup-simplify]: Simplify 1 into 1 68.176 * [backup-simplify]: Simplify (/ PI 1) into PI 68.176 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 68.177 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.178 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 68.178 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 68.178 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 68.179 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 68.181 * [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))) 68.191 * [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)))) 68.191 * [taylor]: Taking taylor expansion of (sqrt k) in n 68.191 * [taylor]: Taking taylor expansion of k in n 68.191 * [backup-simplify]: Simplify k into k 68.191 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 68.191 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 68.191 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 68.191 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 68.191 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 68.191 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 68.191 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 68.191 * [taylor]: Taking taylor expansion of 1/2 in k 68.191 * [backup-simplify]: Simplify 1/2 into 1/2 68.191 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 68.191 * [taylor]: Taking taylor expansion of 1/2 in k 68.191 * [backup-simplify]: Simplify 1/2 into 1/2 68.191 * [taylor]: Taking taylor expansion of (/ 1 k) in k 68.191 * [taylor]: Taking taylor expansion of k in k 68.191 * [backup-simplify]: Simplify 0 into 0 68.191 * [backup-simplify]: Simplify 1 into 1 68.192 * [backup-simplify]: Simplify (/ 1 1) into 1 68.192 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 68.192 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 68.192 * [taylor]: Taking taylor expansion of 2 in k 68.192 * [backup-simplify]: Simplify 2 into 2 68.192 * [taylor]: Taking taylor expansion of (/ PI n) in k 68.192 * [taylor]: Taking taylor expansion of PI in k 68.192 * [backup-simplify]: Simplify PI into PI 68.192 * [taylor]: Taking taylor expansion of n in k 68.192 * [backup-simplify]: Simplify n into n 68.192 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 68.192 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 68.192 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 68.193 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 68.193 * [backup-simplify]: Simplify (- 1/2) into -1/2 68.194 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 68.194 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 68.194 * [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)))) 68.194 * [taylor]: Taking taylor expansion of (sqrt k) in k 68.194 * [taylor]: Taking taylor expansion of k in k 68.194 * [backup-simplify]: Simplify 0 into 0 68.194 * [backup-simplify]: Simplify 1 into 1 68.194 * [backup-simplify]: Simplify (sqrt 0) into 0 68.196 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 68.196 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) (sqrt k)) in k 68.196 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 68.196 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 68.196 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 68.196 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 68.196 * [taylor]: Taking taylor expansion of 1/2 in k 68.196 * [backup-simplify]: Simplify 1/2 into 1/2 68.196 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 68.196 * [taylor]: Taking taylor expansion of 1/2 in k 68.196 * [backup-simplify]: Simplify 1/2 into 1/2 68.196 * [taylor]: Taking taylor expansion of (/ 1 k) in k 68.196 * [taylor]: Taking taylor expansion of k in k 68.196 * [backup-simplify]: Simplify 0 into 0 68.196 * [backup-simplify]: Simplify 1 into 1 68.197 * [backup-simplify]: Simplify (/ 1 1) into 1 68.197 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 68.197 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 68.197 * [taylor]: Taking taylor expansion of 2 in k 68.197 * [backup-simplify]: Simplify 2 into 2 68.197 * [taylor]: Taking taylor expansion of (/ PI n) in k 68.197 * [taylor]: Taking taylor expansion of PI in k 68.197 * [backup-simplify]: Simplify PI into PI 68.197 * [taylor]: Taking taylor expansion of n in k 68.197 * [backup-simplify]: Simplify n into n 68.197 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 68.197 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 68.197 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 68.197 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 68.198 * [backup-simplify]: Simplify (- 1/2) into -1/2 68.198 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 68.198 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 68.199 * [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)))) 68.199 * [taylor]: Taking taylor expansion of (sqrt k) in k 68.199 * [taylor]: Taking taylor expansion of k in k 68.199 * [backup-simplify]: Simplify 0 into 0 68.199 * [backup-simplify]: Simplify 1 into 1 68.199 * [backup-simplify]: Simplify (sqrt 0) into 0 68.200 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 68.201 * [backup-simplify]: Simplify (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 0) into 0 68.201 * [taylor]: Taking taylor expansion of 0 in n 68.201 * [backup-simplify]: Simplify 0 into 0 68.201 * [backup-simplify]: Simplify 0 into 0 68.201 * [backup-simplify]: Simplify (+ (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (* 0 0)) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 68.201 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 68.201 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 68.201 * [taylor]: Taking taylor expansion of +nan.0 in n 68.201 * [backup-simplify]: Simplify +nan.0 into +nan.0 68.201 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 68.201 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 68.201 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 68.201 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 68.201 * [taylor]: Taking taylor expansion of 1/2 in n 68.202 * [backup-simplify]: Simplify 1/2 into 1/2 68.202 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 68.202 * [taylor]: Taking taylor expansion of 1/2 in n 68.202 * [backup-simplify]: Simplify 1/2 into 1/2 68.202 * [taylor]: Taking taylor expansion of (/ 1 k) in n 68.202 * [taylor]: Taking taylor expansion of k in n 68.202 * [backup-simplify]: Simplify k into k 68.202 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 68.202 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 68.202 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 68.202 * [taylor]: Taking taylor expansion of 2 in n 68.202 * [backup-simplify]: Simplify 2 into 2 68.202 * [taylor]: Taking taylor expansion of (/ PI n) in n 68.202 * [taylor]: Taking taylor expansion of PI in n 68.202 * [backup-simplify]: Simplify PI into PI 68.202 * [taylor]: Taking taylor expansion of n in n 68.202 * [backup-simplify]: Simplify 0 into 0 68.202 * [backup-simplify]: Simplify 1 into 1 68.202 * [backup-simplify]: Simplify (/ PI 1) into PI 68.203 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 68.204 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.204 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 68.204 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 68.204 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 68.205 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 68.206 * [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))) 68.207 * [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)))) 68.208 * [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))))) 68.208 * [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)))))) 68.209 * [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)))))) 68.209 * [backup-simplify]: Simplify 0 into 0 68.211 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 68.211 * [backup-simplify]: Simplify (+ (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 68.211 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 68.211 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 68.211 * [taylor]: Taking taylor expansion of +nan.0 in n 68.211 * [backup-simplify]: Simplify +nan.0 into +nan.0 68.211 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 68.211 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 68.211 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 68.212 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 68.212 * [taylor]: Taking taylor expansion of 1/2 in n 68.212 * [backup-simplify]: Simplify 1/2 into 1/2 68.212 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 68.212 * [taylor]: Taking taylor expansion of 1/2 in n 68.212 * [backup-simplify]: Simplify 1/2 into 1/2 68.212 * [taylor]: Taking taylor expansion of (/ 1 k) in n 68.212 * [taylor]: Taking taylor expansion of k in n 68.212 * [backup-simplify]: Simplify k into k 68.212 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 68.212 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 68.212 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 68.212 * [taylor]: Taking taylor expansion of 2 in n 68.212 * [backup-simplify]: Simplify 2 into 2 68.212 * [taylor]: Taking taylor expansion of (/ PI n) in n 68.212 * [taylor]: Taking taylor expansion of PI in n 68.212 * [backup-simplify]: Simplify PI into PI 68.212 * [taylor]: Taking taylor expansion of n in n 68.212 * [backup-simplify]: Simplify 0 into 0 68.212 * [backup-simplify]: Simplify 1 into 1 68.212 * [backup-simplify]: Simplify (/ PI 1) into PI 68.212 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 68.213 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.213 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 68.213 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 68.213 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 68.214 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 68.215 * [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))) 68.216 * [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)))) 68.216 * [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))))) 68.217 * [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)))))) 68.218 * [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)))))) 68.218 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 68.219 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 68.220 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 68.220 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 68.220 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 68.221 * [backup-simplify]: Simplify (- 0) into 0 68.221 * [backup-simplify]: Simplify (+ 0 0) into 0 68.222 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 68.222 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 68.224 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 68.225 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0 68.225 * [backup-simplify]: Simplify (- 0) into 0 68.225 * [backup-simplify]: Simplify 0 into 0 68.225 * [backup-simplify]: Simplify 0 into 0 68.227 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 68.228 * [backup-simplify]: Simplify (+ (* (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) 68.228 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))) in n 68.228 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 68.228 * [taylor]: Taking taylor expansion of +nan.0 in n 68.228 * [backup-simplify]: Simplify +nan.0 into +nan.0 68.228 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 68.228 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 68.228 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 68.228 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 68.228 * [taylor]: Taking taylor expansion of 1/2 in n 68.228 * [backup-simplify]: Simplify 1/2 into 1/2 68.228 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 68.228 * [taylor]: Taking taylor expansion of 1/2 in n 68.228 * [backup-simplify]: Simplify 1/2 into 1/2 68.228 * [taylor]: Taking taylor expansion of (/ 1 k) in n 68.228 * [taylor]: Taking taylor expansion of k in n 68.228 * [backup-simplify]: Simplify k into k 68.228 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 68.228 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 68.228 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 68.228 * [taylor]: Taking taylor expansion of 2 in n 68.228 * [backup-simplify]: Simplify 2 into 2 68.228 * [taylor]: Taking taylor expansion of (/ PI n) in n 68.228 * [taylor]: Taking taylor expansion of PI in n 68.228 * [backup-simplify]: Simplify PI into PI 68.228 * [taylor]: Taking taylor expansion of n in n 68.228 * [backup-simplify]: Simplify 0 into 0 68.228 * [backup-simplify]: Simplify 1 into 1 68.229 * [backup-simplify]: Simplify (/ PI 1) into PI 68.229 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 68.230 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.230 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 68.230 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 68.230 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 68.232 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 68.233 * [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))) 68.234 * [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)))) 68.235 * [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))))) 68.236 * [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)))))) 68.238 * [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)))))) 