49.846 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.109 * * * [progress]: [2/2] Setting up program. 0.111 * [progress]: [Phase 2 of 3] Improving. 0.112 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.112 * * [simplify]: Extracting # 0 : cost 0 0.112 * * [simplify]: Extracting # 1 : cost 0 0.112 * * [simplify]: Extracting # 2 : cost 0 0.112 * * [simplify]: Extracting # 3 : cost 0 0.112 * * [simplify]: Extracting # 4 : cost 0 0.112 * * [simplify]: Extracting # 5 : cost 0 0.112 * * [simplify]: Extracting # 6 : cost 0 0.112 * * [simplify]: Extracting # 7 : cost 0 0.112 * * [simplify]: iteration 0 : 13 enodes (cost 16 ) 0.115 * * [simplify]: Extracting # 0 : cost 0 0.115 * * [simplify]: Extracting # 1 : cost 0 0.115 * * [simplify]: Extracting # 2 : cost 0 0.115 * * [simplify]: Extracting # 3 : cost 0 0.115 * * [simplify]: Extracting # 4 : cost 0 0.115 * * [simplify]: Extracting # 5 : cost 0 0.115 * * [simplify]: iteration 1 : 29 enodes (cost 16 ) 0.121 * * [simplify]: Extracting # 0 : cost 0 0.121 * * [simplify]: Extracting # 1 : cost 0 0.121 * * [simplify]: Extracting # 2 : cost 0 0.121 * * [simplify]: Extracting # 3 : cost 0 0.121 * * [simplify]: Extracting # 4 : cost 0 0.121 * * [simplify]: iteration 2 : 59 enodes (cost 16 ) 0.133 * * [simplify]: Extracting # 0 : cost 0 0.133 * * [simplify]: Extracting # 1 : cost 0 0.133 * * [simplify]: Extracting # 2 : cost 0 0.133 * * [simplify]: Extracting # 3 : cost 0 0.133 * * [simplify]: Extracting # 4 : cost 0 0.133 * * [simplify]: iteration 3 : 120 enodes (cost 16 ) 0.189 * * [simplify]: Extracting # 0 : cost 0 0.189 * * [simplify]: Extracting # 1 : cost 0 0.190 * * [simplify]: Extracting # 2 : cost 0 0.190 * * [simplify]: Extracting # 3 : cost 0 0.190 * * [simplify]: Extracting # 4 : cost 0 0.191 * * [simplify]: iteration 4 : 330 enodes (cost 16 ) 0.480 * * [simplify]: Extracting # 0 : cost 0 0.482 * * [simplify]: Extracting # 1 : cost 0 0.486 * * [simplify]: Extracting # 2 : cost 0 0.489 * * [simplify]: Extracting # 3 : cost 0 0.492 * * [simplify]: Extracting # 4 : cost 0 0.495 * * [simplify]: Extracting # 5 : cost 0 0.498 * * [simplify]: iteration 5 : 1545 enodes (cost 16 ) 1.272 * * [simplify]: Extracting # 0 : cost 0 1.328 * * [simplify]: Extracting # 1 : cost 0 1.335 * * [simplify]: Extracting # 2 : cost 0 1.341 * * [simplify]: Extracting # 3 : cost 0 1.349 * * [simplify]: Extracting # 4 : cost 0 1.355 * * [simplify]: iteration done: 5000 enodes (cost 16 ) 1.355 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1.356 * * [progress]: iteration 1 / 4 1.356 * * * [progress]: picking best candidate 1.358 * * * * [pick]: Picked # 1.358 * * * [progress]: localizing error 1.375 * * * [progress]: generating rewritten candidates 1.376 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 1.418 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 1.460 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 1.472 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 1.561 * * * [progress]: generating series expansions 1.562 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 1.563 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 1.563 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.563 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.563 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.563 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.567 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.567 * [taylor]: Taking taylor expansion of 0.5 in k 1.567 * [backup-simplify]: Simplify 0.5 into 0.5 1.567 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.567 * [taylor]: Taking taylor expansion of 1.0 in k 1.567 * [backup-simplify]: Simplify 1.0 into 1.0 1.567 * [taylor]: Taking taylor expansion of k in k 1.567 * [backup-simplify]: Simplify 0 into 0 1.567 * [backup-simplify]: Simplify 1 into 1 1.567 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.567 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.567 * [taylor]: Taking taylor expansion of 2.0 in k 1.567 * [backup-simplify]: Simplify 2.0 into 2.0 1.567 * [taylor]: Taking taylor expansion of (* n PI) in k 1.567 * [taylor]: Taking taylor expansion of n in k 1.567 * [backup-simplify]: Simplify n into n 1.568 * [taylor]: Taking taylor expansion of PI in k 1.568 * [backup-simplify]: Simplify PI into PI 1.568 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.568 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.568 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.569 * [backup-simplify]: Simplify (- 0) into 0 1.569 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.570 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.570 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.570 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.570 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.570 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.570 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.570 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.570 * [taylor]: Taking taylor expansion of 0.5 in n 1.570 * [backup-simplify]: Simplify 0.5 into 0.5 1.570 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.570 * [taylor]: Taking taylor expansion of 1.0 in n 1.570 * [backup-simplify]: Simplify 1.0 into 1.0 1.570 * [taylor]: Taking taylor expansion of k in n 1.570 * [backup-simplify]: Simplify k into k 1.570 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.570 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.570 * [taylor]: Taking taylor expansion of 2.0 in n 1.570 * [backup-simplify]: Simplify 2.0 into 2.0 1.570 * [taylor]: Taking taylor expansion of (* n PI) in n 1.570 * [taylor]: Taking taylor expansion of n in n 1.570 * [backup-simplify]: Simplify 0 into 0 1.570 * [backup-simplify]: Simplify 1 into 1 1.570 * [taylor]: Taking taylor expansion of PI in n 1.570 * [backup-simplify]: Simplify PI into PI 1.571 * [backup-simplify]: Simplify (* 0 PI) into 0 1.571 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.573 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.574 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.576 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.576 * [backup-simplify]: Simplify (- k) into (- k) 1.576 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.576 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.577 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.578 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.580 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.580 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.580 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.580 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.580 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.580 * [taylor]: Taking taylor expansion of 0.5 in n 1.580 * [backup-simplify]: Simplify 0.5 into 0.5 1.580 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.580 * [taylor]: Taking taylor expansion of 1.0 in n 1.580 * [backup-simplify]: Simplify 1.0 into 1.0 1.580 * [taylor]: Taking taylor expansion of k in n 1.580 * [backup-simplify]: Simplify k into k 1.580 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.580 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.580 * [taylor]: Taking taylor expansion of 2.0 in n 1.580 * [backup-simplify]: Simplify 2.0 into 2.0 1.580 * [taylor]: Taking taylor expansion of (* n PI) in n 1.580 * [taylor]: Taking taylor expansion of n in n 1.580 * [backup-simplify]: Simplify 0 into 0 1.580 * [backup-simplify]: Simplify 1 into 1 1.580 * [taylor]: Taking taylor expansion of PI in n 1.580 * [backup-simplify]: Simplify PI into PI 1.581 * [backup-simplify]: Simplify (* 0 PI) into 0 1.581 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.583 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.584 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.585 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.585 * [backup-simplify]: Simplify (- k) into (- k) 1.585 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.585 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.587 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.588 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.589 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.589 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.589 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.589 * [taylor]: Taking taylor expansion of 0.5 in k 1.589 * [backup-simplify]: Simplify 0.5 into 0.5 1.589 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.589 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.589 * [taylor]: Taking taylor expansion of 1.0 in k 1.589 * [backup-simplify]: Simplify 1.0 into 1.0 1.589 * [taylor]: Taking taylor expansion of k in k 1.589 * [backup-simplify]: Simplify 0 into 0 1.589 * [backup-simplify]: Simplify 1 into 1 1.590 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.590 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.590 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.590 * [taylor]: Taking taylor expansion of 2.0 in k 1.590 * [backup-simplify]: Simplify 2.0 into 2.0 1.590 * [taylor]: Taking taylor expansion of PI in k 1.590 * [backup-simplify]: Simplify PI into PI 1.590 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.591 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.591 * [taylor]: Taking taylor expansion of (log n) in k 1.591 * [taylor]: Taking taylor expansion of n in k 1.591 * [backup-simplify]: Simplify n into n 1.591 * [backup-simplify]: Simplify (log n) into (log n) 1.592 * [backup-simplify]: Simplify (- 0) into 0 1.592 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.593 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.594 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.596 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 1.597 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.598 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.599 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.600 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.602 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.602 * [backup-simplify]: Simplify (- 0) into 0 1.603 * [backup-simplify]: Simplify (+ 0 0) into 0 1.603 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 1.605 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.606 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.608 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.608 * [taylor]: Taking taylor expansion of 0 in k 1.608 * [backup-simplify]: Simplify 0 into 0 1.608 * [backup-simplify]: Simplify 0 into 0 1.609 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.611 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.612 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.612 * [backup-simplify]: Simplify (+ 0 0) into 0 1.613 * [backup-simplify]: Simplify (- 1) into -1 1.613 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.614 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.617 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1.620 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 1.623 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 1.625 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.626 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.629 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.630 * [backup-simplify]: Simplify (- 0) into 0 1.630 * [backup-simplify]: Simplify (+ 0 0) into 0 1.631 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.633 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.634 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.637 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.637 * [taylor]: Taking taylor expansion of 0 in k 1.637 * [backup-simplify]: Simplify 0 into 0 1.637 * [backup-simplify]: Simplify 0 into 0 1.637 * [backup-simplify]: Simplify 0 into 0 1.638 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.641 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.643 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.644 * [backup-simplify]: Simplify (+ 0 0) into 0 1.644 * [backup-simplify]: Simplify (- 0) into 0 1.644 * [backup-simplify]: Simplify (+ 0 0) into 0 1.646 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.649 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.653 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 1.658 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 1.669 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 1.670 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 1.671 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.671 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.671 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.671 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.671 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.671 * [taylor]: Taking taylor expansion of 0.5 in k 1.671 * [backup-simplify]: Simplify 0.5 into 0.5 1.671 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.671 * [taylor]: Taking taylor expansion of 1.0 in k 1.671 * [backup-simplify]: Simplify 1.0 into 1.0 1.671 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.671 * [taylor]: Taking taylor expansion of k in k 1.671 * [backup-simplify]: Simplify 0 into 0 1.671 * [backup-simplify]: Simplify 1 into 1 1.671 * [backup-simplify]: Simplify (/ 1 1) into 1 1.671 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.671 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.671 * [taylor]: Taking taylor expansion of 2.0 in