68.242 * [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)))))))) 68.243 * [backup-simplify]: Simplify (/ (pow (/ 1 (- k)) (- 1/2)) (/ 1 (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))))) into (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 68.243 * [approximate]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (k n) around 0 68.243 * [taylor]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 68.243 * [taylor]: Taking taylor expansion of (sqrt (/ k -1)) in n 68.243 * [taylor]: Taking taylor expansion of (/ k -1) in n 68.243 * [taylor]: Taking taylor expansion of k in n 68.244 * [backup-simplify]: Simplify k into k 68.244 * [taylor]: Taking taylor expansion of -1 in n 68.244 * [backup-simplify]: Simplify -1 into -1 68.244 * [backup-simplify]: Simplify (/ k -1) into (* -1 k) 68.244 * [backup-simplify]: Simplify (sqrt (* -1 k)) into (sqrt (* -1 k)) 68.245 * [backup-simplify]: Simplify (- (/ 0 -1) (+ (* (* -1 k) (/ 0 -1)))) into 0 68.245 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (* -1 k)))) into 0 68.245 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 68.245 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 68.245 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 68.245 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 68.245 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 68.245 * [taylor]: Taking taylor expansion of 1/2 in n 68.245 * [backup-simplify]: Simplify 1/2 into 1/2 68.245 * [taylor]: Taking taylor expansion of (/ 1 k) in n 68.245 * [taylor]: Taking taylor expansion of k in n 68.245 * [backup-simplify]: Simplify k into k 68.245 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 68.245 * [taylor]: Taking taylor expansion of 1/2 in n 68.245 * [backup-simplify]: Simplify 1/2 into 1/2 68.245 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 68.245 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 68.245 * [taylor]: Taking taylor expansion of -2 in n 68.245 * [backup-simplify]: Simplify -2 into -2 68.245 * [taylor]: Taking taylor expansion of (/ PI n) in n 68.245 * [taylor]: Taking taylor expansion of PI in n 68.245 * [backup-simplify]: Simplify PI into PI 68.245 * [taylor]: Taking taylor expansion of n in n 68.245 * [backup-simplify]: Simplify 0 into 0 68.245 * [backup-simplify]: Simplify 1 into 1 68.245 * [backup-simplify]: Simplify (/ PI 1) into PI 68.246 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 68.246 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 68.247 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 68.247 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 68.247 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 68.248 * [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))) 68.249 * [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)))) 68.249 * [taylor]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 68.249 * [taylor]: Taking taylor expansion of (sqrt (/ k -1)) in k 68.249 * [taylor]: Taking taylor expansion of (/ k -1) in k 68.249 * [taylor]: Taking taylor expansion of k in k 68.249 * [backup-simplify]: Simplify 0 into 0 68.249 * [backup-simplify]: Simplify 1 into 1 68.249 * [taylor]: Taking taylor expansion of -1 in k 68.249 * [backup-simplify]: Simplify -1 into -1 68.249 * [backup-simplify]: Simplify (/ 1 -1) into -1 68.250 * [backup-simplify]: Simplify (sqrt 0) into 0 68.250 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 68.250 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 68.250 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 68.250 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 68.251 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 68.251 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 68.251 * [taylor]: Taking taylor expansion of 1/2 in k 68.251 * [backup-simplify]: Simplify 1/2 into 1/2 68.251 * [taylor]: Taking taylor expansion of (/ 1 k) in k 68.251 * [taylor]: Taking taylor expansion of k in k 68.251 * [backup-simplify]: Simplify 0 into 0 68.251 * [backup-simplify]: Simplify 1 into 1 68.251 * [backup-simplify]: Simplify (/ 1 1) into 1 68.251 * [taylor]: Taking taylor expansion of 1/2 in k 68.251 * [backup-simplify]: Simplify 1/2 into 1/2 68.251 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 68.251 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 68.251 * [taylor]: Taking taylor expansion of -2 in k 68.251 * [backup-simplify]: Simplify -2 into -2 68.251 * [taylor]: Taking taylor expansion of (/ PI n) in k 68.251 * [taylor]: Taking taylor expansion of PI in k 68.251 * [backup-simplify]: Simplify PI into PI 68.251 * [taylor]: Taking taylor expansion of n in k 68.251 * [backup-simplify]: Simplify n into n 68.251 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 68.251 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 68.251 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 68.251 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 68.252 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 68.252 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 68.252 * [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))) 68.252 * [taylor]: Taking taylor expansion of (* (sqrt (/ k -1)) (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 68.252 * [taylor]: Taking taylor expansion of (sqrt (/ k -1)) in k 68.252 * [taylor]: Taking taylor expansion of (/ k -1) in k 68.252 * [taylor]: Taking taylor expansion of k in k 68.252 * [backup-simplify]: Simplify 0 into 0 68.252 * [backup-simplify]: Simplify 1 into 1 68.252 * [taylor]: Taking taylor expansion of -1 in k 68.252 * [backup-simplify]: Simplify -1 into -1 68.252 * [backup-simplify]: Simplify (/ 1 -1) into -1 68.253 * [backup-simplify]: Simplify (sqrt 0) into 0 68.253 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 68.253 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 68.253 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 68.253 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 68.253 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 68.253 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 68.254 * [taylor]: Taking taylor expansion of 1/2 in k 68.254 * [backup-simplify]: Simplify 1/2 into 1/2 68.254 * [taylor]: Taking taylor expansion of (/ 1 k) in k 68.254 * [taylor]: Taking taylor expansion of k in k 68.254 * [backup-simplify]: Simplify 0 into 0 68.254 * [backup-simplify]: Simplify 1 into 1 68.254 * [backup-simplify]: Simplify (/ 1 1) into 1 68.254 * [taylor]: Taking taylor expansion of 1/2 in k 68.254 * [backup-simplify]: Simplify 1/2 into 1/2 68.254 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 68.254 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 68.254 * [taylor]: Taking taylor expansion of -2 in k 68.254 * [backup-simplify]: Simplify -2 into -2 68.254 * [taylor]: Taking taylor expansion of (/ PI n) in k 68.254 * [taylor]: Taking taylor expansion of PI in k 68.254 * [backup-simplify]: Simplify PI into PI 68.254 * [taylor]: Taking taylor expansion of n in k 68.254 * [backup-simplify]: Simplify n into n 68.254 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 68.254 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 68.254 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 68.254 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 68.255 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 68.255 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 68.255 * [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))) 68.255 * [backup-simplify]: Simplify (* 0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into 0 68.255 * [taylor]: Taking taylor expansion of 0 in n 68.255 * [backup-simplify]: Simplify 0 into 0 68.255 * [backup-simplify]: Simplify 0 into 0 68.255 * [backup-simplify]: Simplify (+ (* 0 0) (* +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))))) 68.256 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 68.256 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 68.256 * [taylor]: Taking taylor expansion of +nan.0 in n 68.256 * [backup-simplify]: Simplify +nan.0 into +nan.0 68.256 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 68.256 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 68.256 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 68.256 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 68.256 * [taylor]: Taking taylor expansion of -2 in n 68.256 * [backup-simplify]: Simplify -2 into -2 68.256 * [taylor]: Taking taylor expansion of (/ PI n) in n 68.256 * [taylor]: Taking taylor expansion of PI in n 68.256 * [backup-simplify]: Simplify PI into PI 68.256 * [taylor]: Taking taylor expansion of n in n 68.256 * [backup-simplify]: Simplify 0 into 0 68.256 * [backup-simplify]: Simplify 1 into 1 68.256 * [backup-simplify]: Simplify (/ PI 1) into PI 68.256 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 68.257 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 68.257 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 68.257 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 68.257 * [taylor]: Taking taylor expansion of 1/2 in n 68.257 * [backup-simplify]: Simplify 1/2 into 1/2 68.257 * [taylor]: Taking taylor expansion of (/ 1 k) in n 68.257 * [taylor]: Taking taylor expansion of k in n 68.257 * [backup-simplify]: Simplify k into k 68.257 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 68.257 * [taylor]: Taking taylor expansion of 1/2 in n 68.257 * [backup-simplify]: Simplify 1/2 into 1/2 68.258 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 68.258 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 68.258 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 68.259 * [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))) 68.260 * [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)))) 68.260 * [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))))) 68.261 * [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)))))) 68.262 * [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)))))) 68.262 * [backup-simplify]: Simplify 0 into 0 68.262 * [backup-simplify]: Simplify (- (/ 0 -1) (+ (* -1 (/ 0 -1)))) into 0 68.264 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 68.265 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +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))))) 68.265 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 68.265 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 68.265 * [taylor]: Taking taylor expansion of +nan.0 in n 68.265 * [backup-simplify]: Simplify +nan.0 into +nan.0 68.265 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 68.265 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 68.265 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 68.265 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 68.265 * [taylor]: Taking taylor expansion of -2 in n 68.265 * [backup-simplify]: Simplify -2 into -2 68.265 * [taylor]: Taking taylor expansion of (/ PI n) in n 68.265 * [taylor]: Taking taylor expansion of PI in n 68.265 * [backup-simplify]: Simplify PI into PI 68.265 * [taylor]: Taking taylor expansion of n in n 68.265 * [backup-simplify]: Simplify 0 into 0 68.265 * [backup-simplify]: Simplify 1 into 1 68.265 * [backup-simplify]: Simplify (/ PI 1) into PI 68.266 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 68.266 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 68.266 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 68.266 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 68.266 * [taylor]: Taking taylor expansion of 1/2 in n 68.266 * [backup-simplify]: Simplify 1/2 into 1/2 68.267 * [taylor]: Taking taylor expansion of (/ 1 k) in n 68.267 * [taylor]: Taking taylor expansion of k in n 68.267 * [backup-simplify]: Simplify k into k 68.267 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 68.267 * [taylor]: Taking taylor expansion of 1/2 in n 68.267 * [backup-simplify]: Simplify 1/2 into 1/2 68.267 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 68.268 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 68.268 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 68.268 * [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))) 68.269 * [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)))) 68.270 * [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))))) 68.271 * [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)))))) 68.271 * [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)))))) 68.272 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 68.272 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 68.273 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 68.273 * [backup-simplify]: Simplify (+ 0 0) into 0 68.273 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 68.274 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 68.275 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 68.276 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0 68.277 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 68.278 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into 0 68.279 * [backup-simplify]: Simplify (- 0) into 0 68.279 * [backup-simplify]: Simplify 0 into 0 68.279 * [backup-simplify]: Simplify 0 into 0 68.280 * [backup-simplify]: Simplify (- (/ 0 -1) (+ (* -1 (/ 0 -1)) (* 0 (/ 0 -1)))) into 0 68.284 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 68.286 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +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))))) 68.286 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))) in n 68.286 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) in n 68.286 * [taylor]: Taking taylor expansion of +nan.0 in n 68.286 * [backup-simplify]: Simplify +nan.0 into +nan.0 68.286 * [taylor]: Taking taylor expansion of (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) in n 68.286 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)) in n 68.286 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 68.286 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 68.287 * [taylor]: Taking taylor expansion of -2 in n 68.287 * [backup-simplify]: Simplify -2 into -2 68.287 * [taylor]: Taking taylor expansion of (/ PI n) in n 68.287 * [taylor]: Taking taylor expansion of PI in n 68.287 * [backup-simplify]: Simplify PI into PI 68.287 * [taylor]: Taking taylor expansion of n in n 68.287 * [backup-simplify]: Simplify 0 into 0 68.287 * [backup-simplify]: Simplify 1 into 1 68.287 * [backup-simplify]: Simplify (/ PI 1) into PI 68.288 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 68.289 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 68.289 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 68.289 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 68.289 * [taylor]: Taking taylor expansion of 1/2 in n 68.289 * [backup-simplify]: Simplify 1/2 into 1/2 68.289 * [taylor]: Taking taylor expansion of (/ 1 k) in n 68.289 * [taylor]: Taking taylor expansion of k in n 68.289 * [backup-simplify]: Simplify k into k 68.289 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 68.289 * [taylor]: Taking taylor expansion of 1/2 in n 68.289 * [backup-simplify]: Simplify 1/2 into 1/2 68.291 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 68.291 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 68.291 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 68.292 * [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))) 68.295 * [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)))) 68.296 * [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))))) 68.298 * [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)))))) 68.306 * [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)))))) 68.311 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* 1 (/ 1 (- k))) 3)) (+ (* (- (* +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)))))) 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 3))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))))))) 68.312 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2) 68.312 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) 68.312 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0 68.312 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 68.312 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 68.312 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 68.312 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 68.312 * [taylor]: Taking taylor expansion of 1/2 in k 68.312 * [backup-simplify]: Simplify 1/2 into 1/2 68.312 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 68.312 * [taylor]: Taking taylor expansion of 1/2 in k 68.312 * [backup-simplify]: Simplify 1/2 into 1/2 68.312 * [taylor]: Taking taylor expansion of k in k 68.312 * [backup-simplify]: Simplify 0 into 0 68.312 * [backup-simplify]: Simplify 1 into 1 68.312 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 68.312 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 68.312 * [taylor]: Taking taylor expansion of 2 in k 68.312 * [backup-simplify]: Simplify 2 into 2 68.312 * [taylor]: Taking taylor expansion of (* n PI) in k 68.312 * [taylor]: Taking taylor expansion of n in k 68.312 * [backup-simplify]: Simplify n into n 68.312 * [taylor]: Taking taylor expansion of PI in k 68.312 * [backup-simplify]: Simplify PI into PI 68.312 * [backup-simplify]: Simplify (* n PI) into (* n PI) 68.312 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 68.313 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 68.313 * [backup-simplify]: Simplify (* 1/2 0) into 0 68.314 * [backup-simplify]: Simplify (- 0) into 0 68.314 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 68.314 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 68.314 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 68.314 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 68.314 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 68.314 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 68.314 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 68.314 * [taylor]: Taking taylor expansion of 1/2 in n 68.314 * [backup-simplify]: Simplify 1/2 into 1/2 68.314 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 68.314 * [taylor]: Taking taylor expansion of 1/2 in n 68.315 * [backup-simplify]: Simplify 1/2 into 1/2 68.315 * [taylor]: Taking taylor expansion of k in n 68.315 * [backup-simplify]: Simplify k into k 68.315 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 68.315 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 68.315 * [taylor]: Taking taylor expansion of 2 in n 68.315 * [backup-simplify]: Simplify 2 into 2 68.315 * [taylor]: Taking taylor expansion of (* n PI) in n 68.315 * [taylor]: Taking taylor expansion of n in n 68.315 * [backup-simplify]: Simplify 0 into 0 68.315 * [backup-simplify]: Simplify 1 into 1 68.315 * [taylor]: Taking taylor expansion of PI in n 68.315 * [backup-simplify]: Simplify PI into PI 68.316 * [backup-simplify]: Simplify (* 0 PI) into 0 68.316 * [backup-simplify]: Simplify (* 2 0) into 0 68.318 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 68.319 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 68.320 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.321 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 68.321 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 68.321 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 68.322 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 68.323 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 68.324 * [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))))) 68.324 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 68.324 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 68.324 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 68.324 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 68.324 * [taylor]: Taking taylor expansion of 1/2 in n 68.324 * [backup-simplify]: Simplify 1/2 into 1/2 68.325 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 68.325 * [taylor]: Taking taylor expansion of 1/2 in n 68.325 * [backup-simplify]: Simplify 1/2 into 1/2 68.325 * [taylor]: Taking taylor expansion of k in n 68.325 * [backup-simplify]: Simplify k into k 68.325 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 68.325 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 68.325 * [taylor]: Taking taylor expansion of 2 in n 68.325 * [backup-simplify]: Simplify 2 into 2 68.325 * [taylor]: Taking taylor expansion of (* n PI) in n 68.325 * [taylor]: Taking taylor expansion of n in n 68.325 * [backup-simplify]: Simplify 0 into 0 68.325 * [backup-simplify]: Simplify 1 into 1 68.325 * [taylor]: Taking taylor expansion of PI in n 68.325 * [backup-simplify]: Simplify PI into PI 68.325 * [backup-simplify]: Simplify (* 0 PI) into 0 68.326 * [backup-simplify]: Simplify (* 2 0) into 0 68.327 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 68.329 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 68.330 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.330 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 68.330 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 68.330 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 68.331 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 68.332 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 68.334 * [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))))) 68.334 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 68.334 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 68.334 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 68.334 * [taylor]: Taking taylor expansion of 1/2 in k 68.334 * [backup-simplify]: Simplify 1/2 into 1/2 68.334 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 68.334 * [taylor]: Taking taylor expansion of 1/2 in k 68.334 * [backup-simplify]: Simplify 1/2 into 1/2 68.334 * [taylor]: Taking taylor expansion of k in k 68.334 * [backup-simplify]: Simplify 0 into 0 68.334 * [backup-simplify]: Simplify 1 into 1 68.334 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 68.334 * [taylor]: Taking taylor expansion of (log n) in k 68.334 * [taylor]: Taking taylor expansion of n in k 68.334 * [backup-simplify]: Simplify n into n 68.334 * [backup-simplify]: Simplify (log n) into (log n) 68.334 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 68.334 * [taylor]: Taking taylor expansion of (* 2 PI) in k 68.334 * [taylor]: Taking taylor expansion of 2 in k 68.334 * [backup-simplify]: Simplify 2 into 2 68.334 * [taylor]: Taking taylor expansion of PI in k 68.334 * [backup-simplify]: Simplify PI into PI 68.335 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 68.336 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.336 * [backup-simplify]: Simplify (* 1/2 0) into 0 68.337 * [backup-simplify]: Simplify (- 0) into 0 68.337 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 68.338 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 68.339 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 68.340 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 68.342 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 68.343 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 68.344 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 68.346 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 68.346 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 68.347 * [backup-simplify]: Simplify (- 0) into 0 68.347 * [backup-simplify]: Simplify (+ 0 0) into 0 68.348 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 68.349 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 68.351 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 68.351 * [taylor]: Taking taylor expansion of 0 in k 68.351 * [backup-simplify]: Simplify 0 into 0 68.351 * [backup-simplify]: Simplify 0 into 0 68.352 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 68.353 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 68.355 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 68.355 * [backup-simplify]: Simplify (+ 0 0) into 0 68.356 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 68.356 * [backup-simplify]: Simplify (- 1/2) into -1/2 68.357 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 68.358 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 68.361 * [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))))))) 68.364 * [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))))))) 68.365 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 68.367 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 68.370 * [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 68.371 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 68.372 * [backup-simplify]: Simplify (- 0) into 0 68.372 * [backup-simplify]: Simplify (+ 0 0) into 0 68.374 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 68.376 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 68.378 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 68.378 * [taylor]: Taking taylor expansion of 0 in k 68.379 * [backup-simplify]: Simplify 0 into 0 68.379 * [backup-simplify]: Simplify 0 into 0 68.379 * [backup-simplify]: Simplify 0 into 0 68.381 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 68.382 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 68.385 * [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 68.386 * [backup-simplify]: Simplify (+ 0 0) into 0 68.387 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 68.388 * [backup-simplify]: Simplify (- 0) into 0 68.388 * [backup-simplify]: Simplify (+ 0 0) into 0 68.390 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 68.395 * [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))))) 68.400 * [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))))) 68.409 * [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))))) 68.409 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) 68.409 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0 68.409 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 68.410 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 68.410 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 68.410 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 68.410 * [taylor]: Taking taylor expansion of 1/2 in k 68.410 * [backup-simplify]: Simplify 1/2 into 1/2 68.410 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 68.410 * [taylor]: Taking taylor expansion of 1/2 in k 68.410 * [backup-simplify]: Simplify 1/2 into 1/2 68.410 * [taylor]: Taking taylor expansion of (/ 1 k) in k 68.410 * [taylor]: Taking taylor expansion of k in k 68.410 * [backup-simplify]: Simplify 0 into 0 68.410 * [backup-simplify]: Simplify 1 into 1 68.410 * [backup-simplify]: Simplify (/ 1 1) into 1 68.410 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 68.410 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 68.410 * [taylor]: Taking taylor expansion of 2 in k 68.410 * [backup-simplify]: Simplify 2 into 2 68.410 * [taylor]: Taking taylor expansion of (/ PI n) in k 68.410 * [taylor]: Taking taylor expansion of PI in k 68.410 * [backup-simplify]: Simplify PI into PI 68.410 * [taylor]: Taking taylor expansion of n in k 68.410 * [backup-simplify]: Simplify n into n 68.410 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 68.411 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 68.411 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 68.411 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 68.411 * [backup-simplify]: Simplify (- 1/2) into -1/2 68.412 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 68.412 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 68.412 * [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)))) 68.412 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 68.412 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 68.412 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 68.412 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 68.412 * [taylor]: Taking taylor expansion of 1/2 in n 68.412 * [backup-simplify]: Simplify 1/2 into 1/2 68.412 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 68.412 * [taylor]: Taking taylor expansion of 1/2 in n 68.412 * [backup-simplify]: Simplify 1/2 into 1/2 68.412 * [taylor]: Taking taylor expansion of (/ 1 k) in n 68.412 * [taylor]: Taking taylor expansion of k in n 68.412 * [backup-simplify]: Simplify k into k 68.412 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 68.412 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 68.412 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 68.412 * [taylor]: Taking taylor expansion of 2 in n 68.413 * [backup-simplify]: Simplify 2 into 2 68.413 * [taylor]: Taking taylor expansion of (/ PI n) in n 68.413 * [taylor]: Taking taylor expansion of PI in n 68.413 * [backup-simplify]: Simplify PI into PI 68.413 * [taylor]: Taking taylor expansion of n in n 68.413 * [backup-simplify]: Simplify 0 into 0 68.413 * [backup-simplify]: Simplify 1 into 1 68.413 * [backup-simplify]: Simplify (/ PI 1) into PI 68.414 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 68.415 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.415 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 68.415 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 68.415 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 68.416 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 68.417 * [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))) 68.419 * [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)))) 68.419 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 68.419 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 68.419 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 68.419 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 68.419 * [taylor]: Taking taylor expansion of 1/2 in n 68.419 * [backup-simplify]: Simplify 1/2 into 1/2 68.419 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 68.419 * [taylor]: Taking taylor expansion of 1/2 in n 68.419 * [backup-simplify]: Simplify 1/2 into 1/2 68.419 * [taylor]: Taking taylor expansion of (/ 1 k) in n 68.419 * [taylor]: Taking taylor expansion of k in n 68.419 * [backup-simplify]: Simplify k into k 68.419 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 68.419 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 68.419 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 68.419 * [taylor]: Taking taylor expansion of 2 in n 68.419 * [backup-simplify]: Simplify 2 into 2 68.419 * [taylor]: Taking taylor expansion of (/ PI n) in n 68.419 * [taylor]: Taking taylor expansion of PI in n 68.419 * [backup-simplify]: Simplify PI into PI 68.419 * [taylor]: Taking taylor expansion of n in n 68.419 * [backup-simplify]: Simplify 0 into 0 68.419 * [backup-simplify]: Simplify 1 into 1 68.420 * [backup-simplify]: Simplify (/ PI 1) into PI 68.420 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 68.421 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.421 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 68.422 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 68.422 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 68.423 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 68.424 * [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))) 68.425 * [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)))) 68.426 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 68.426 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 68.426 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 68.426 * [taylor]: Taking taylor expansion of 1/2 in k 68.426 * [backup-simplify]: Simplify 1/2 into 1/2 68.426 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 68.426 * [taylor]: Taking taylor expansion of 1/2 in k 68.426 * [backup-simplify]: Simplify 1/2 into 1/2 68.426 * [taylor]: Taking taylor expansion of (/ 1 k) in k 68.426 * [taylor]: Taking taylor expansion of k in k 68.426 * [backup-simplify]: Simplify 0 into 0 68.426 * [backup-simplify]: Simplify 1 into 1 68.426 * [backup-simplify]: Simplify (/ 1 1) into 1 68.426 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 68.426 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 68.426 * [taylor]: Taking taylor expansion of (* 2 PI) in k 68.426 * [taylor]: Taking taylor expansion of 2 in k 68.427 * [backup-simplify]: Simplify 2 into 2 68.427 * [taylor]: Taking taylor expansion of PI in k 68.427 * [backup-simplify]: Simplify PI into PI 68.427 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 68.428 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.428 * [taylor]: Taking taylor expansion of (log n) in k 68.428 * [taylor]: Taking taylor expansion of n in k 68.428 * [backup-simplify]: Simplify n into n 68.428 * [backup-simplify]: Simplify (log n) into (log n) 68.429 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 68.429 * [backup-simplify]: Simplify (- 1/2) into -1/2 68.430 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 68.430 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 68.431 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 68.432 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 68.433 * [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)))) 68.434 * [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)))) 68.435 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 68.436 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 68.438 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 68.438 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 68.439 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 68.439 * [backup-simplify]: Simplify (- 0) into 0 68.439 * [backup-simplify]: Simplify (+ 0 0) into 0 68.441 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 68.442 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 68.444 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 68.444 * [taylor]: Taking taylor expansion of 0 in k 68.444 * [backup-simplify]: Simplify 0 into 0 68.444 * [backup-simplify]: Simplify 0 into 0 68.444 * [backup-simplify]: Simplify 0 into 0 68.446 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 68.447 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 68.459 * [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 68.460 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 68.461 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 68.462 * [backup-simplify]: Simplify (- 0) into 0 68.462 * [backup-simplify]: Simplify (+ 0 0) into 0 68.463 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 68.465 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 68.467 * [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 68.467 * [taylor]: Taking taylor expansion of 0 in k 68.468 * [backup-simplify]: Simplify 0 into 0 68.468 * [backup-simplify]: Simplify 0 into 0 68.468 * [backup-simplify]: Simplify 0 into 0 68.468 * [backup-simplify]: Simplify 0 into 0 68.469 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 68.470 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 68.476 * [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 68.476 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 68.478 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 68.478 * [backup-simplify]: Simplify (- 0) into 0 68.478 * [backup-simplify]: Simplify (+ 0 0) into 0 68.480 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 68.482 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 68.485 * [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 68.485 * [taylor]: Taking taylor expansion of 0 in k 68.485 * [backup-simplify]: Simplify 0 into 0 68.485 * [backup-simplify]: Simplify 0 into 0 68.486 * [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))))) 68.487 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) 68.487 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0 68.487 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 68.487 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 68.487 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 68.487 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 68.487 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 68.487 * [taylor]: Taking taylor expansion of 1/2 in k 68.487 * [backup-simplify]: Simplify 1/2 into 1/2 68.487 * [taylor]: Taking taylor expansion of (/ 1 k) in k 68.487 * [taylor]: Taking taylor expansion of k in k 68.487 * [backup-simplify]: Simplify 0 into 0 68.487 * [backup-simplify]: Simplify 1 into 1 68.488 * [backup-simplify]: Simplify (/ 1 1) into 1 68.488 * [taylor]: Taking taylor expansion of 1/2 in k 68.488 * [backup-simplify]: Simplify 1/2 into 1/2 68.488 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 68.488 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 68.488 * [taylor]: Taking taylor expansion of -2 in k 68.488 * [backup-simplify]: Simplify -2 into -2 68.488 * [taylor]: Taking taylor expansion of (/ PI n) in k 68.488 * [taylor]: Taking taylor expansion of PI in k 68.488 * [backup-simplify]: Simplify PI into PI 68.488 * [taylor]: Taking taylor expansion of n in k 68.488 * [backup-simplify]: Simplify n into n 68.488 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 68.488 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 68.488 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 68.489 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 68.489 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 68.489 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 68.490 * [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))) 68.490 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 68.490 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 68.490 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 68.490 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 68.490 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 68.490 * [taylor]: Taking taylor expansion of 1/2 in n 68.490 * [backup-simplify]: Simplify 1/2 into 1/2 68.490 * [taylor]: Taking taylor expansion of (/ 1 k) in n 68.490 * [taylor]: Taking taylor expansion of k in n 68.490 * [backup-simplify]: Simplify k into k 68.490 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 68.490 * [taylor]: Taking taylor expansion of 1/2 in n 68.490 * [backup-simplify]: Simplify 1/2 into 1/2 68.490 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 68.490 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 68.490 * [taylor]: Taking taylor expansion of -2 in n 68.490 * [backup-simplify]: Simplify -2 into -2 68.490 * [taylor]: Taking taylor expansion of (/ PI n) in n 68.490 * [taylor]: Taking taylor expansion of PI in n 68.490 * [backup-simplify]: Simplify PI into PI 68.490 * [taylor]: Taking taylor expansion of n in n 68.490 * [backup-simplify]: Simplify 0 into 0 68.490 * [backup-simplify]: Simplify 1 into 1 68.491 * [backup-simplify]: Simplify (/ PI 1) into PI 68.491 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 68.493 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 68.493 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 68.493 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 68.496 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 68.498 * [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))) 68.499 * [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)))) 68.499 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 68.499 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 68.499 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 68.499 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 68.499 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 68.499 * [taylor]: Taking taylor expansion of 1/2 in n 68.499 * [backup-simplify]: Simplify 1/2 into 1/2 68.499 * [taylor]: Taking taylor expansion of (/ 1 k) in n 68.499 * [taylor]: Taking taylor expansion of k in n 68.499 * [backup-simplify]: Simplify k into k 68.499 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 68.500 * [taylor]: Taking taylor expansion of 1/2 in n 68.500 * [backup-simplify]: Simplify 1/2 into 1/2 68.500 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 68.500 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 68.500 * [taylor]: Taking taylor expansion of -2 in n 68.500 * [backup-simplify]: Simplify -2 into -2 68.500 * [taylor]: Taking taylor expansion of (/ PI n) in n 68.500 * [taylor]: Taking taylor expansion of PI in n 68.500 * [backup-simplify]: Simplify PI into PI 68.500 * [taylor]: Taking taylor expansion of n in n 68.500 * [backup-simplify]: Simplify 0 into 0 68.500 * [backup-simplify]: Simplify 1 into 1 68.500 * [backup-simplify]: Simplify (/ PI 1) into PI 68.501 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 68.502 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 68.502 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 68.502 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 68.504 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 68.505 * [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))) 68.506 * [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)))) 68.506 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 68.506 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 68.507 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 68.507 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 68.507 * [taylor]: Taking taylor expansion of 1/2 in k 68.507 * [backup-simplify]: Simplify 1/2 into 1/2 68.507 * [taylor]: Taking taylor expansion of (/ 1 k) in k 68.507 * [taylor]: Taking taylor expansion of k in k 68.507 * [backup-simplify]: Simplify 0 into 0 68.507 * [backup-simplify]: Simplify 1 into 1 68.507 * [backup-simplify]: Simplify (/ 1 1) into 1 68.507 * [taylor]: Taking taylor expansion of 1/2 in k 68.507 * [backup-simplify]: Simplify 1/2 into 1/2 68.507 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 68.507 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 68.507 * [taylor]: Taking taylor expansion of (* -2 PI) in k 68.507 * [taylor]: Taking taylor expansion of -2 in k 68.507 * [backup-simplify]: Simplify -2 into -2 68.507 * [taylor]: Taking taylor expansion of PI in k 68.507 * [backup-simplify]: Simplify PI into PI 68.508 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 68.509 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 68.509 * [taylor]: Taking taylor expansion of (log n) in k 68.509 * [taylor]: Taking taylor expansion of n in k 68.509 * [backup-simplify]: Simplify n into n 68.509 * [backup-simplify]: Simplify (log n) into (log n) 68.510 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 68.510 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 68.510 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 68.511 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 68.512 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 68.514 * [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)))) 68.515 * [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)))) 68.516 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 68.517 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 68.519 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 68.519 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 68.520 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 68.520 * [backup-simplify]: Simplify (+ 0 0) into 0 68.521 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 68.523 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 68.525 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 68.525 * [taylor]: Taking taylor expansion of 0 in k 68.525 * [backup-simplify]: Simplify 0 into 0 68.525 * [backup-simplify]: Simplify 0 into 0 68.525 * [backup-simplify]: Simplify 0 into 0 68.526 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 68.527 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 68.531 * [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 68.531 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 68.532 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 68.532 * [backup-simplify]: Simplify (+ 0 0) into 0 68.534 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 68.536 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 68.538 * [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 68.538 * [taylor]: Taking taylor expansion of 0 in k 68.539 * [backup-simplify]: Simplify 0 into 0 68.539 * [backup-simplify]: Simplify 0 into 0 68.539 * [backup-simplify]: Simplify 0 into 0 68.539 * [backup-simplify]: Simplify 0 into 0 68.540 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 68.542 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 68.548 * [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 68.548 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 68.550 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 68.550 * [backup-simplify]: Simplify (+ 0 0) into 0 68.552 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 68.554 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 68.557 * [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 68.557 * [taylor]: Taking taylor expansion of 0 in k 68.557 * [backup-simplify]: Simplify 0 into 0 68.557 * [backup-simplify]: Simplify 0 into 0 68.558 * [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))))) 68.558 * * * * [progress]: [ 4 / 4 ] generating series at (2 2) 68.558 * [backup-simplify]: Simplify (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) into (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) 68.558 * [approximate]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0 68.558 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k 68.558 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k 68.558 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k 68.558 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k 68.558 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 68.558 * [taylor]: Taking taylor expansion of 1/2 in k 68.558 * [backup-simplify]: Simplify 1/2 into 1/2 68.558 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 68.558 * [taylor]: Taking taylor expansion of 1/2 in k 68.558 * [backup-simplify]: Simplify 1/2 into 1/2 68.558 * [taylor]: Taking taylor expansion of k in k 68.558 * [backup-simplify]: Simplify 0 into 0 68.558 * [backup-simplify]: Simplify 1 into 1 68.558 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k 68.558 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k 68.558 * [taylor]: Taking taylor expansion of 2 in k 68.558 * [backup-simplify]: Simplify 2 into 2 68.559 * [taylor]: Taking taylor expansion of (* n PI) in k 68.559 * [taylor]: Taking taylor expansion of n in k 68.559 * [backup-simplify]: Simplify n into n 68.559 * [taylor]: Taking taylor expansion of PI in k 68.559 * [backup-simplify]: Simplify PI into PI 68.559 * [backup-simplify]: Simplify (* n PI) into (* n PI) 68.559 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI)) 68.559 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI))) 68.559 * [backup-simplify]: Simplify (* 1/2 0) into 0 68.559 * [backup-simplify]: Simplify (- 0) into 0 68.559 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 68.560 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI)))) 68.560 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2) 68.560 * [backup-simplify]: Simplify (/ 1 (pow (* 2 (* n PI)) 1/2)) into (sqrt (/ 1 (* PI (* n 2)))) 68.560 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 68.560 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 68.560 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 68.560 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 68.560 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 68.560 * [taylor]: Taking taylor expansion of 1/2 in n 68.560 * [backup-simplify]: Simplify 1/2 into 1/2 68.560 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 68.560 * [taylor]: Taking taylor expansion of 1/2 in n 68.560 * [backup-simplify]: Simplify 1/2 into 1/2 68.560 * [taylor]: Taking taylor expansion of k in n 68.560 * [backup-simplify]: Simplify k into k 68.560 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 68.560 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 68.560 * [taylor]: Taking taylor expansion of 2 in n 68.560 * [backup-simplify]: Simplify 2 into 2 68.560 * [taylor]: Taking taylor expansion of (* n PI) in n 68.560 * [taylor]: Taking taylor expansion of n in n 68.560 * [backup-simplify]: Simplify 0 into 0 68.560 * [backup-simplify]: Simplify 1 into 1 68.560 * [taylor]: Taking taylor expansion of PI in n 68.560 * [backup-simplify]: Simplify PI into PI 68.560 * [backup-simplify]: Simplify (* 0 PI) into 0 68.561 * [backup-simplify]: Simplify (* 2 0) into 0 68.562 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 68.563 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 68.563 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.563 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 68.563 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 68.563 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 68.564 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 68.565 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 68.566 * [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))))) 68.566 * [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)))))) 68.566 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n 68.566 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n 68.566 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n 68.566 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n 68.566 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n 68.567 * [taylor]: Taking taylor expansion of 1/2 in n 68.567 * [backup-simplify]: Simplify 1/2 into 1/2 68.567 * [taylor]: Taking taylor expansion of (* 1/2 k) in n 68.567 * [taylor]: Taking taylor expansion of 1/2 in n 68.567 * [backup-simplify]: Simplify 1/2 into 1/2 68.567 * [taylor]: Taking taylor expansion of k in n 68.567 * [backup-simplify]: Simplify k into k 68.567 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n 68.567 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n 68.567 * [taylor]: Taking taylor expansion of 2 in n 68.567 * [backup-simplify]: Simplify 2 into 2 68.567 * [taylor]: Taking taylor expansion of (* n PI) in n 68.567 * [taylor]: Taking taylor expansion of n in n 68.567 * [backup-simplify]: Simplify 0 into 0 68.567 * [backup-simplify]: Simplify 1 into 1 68.567 * [taylor]: Taking taylor expansion of PI in n 68.567 * [backup-simplify]: Simplify PI into PI 68.567 * [backup-simplify]: Simplify (* 0 PI) into 0 68.567 * [backup-simplify]: Simplify (* 2 0) into 0 68.568 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 68.569 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI) 68.570 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.570 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k) 68.570 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k)) 68.570 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k)) 68.571 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 68.572 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) 68.572 * [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))))) 68.573 * [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)))))) 68.573 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k 68.573 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k 68.573 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k 68.573 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k 68.573 * [taylor]: Taking taylor expansion of 1/2 in k 68.573 * [backup-simplify]: Simplify 1/2 into 1/2 68.573 * [taylor]: Taking taylor expansion of (* 1/2 k) in k 68.573 * [taylor]: Taking taylor expansion of 1/2 in k 68.573 * [backup-simplify]: Simplify 1/2 into 1/2 68.573 * [taylor]: Taking taylor expansion of k in k 68.573 * [backup-simplify]: Simplify 0 into 0 68.573 * [backup-simplify]: Simplify 1 into 1 68.573 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k 68.573 * [taylor]: Taking taylor expansion of (log n) in k 68.573 * [taylor]: Taking taylor expansion of n in k 68.573 * [backup-simplify]: Simplify n into n 68.573 * [backup-simplify]: Simplify (log n) into (log n) 68.573 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 68.573 * [taylor]: Taking taylor expansion of (* 2 PI) in k 68.573 * [taylor]: Taking taylor expansion of 2 in k 68.573 * [backup-simplify]: Simplify 2 into 2 68.573 * [taylor]: Taking taylor expansion of PI in k 68.573 * [backup-simplify]: Simplify PI into PI 68.574 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 68.574 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.575 * [backup-simplify]: Simplify (* 1/2 0) into 0 68.575 * [backup-simplify]: Simplify (- 0) into 0 68.575 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 68.576 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 68.577 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI)))) 68.577 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 68.578 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) 68.579 * [backup-simplify]: Simplify (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) into (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) 68.579 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 68.580 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0 68.581 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 68.581 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0 68.582 * [backup-simplify]: Simplify (- 0) into 0 68.582 * [backup-simplify]: Simplify (+ 0 0) into 0 68.583 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 68.584 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0 68.585 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0 68.586 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (/ 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 68.586 * [taylor]: Taking taylor expansion of 0 in k 68.586 * [backup-simplify]: Simplify 0 into 0 68.586 * [backup-simplify]: Simplify 0 into 0 68.587 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 68.587 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 68.588 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 68.588 * [backup-simplify]: Simplify (+ 0 0) into 0 68.595 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2 68.595 * [backup-simplify]: Simplify (- 1/2) into -1/2 68.596 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 68.597 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 68.598 * [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))))))) 68.602 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (/ (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) 68.604 * [backup-simplify]: Simplify (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) into (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) 68.605 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 68.606 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 68.607 * [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 68.608 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0 68.608 * [backup-simplify]: Simplify (- 0) into 0 68.608 * [backup-simplify]: Simplify (+ 0 0) into 0 68.609 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI))) 68.610 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 68.612 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 68.614 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (/ 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0 68.614 * [taylor]: Taking taylor expansion of 0 in k 68.615 * [backup-simplify]: Simplify 0 into 0 68.615 * [backup-simplify]: Simplify 0 into 0 68.615 * [backup-simplify]: Simplify 0 into 0 68.616 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 68.617 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 68.621 * [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 68.621 * [backup-simplify]: Simplify (+ 0 0) into 0 68.622 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0 68.622 * [backup-simplify]: Simplify (- 0) into 0 68.623 * [backup-simplify]: Simplify (+ 0 0) into 0 68.625 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0 68.629 * [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))))) 68.644 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (/ (* (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))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (/ (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) 68.649 * [backup-simplify]: Simplify (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) 68.656 * [backup-simplify]: Simplify (+ (* (+ (* 1/4 (/ (* (log n) (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/8 (/ (pow (log (* 2 PI)) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/8 (/ (pow (log n) 2) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) (pow (* k 1) 2)) (+ (* (+ (* 1/2 (/ (log (* 2 PI)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* 1/2 (/ (log n) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) (* k 1)) (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))) into (+ (* 1/8 (/ (* (pow (log (* 2 PI)) 2) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (/ (* k (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (/ (* (log n) k) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/4 (/ (* (log (* 2 PI)) (* (log n) (pow k 2))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (* 1/8 (/ (* (pow (log n) 2) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))))) 68.657 * [backup-simplify]: Simplify (/ 1 (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2)))) into (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) 68.657 * [approximate]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0 68.657 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k 68.657 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k 68.657 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k 68.657 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k 68.657 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 68.657 * [taylor]: Taking taylor expansion of 1/2 in k 68.657 * [backup-simplify]: Simplify 1/2 into 1/2 68.657 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 68.657 * [taylor]: Taking taylor expansion of 1/2 in k 68.657 * [backup-simplify]: Simplify 1/2 into 1/2 68.657 * [taylor]: Taking taylor expansion of (/ 1 k) in k 68.657 * [taylor]: Taking taylor expansion of k in k 68.657 * [backup-simplify]: Simplify 0 into 0 68.657 * [backup-simplify]: Simplify 1 into 1 68.657 * [backup-simplify]: Simplify (/ 1 1) into 1 68.657 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k 68.657 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k 68.657 * [taylor]: Taking taylor expansion of 2 in k 68.657 * [backup-simplify]: Simplify 2 into 2 68.657 * [taylor]: Taking taylor expansion of (/ PI n) in k 68.657 * [taylor]: Taking taylor expansion of PI in k 68.657 * [backup-simplify]: Simplify PI into PI 68.657 * [taylor]: Taking taylor expansion of n in k 68.657 * [backup-simplify]: Simplify n into n 68.657 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 68.657 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n)) 68.657 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n))) 68.658 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 68.658 * [backup-simplify]: Simplify (- 1/2) into -1/2 68.658 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 68.658 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n)))) 68.658 * [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)))) 68.658 * [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))))) 68.659 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 68.659 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 68.659 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 68.659 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 68.659 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 68.659 * [taylor]: Taking taylor expansion of 1/2 in n 68.659 * [backup-simplify]: Simplify 1/2 into 1/2 68.659 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 68.659 * [taylor]: Taking taylor expansion of 1/2 in n 68.659 * [backup-simplify]: Simplify 1/2 into 1/2 68.659 * [taylor]: Taking taylor expansion of (/ 1 k) in n 68.659 * [taylor]: Taking taylor expansion of k in n 68.659 * [backup-simplify]: Simplify k into k 68.659 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 68.659 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 68.659 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 68.659 * [taylor]: Taking taylor expansion of 2 in n 68.659 * [backup-simplify]: Simplify 2 into 2 68.659 * [taylor]: Taking taylor expansion of (/ PI n) in n 68.659 * [taylor]: Taking taylor expansion of PI in n 68.659 * [backup-simplify]: Simplify PI into PI 68.659 * [taylor]: Taking taylor expansion of n in n 68.659 * [backup-simplify]: Simplify 0 into 0 68.659 * [backup-simplify]: Simplify 1 into 1 68.659 * [backup-simplify]: Simplify (/ PI 1) into PI 68.660 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 68.660 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.660 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 68.660 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 68.660 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 68.661 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 68.662 * [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))) 68.663 * [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)))) 68.663 * [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))))) 68.663 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n 68.663 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n 68.664 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n 68.664 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n 68.664 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n 68.664 * [taylor]: Taking taylor expansion of 1/2 in n 68.664 * [backup-simplify]: Simplify 1/2 into 1/2 68.664 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 68.664 * [taylor]: Taking taylor expansion of 1/2 in n 68.664 * [backup-simplify]: Simplify 1/2 into 1/2 68.664 * [taylor]: Taking taylor expansion of (/ 1 k) in n 68.664 * [taylor]: Taking taylor expansion of k in n 68.664 * [backup-simplify]: Simplify k into k 68.664 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 68.664 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n 68.664 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n 68.664 * [taylor]: Taking taylor expansion of 2 in n 68.664 * [backup-simplify]: Simplify 2 into 2 68.664 * [taylor]: Taking taylor expansion of (/ PI n) in n 68.664 * [taylor]: Taking taylor expansion of PI in n 68.664 * [backup-simplify]: Simplify PI into PI 68.664 * [taylor]: Taking taylor expansion of n in n 68.664 * [backup-simplify]: Simplify 0 into 0 68.664 * [backup-simplify]: Simplify 1 into 1 68.664 * [backup-simplify]: Simplify (/ PI 1) into PI 68.664 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 68.665 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.665 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 68.665 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k))) 68.665 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k))) 68.666 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 68.667 * [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))) 68.668 * [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)))) 68.668 * [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))))) 68.668 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k 68.668 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k 68.668 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k 68.669 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k 68.669 * [taylor]: Taking taylor expansion of 1/2 in k 68.669 * [backup-simplify]: Simplify 1/2 into 1/2 68.669 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 68.669 * [taylor]: Taking taylor expansion of 1/2 in k 68.669 * [backup-simplify]: Simplify 1/2 into 1/2 68.669 * [taylor]: Taking taylor expansion of (/ 1 k) in k 68.669 * [taylor]: Taking taylor expansion of k in k 68.669 * [backup-simplify]: Simplify 0 into 0 68.669 * [backup-simplify]: Simplify 1 into 1 68.669 * [backup-simplify]: Simplify (/ 1 1) into 1 68.669 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k 68.669 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k 68.669 * [taylor]: Taking taylor expansion of (* 2 PI) in k 68.669 * [taylor]: Taking taylor expansion of 2 in k 68.669 * [backup-simplify]: Simplify 2 into 2 68.669 * [taylor]: Taking taylor expansion of PI in k 68.669 * [backup-simplify]: Simplify PI into PI 68.669 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI) 68.670 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI)) 68.670 * [taylor]: Taking taylor expansion of (log n) in k 68.670 * [taylor]: Taking taylor expansion of n in k 68.670 * [backup-simplify]: Simplify n into n 68.670 * [backup-simplify]: Simplify (log n) into (log n) 68.670 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 68.671 * [backup-simplify]: Simplify (- 1/2) into -1/2 68.671 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2 68.671 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 68.672 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n)) 68.672 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n))) 68.673 * [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)))) 68.674 * [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))))) 68.674 * [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))))) 68.675 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 68.675 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0 68.676 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0 68.677 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 68.677 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 68.677 * [backup-simplify]: Simplify (- 0) into 0 68.677 * [backup-simplify]: Simplify (+ 0 0) into 0 68.678 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 68.679 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0 68.680 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 68.682 * [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 68.682 * [taylor]: Taking taylor expansion of 0 in k 68.682 * [backup-simplify]: Simplify 0 into 0 68.682 * [backup-simplify]: Simplify 0 into 0 68.683 * [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 68.683 * [backup-simplify]: Simplify 0 into 0 68.684 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 68.685 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0 68.687 * [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 68.687 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 68.687 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 68.687 * [backup-simplify]: Simplify (- 0) into 0 68.688 * [backup-simplify]: Simplify (+ 0 0) into 0 68.689 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 68.690 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0 68.691 * [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 68.699 * [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)))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 68.699 * [taylor]: Taking taylor expansion of 0 in k 68.699 * [backup-simplify]: Simplify 0 into 0 68.699 * [backup-simplify]: Simplify 0 into 0 68.699 * [backup-simplify]: Simplify 0 into 0 68.701 * [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)))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 68.701 * [backup-simplify]: Simplify 0 into 0 68.702 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 68.703 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 68.706 * [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 68.706 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 68.707 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 68.707 * [backup-simplify]: Simplify (- 0) into 0 68.708 * [backup-simplify]: Simplify (+ 0 0) into 0 68.709 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n)) 68.710 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0 68.711 * [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 68.714 * [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)))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0 68.714 * [taylor]: Taking taylor expansion of 0 in k 68.714 * [backup-simplify]: Simplify 0 into 0 68.714 * [backup-simplify]: Simplify 0 into 0 68.715 * [backup-simplify]: Simplify (/ 1 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) 68.715 * [backup-simplify]: Simplify (/ 1 (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2)))) into (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) 68.715 * [approximate]: Taking taylor expansion of (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0 68.715 * [taylor]: Taking taylor expansion of (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in k 68.716 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k 68.716 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k 68.716 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k 68.716 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 68.716 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 68.716 * [taylor]: Taking taylor expansion of 1/2 in k 68.716 * [backup-simplify]: Simplify 1/2 into 1/2 68.716 * [taylor]: Taking taylor expansion of (/ 1 k) in k 68.716 * [taylor]: Taking taylor expansion of k in k 68.716 * [backup-simplify]: Simplify 0 into 0 68.716 * [backup-simplify]: Simplify 1 into 1 68.716 * [backup-simplify]: Simplify (/ 1 1) into 1 68.716 * [taylor]: Taking taylor expansion of 1/2 in k 68.716 * [backup-simplify]: Simplify 1/2 into 1/2 68.716 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k 68.716 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k 68.716 * [taylor]: Taking taylor expansion of -2 in k 68.716 * [backup-simplify]: Simplify -2 into -2 68.716 * [taylor]: Taking taylor expansion of (/ PI n) in k 68.716 * [taylor]: Taking taylor expansion of PI in k 68.716 * [backup-simplify]: Simplify PI into PI 68.716 * [taylor]: Taking taylor expansion of n in k 68.716 * [backup-simplify]: Simplify n into n 68.716 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 68.716 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n)) 68.716 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n))) 68.717 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 68.717 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 68.717 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n)))) 68.717 * [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))) 68.717 * [backup-simplify]: Simplify (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) into (/ 1 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) 68.717 * [taylor]: Taking taylor expansion of (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 68.717 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 68.717 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 68.717 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 68.717 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 68.717 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 68.717 * [taylor]: Taking taylor expansion of 1/2 in n 68.717 * [backup-simplify]: Simplify 1/2 into 1/2 68.717 * [taylor]: Taking taylor expansion of (/ 1 k) in n 68.717 * [taylor]: Taking taylor expansion of k in n 68.717 * [backup-simplify]: Simplify k into k 68.717 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 68.717 * [taylor]: Taking taylor expansion of 1/2 in n 68.717 * [backup-simplify]: Simplify 1/2 into 1/2 68.717 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 68.717 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 68.717 * [taylor]: Taking taylor expansion of -2 in n 68.717 * [backup-simplify]: Simplify -2 into -2 68.717 * [taylor]: Taking taylor expansion of (/ PI n) in n 68.718 * [taylor]: Taking taylor expansion of PI in n 68.718 * [backup-simplify]: Simplify PI into PI 68.718 * [taylor]: Taking taylor expansion of n in n 68.718 * [backup-simplify]: Simplify 0 into 0 68.718 * [backup-simplify]: Simplify 1 into 1 68.718 * [backup-simplify]: Simplify (/ PI 1) into PI 68.718 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 68.719 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 68.719 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 68.719 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 68.720 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 68.721 * [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))) 68.721 * [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)))) 68.722 * [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))))) 68.722 * [taylor]: Taking taylor expansion of (/ 1 (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))) in n 68.722 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n 68.722 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n 68.722 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n 68.722 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n 68.722 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n 68.722 * [taylor]: Taking taylor expansion of 1/2 in n 68.722 * [backup-simplify]: Simplify 1/2 into 1/2 68.722 * [taylor]: Taking taylor expansion of (/ 1 k) in n 68.722 * [taylor]: Taking taylor expansion of k in n 68.722 * [backup-simplify]: Simplify k into k 68.722 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 68.722 * [taylor]: Taking taylor expansion of 1/2 in n 68.722 * [backup-simplify]: Simplify 1/2 into 1/2 68.722 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n 68.722 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n 68.722 * [taylor]: Taking taylor expansion of -2 in n 68.722 * [backup-simplify]: Simplify -2 into -2 68.722 * [taylor]: Taking taylor expansion of (/ PI n) in n 68.722 * [taylor]: Taking taylor expansion of PI in n 68.723 * [backup-simplify]: Simplify PI into PI 68.723 * [taylor]: Taking taylor expansion of n in n 68.723 * [backup-simplify]: Simplify 0 into 0 68.723 * [backup-simplify]: Simplify 1 into 1 68.723 * [backup-simplify]: Simplify (/ PI 1) into PI 68.723 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 68.724 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 68.724 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k) 68.724 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2) 68.725 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 68.726 * [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))) 68.726 * [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)))) 68.727 * [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))))) 68.727 * [taylor]: Taking taylor expansion of (/ 1 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k 68.727 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k 68.727 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k 68.727 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k 68.727 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k 68.727 * [taylor]: Taking taylor expansion of 1/2 in k 68.727 * [backup-simplify]: Simplify 1/2 into 1/2 68.727 * [taylor]: Taking taylor expansion of (/ 1 k) in k 68.727 * [taylor]: Taking taylor expansion of k in k 68.727 * [backup-simplify]: Simplify 0 into 0 68.727 * [backup-simplify]: Simplify 1 into 1 68.728 * [backup-simplify]: Simplify (/ 1 1) into 1 68.728 * [taylor]: Taking taylor expansion of 1/2 in k 68.728 * [backup-simplify]: Simplify 1/2 into 1/2 68.728 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k 68.728 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k 68.728 * [taylor]: Taking taylor expansion of (* -2 PI) in k 68.728 * [taylor]: Taking taylor expansion of -2 in k 68.728 * [backup-simplify]: Simplify -2 into -2 68.728 * [taylor]: Taking taylor expansion of PI in k 68.728 * [backup-simplify]: Simplify PI into PI 68.728 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI) 68.729 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI)) 68.729 * [taylor]: Taking taylor expansion of (log n) in k 68.729 * [taylor]: Taking taylor expansion of n in k 68.729 * [backup-simplify]: Simplify n into n 68.729 * [backup-simplify]: Simplify (log n) into (log n) 68.729 * [backup-simplify]: Simplify (* 1/2 1) into 1/2 68.729 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2 68.729 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 68.730 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n)) 68.731 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n))) 68.731 * [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)))) 68.732 * [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))))) 68.733 * [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))))) 68.734 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 68.734 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0 68.735 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0 68.735 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 68.735 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0 68.736 * [backup-simplify]: Simplify (+ 0 0) into 0 68.737 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 68.737 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0 68.739 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0 68.740 * [backup-simplify]: Simplify (- (+ (* (/ 1 (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 68.740 * [taylor]: Taking taylor expansion of 0 in k 68.740 * [backup-simplify]: Simplify 0 into 0 68.740 * [backup-simplify]: Simplify 0 into 0 68.742 * [backup-simplify]: Simplify (- (+ (* (/ 1 (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 68.742 * [backup-simplify]: Simplify 0 into 0 68.742 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 68.743 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0 68.745 * [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 68.745 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 68.746 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0 68.746 * [backup-simplify]: Simplify (+ 0 0) into 0 68.747 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 68.748 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0 68.749 * [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 68.751 * [backup-simplify]: Simplify (- (+ (* (/ 1 (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)))))) (* 0 (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 68.752 * [taylor]: Taking taylor expansion of 0 in k 68.752 * [backup-simplify]: Simplify 0 into 0 68.752 * [backup-simplify]: Simplify 0 into 0 68.752 * [backup-simplify]: Simplify 0 into 0 68.754 * [backup-simplify]: Simplify (- (+ (* (/ 1 (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)))))) (* 0 (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 68.754 * [backup-simplify]: Simplify 0 into 0 68.755 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 68.755 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 68.759 * [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 68.759 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 68.760 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0 68.760 * [backup-simplify]: Simplify (+ 0 0) into 0 68.761 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n)) 68.762 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0 68.764 * [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 68.767 * [backup-simplify]: Simplify (- (+ (* (/ 1 (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)))))) (* 0 (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (* 0 (/ 0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))) into 0 68.767 * [taylor]: Taking taylor expansion of 0 in k 68.767 * [backup-simplify]: Simplify 0 into 0 68.767 * [backup-simplify]: Simplify 0 into 0 68.768 * [backup-simplify]: Simplify (/ 1 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 68.768 * * * [progress]: simplifying candidates 68.768 * * * * [progress]: [ 1 / 1536 ] simplifiying candidate # 68.768 * * * * [progress]: [ 2 / 1536 ] simplifiying candidate # 68.768 * * * * [progress]: [ 3 / 1536 ] simplifiying candidate # 68.768 * * * * [progress]: [ 4 / 1536 ] simplifiying candidate # 68.768 * * * * [progress]: [ 5 / 1536 ] simplifiying candidate # 68.768 * * * * [progress]: [ 6 / 1536 ] simplifiying candidate # 68.768 * * * * [progress]: [ 7 / 1536 ] simplifiying candidate # 68.768 * * * * [progress]: [ 8 / 1536 ] simplifiying candidate # 68.768 * * * * [progress]: [ 9 / 1536 ] simplifiying candidate # 68.768 * * * * [progress]: [ 10 / 1536 ] simplifiying candidate # 68.768 * * * * [progress]: [ 11 / 1536 ] simplifiying candidate # 68.768 * * * * [progress]: [ 12 / 1536 ] simplifiying candidate # 68.768 * * * * [progress]: [ 13 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 14 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 15 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 16 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 17 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 18 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 19 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 20 / 1536 ] simplifiying candidate #real (real->posit16 (* (* n 2) PI))) (- 1/2 (/ k 2))))))> 68.769 * * * * [progress]: [ 21 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 22 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 23 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 24 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 25 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 26 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 27 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 28 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 29 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 30 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 31 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 32 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 33 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 34 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 35 / 1536 ] simplifiying candidate # 68.769 * * * * [progress]: [ 36 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 37 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 38 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 39 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 40 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 41 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 42 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 43 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 44 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 45 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 46 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 47 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 48 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 49 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 50 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 51 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 52 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 53 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 54 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 55 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 56 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 57 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 58 / 1536 ] simplifiying candidate # 68.770 * * * * [progress]: [ 59 / 1536 ] simplifiying candidate # 68.771 * * * * [progress]: [ 60 / 1536 ] simplifiying candidate # 68.771 * * * * [progress]: [ 61 / 1536 ] simplifiying candidate # 68.771 * * * * [progress]: [ 62 / 1536 ] simplifiying candidate # 68.771 * * * * [progress]: [ 63 / 1536 ] simplifiying candidate # 68.771 * * * * [progress]: [ 64 / 1536 ] simplifiying candidate # 68.771 * * * * [progress]: [ 65 / 1536 ] simplifiying candidate # 68.771 * * * * [progress]: [ 66 / 1536 ] simplifiying candidate # 68.771 * * * * [progress]: [ 67 / 1536 ] simplifiying candidate # 68.771 * * * * 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2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (/ 1 (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1))))) (/ 1 (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ k 2)) 1 (* (/ k 2) 1)))) (/ 1 (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ 1 2)) k (* (/ 1 2) k)))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (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))))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) (/ 1 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) 1))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ k 2)) 1 (* (/ k 2) 1)))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ 1 2) k))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ 1 2)) k (* (/ 1 2) k)))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (cbrt (/ k 2))) (* (cbrt (/ k 2)) (cbrt (/ k 2))) (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (sqrt (/ k 2)) (sqrt (/ k 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (sqrt (/ k 2))) (sqrt (/ k 2)) (* (sqrt (/ k 2)) (sqrt (/ k 2)))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (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))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (cbrt k) (sqrt 2))) (/ (* (cbrt k) (cbrt k)) (sqrt 2)) (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2)))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (cbrt k) 2)) (/ (* (cbrt k) (cbrt k)) 1) (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (sqrt k) (cbrt 2))) (/ (sqrt k) (* (cbrt 2) (cbrt 2))) (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (sqrt k) (sqrt 2))) (/ (sqrt k) (sqrt 2)) (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2)))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (sqrt k) 2) (/ (sqrt k) 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ (sqrt k) 2)) (/ (sqrt k) 1) (* (/ (sqrt k) 2) (/ (sqrt k) 1))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ k (cbrt 2))) (/ 1 (* (cbrt 2) (cbrt 2))) (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ k (sqrt 2))) (/ 1 (sqrt 2)) (* (/ k (sqrt 2)) (/ 1 (sqrt 2)))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ k 2) (/ 1 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ k 2)) (/ 1 1) (* (/ k 2) (/ 1 1))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ k 2) 1))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ k 2)) 1 (* (/ k 2) 1)))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ 1 2) k))))) (/ 1 (pow (* (* n 2) PI) (fma (- (/ 1 2)) k (* (/ 1 2) k)))) (/ 1 (pow (* (* n 2) PI) 1/2)) (/ 1 (pow (* (* n 2) PI) (- (/ k 2)))) (/ 1 (pow (* (* n 2) PI) 1/2)) (/ 1 (pow (* (* n 2) PI) (- (/ k 2)))) (/ 1 (pow (* n 2) (- 1/2 (/ k 2)))) (/ 1 (pow PI (- 1/2 (/ k 2)))) (/ 1 (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))) (/ 1 (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (/ 1 (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (/ 1 (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (/ 1 1) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (/ 1 (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (/ 1 (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (/ 1 (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) (/ 1 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ k 2) 1))))) (/ 1 (pow (* (* n 2) PI) (fma (* (cbrt 1/2) (cbrt 1/2)) (cbrt 1/2) (- (* (/ 1 2) k))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (sqrt (/ k 2)) (sqrt (/ k 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ (sqrt k) 2) (/ (sqrt k) 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) (/ 1 1)))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ k 2) 1))))) (/ 1 (pow (* (* n 2) PI) (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ 1 2) k))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (cbrt (/ k 2)) (* (cbrt (/ k 2)) (cbrt (/ k 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (sqrt (/ k 2)) (sqrt (/ k 2))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (cbrt k) (cbrt 2)) (/ (* (cbrt k) (cbrt k)) (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (cbrt k) (sqrt 2)) (/ (* (cbrt k) (cbrt k)) (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (cbrt k) 2) (/ (* (cbrt k) (cbrt k)) 1)))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (sqrt k) (cbrt 2)) (/ (sqrt k) (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (sqrt k) (sqrt 2)) (/ (sqrt k) (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ (sqrt k) 2) (/ (sqrt k) 1)))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ k (cbrt 2)) (/ 1 (* (cbrt 2) (cbrt 2)))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ k (sqrt 2)) (/ 1 (sqrt 2))))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ k 2) (/ 1 1)))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ k 2) 1))))) (/ 1 (pow (* (* n 2) PI) (fma 1 1/2 (- (* (/ 1 2) k))))) (/ 1 (pow (* (* n 2) PI) 1/2)) (/ 1 (pow (* (* n 2) PI) 1/2)) (/ 1 (pow (* n 2) (- 1/2 (/ k 2)))) (/ 1 (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))) (/ 1 (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (/ 1 1) (/ 1 (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt 1)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (/ 1 (pow (* (* n 2) PI) 1/2)) (real->posit16 (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* 2 (* n PI)) (* 2 (* n PI)) (* 2 (* n PI)) (- (+ (* +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 3))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2)))))))) (- (+ (* 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))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (+ (* 1/8 (/ (* (pow (log (* 2 PI)) 2) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (/ (* k (log (* 2 PI))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/2 (/ (* (log n) k) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (* 1/4 (/ (* (log (* 2 PI)) (* (log n) (pow k 2))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (+ (/ 1 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (* 1/8 (/ (* (pow (log n) 2) (pow k 2)) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))))))) (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (/ 1 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 69.000 * * [simplify]: iteration 0: 2099 enodes 70.467 * * [simplify]: iteration complete: 5001 enodes 70.471 * * [simplify]: Extracting #0: cost 1417 inf + 0 70.487 * * [simplify]: Extracting #1: cost 2754 inf + 1 70.497 * * [simplify]: Extracting #2: cost 2848 inf + 4437 70.519 * * [simplify]: Extracting #3: cost 2643 inf + 73232 70.579 * * [simplify]: Extracting #4: cost 1692 inf + 516210 70.675 * * [simplify]: Extracting #5: cost 1283 inf + 777227 70.824 * * [simplify]: Extracting #6: cost 873 inf + 1099507 71.028 * * [simplify]: Extracting #7: cost 308 inf + 1635232 71.318 * * [simplify]: Extracting #8: cost 38 inf + 1911495 71.543 * * [simplify]: Extracting #9: cost 26 inf + 1926660 71.815 * * [simplify]: Extracting #10: cost 22 inf + 1931891 72.048 * * [simplify]: Extracting #11: cost 15 inf + 1931843 72.298 * * [simplify]: Extracting #12: cost 9 inf + 1934604 72.569 * * [simplify]: Extracting #13: cost 6 inf + 1936714 72.795 * * [simplify]: Extracting #14: cost 3 inf + 1939754 73.024 * * [simplify]: Extracting #15: cost 0 inf + 1943064 73.251 * * [simplify]: Extracting #16: cost 0 inf + 1942944 73.577 * [simplify]: Simplified to: (expm1 (* (* n 2) PI)) (log1p (* (* n 2) PI)) (* (* n 2) PI) (* (* n 2) PI) (log (* (* n 2) PI)) (log (* (* n 2) PI)) (log (* (* n 2) PI)) (exp (* (* n 2) PI)) (* (* (* n n) n) (* (* 2 (* 2 2)) (* (* PI PI) PI))) (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI)) (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI)) (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI)) (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI)) (* (* n 2) (* (cbrt PI) (cbrt PI))) (* (* n 2) (sqrt PI)) (* n 2) (* 2 PI) (real->posit16 (* (* n 2) PI)) (expm1 (* (/ (pow k (- 1/2)) 1) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (log1p (* (/ (pow k (- 1/2)) 1) (pow (* (* n 2) PI) (- 1/2 (/ k 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(/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt 1)) (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (/ 1 (sqrt (* (* n 2) PI))) (real->posit16 (/ 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (* 2 n) PI) (* (* 2 n) PI) (* (* 2 n) PI) (- (fma +nan.0 (* (sqrt 2) (* (* n PI) k)) (- (+ (* (* +nan.0 (sqrt 2)) (* n PI)) (- (fma +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* (* n PI) k))) (- (+ (* (* +nan.0 (sqrt 2)) (* (* n PI) (* (log n) k))) (- (* (* +nan.0 (sqrt 2)) (* (* n n) (* PI PI)))))))))))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (* k (* k k))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) k) (* (- +nan.0) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (* k k))))))) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k) (- (fma +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* k (* k k))) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (* k k)))))))) (- (fma 1/4 (* (* (log (* 2 PI)) (exp (* 1/2 (log (* (* n 2) PI))))) (* (log n) (* k k))) (fma 1/8 (* (* (exp (* 1/2 (log (* (* n 2) PI)))) (* (log n) (log n))) (* k k)) (+ (exp (* 1/2 (log (* (* n 2) PI)))) (* 1/8 (* (* (log (* 2 PI)) (log (* 2 PI))) (* (exp (* 1/2 (log (* (* n 2) PI)))) (* k k))))))) (* 1/2 (+ (* (exp (* 1/2 (log (* (* n 2) PI)))) (* (log n) k)) (* (log (* 2 PI)) (* (exp (* 1/2 (log (* (* n 2) PI)))) k))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n))))) (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (fma 1/8 (/ (* (* (log (* 2 PI)) (log (* 2 PI))) (* k k)) (exp (* 1/2 (log (* (* n 2) PI))))) (fma 1/2 (/ (* k (log (* 2 PI))) (exp (* 1/2 (log (* (* n 2) PI))))) (fma 1/2 (/ (* (log n) k) (exp (* 1/2 (log (* (* n 2) PI))))) (fma 1/4 (/ (log (* 2 PI)) (/ (exp (* 1/2 (log (* (* n 2) PI)))) (* (log n) (* k k)))) (+ (exp (- (* 1/2 (log (* (* n 2) PI))))) (* 1/8 (/ (* (log n) (log n)) (/ (exp (* 1/2 (log (* (* n 2) PI)))) (* k k))))))))) (exp (- (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (- (log n)))))) (exp (- (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 74.047 * * * [progress]: adding candidates to table 87.107 * [progress]: [Phase 3 of 3] Extracting. 87.107 * * [regime]: Finding splitpoints for: (# # # # #) 87.108 * * * [regime-changes]: Trying 2 branch expressions: (n k) 87.108 * * * * [regimes]: Trying to branch on n from (# # # # #) 87.145 * * * * [regimes]: Trying to branch on k from (# # # # #) 87.215 * * * [regime]: Found split indices: #