k 1.672 * [backup-simplify]: Simplify 2.0 into 2.0 1.672 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.672 * [taylor]: Taking taylor expansion of PI in k 1.672 * [backup-simplify]: Simplify PI into PI 1.672 * [taylor]: Taking taylor expansion of n in k 1.672 * [backup-simplify]: Simplify n into n 1.672 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.672 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.672 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.672 * [backup-simplify]: Simplify (- 1) into -1 1.673 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.673 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.673 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.674 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 1.674 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.674 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.674 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.674 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.674 * [taylor]: Taking taylor expansion of 0.5 in n 1.674 * [backup-simplify]: Simplify 0.5 into 0.5 1.674 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.674 * [taylor]: Taking taylor expansion of 1.0 in n 1.674 * [backup-simplify]: Simplify 1.0 into 1.0 1.674 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.674 * [taylor]: Taking taylor expansion of k in n 1.674 * [backup-simplify]: Simplify k into k 1.675 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.675 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.675 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.675 * [taylor]: Taking taylor expansion of 2.0 in n 1.675 * [backup-simplify]: Simplify 2.0 into 2.0 1.675 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.675 * [taylor]: Taking taylor expansion of PI in n 1.675 * [backup-simplify]: Simplify PI into PI 1.675 * [taylor]: Taking taylor expansion of n in n 1.675 * [backup-simplify]: Simplify 0 into 0 1.675 * [backup-simplify]: Simplify 1 into 1 1.675 * [backup-simplify]: Simplify (/ PI 1) into PI 1.676 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.677 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.677 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.677 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.677 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.679 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.680 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.681 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.681 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.682 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.682 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.682 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.682 * [taylor]: Taking taylor expansion of 0.5 in n 1.682 * [backup-simplify]: Simplify 0.5 into 0.5 1.682 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.682 * [taylor]: Taking taylor expansion of 1.0 in n 1.682 * [backup-simplify]: Simplify 1.0 into 1.0 1.682 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.682 * [taylor]: Taking taylor expansion of k in n 1.682 * [backup-simplify]: Simplify k into k 1.682 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.682 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.682 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.682 * [taylor]: Taking taylor expansion of 2.0 in n 1.682 * [backup-simplify]: Simplify 2.0 into 2.0 1.682 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.682 * [taylor]: Taking taylor expansion of PI in n 1.682 * [backup-simplify]: Simplify PI into PI 1.682 * [taylor]: Taking taylor expansion of n in n 1.682 * [backup-simplify]: Simplify 0 into 0 1.682 * [backup-simplify]: Simplify 1 into 1 1.683 * [backup-simplify]: Simplify (/ PI 1) into PI 1.683 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.684 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.684 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.685 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.685 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.686 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.687 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 1.689 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.689 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.689 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.689 * [taylor]: Taking taylor expansion of 0.5 in k 1.689 * [backup-simplify]: Simplify 0.5 into 0.5 1.689 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.689 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.689 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.689 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.689 * [taylor]: Taking taylor expansion of 2.0 in k 1.689 * [backup-simplify]: Simplify 2.0 into 2.0 1.689 * [taylor]: Taking taylor expansion of PI in k 1.689 * [backup-simplify]: Simplify PI into PI 1.690 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.691 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.691 * [taylor]: Taking taylor expansion of (log n) in k 1.691 * [taylor]: Taking taylor expansion of n in k 1.691 * [backup-simplify]: Simplify n into n 1.691 * [backup-simplify]: Simplify (log n) into (log n) 1.691 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.691 * [taylor]: Taking taylor expansion of 1.0 in k 1.691 * [backup-simplify]: Simplify 1.0 into 1.0 1.691 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.691 * [taylor]: Taking taylor expansion of k in k 1.691 * [backup-simplify]: Simplify 0 into 0 1.691 * [backup-simplify]: Simplify 1 into 1 1.692 * [backup-simplify]: Simplify (/ 1 1) into 1 1.692 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.693 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.693 * [backup-simplify]: Simplify (- 1) into -1 1.694 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.695 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.696 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 1.697 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.699 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 1.700 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.700 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.703 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.703 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.703 * [backup-simplify]: Simplify (- 0) into 0 1.704 * [backup-simplify]: Simplify (+ 0 0) into 0 1.704 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.706 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.707 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.709 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.709 * [taylor]: Taking taylor expansion of 0 in k 1.709 * [backup-simplify]: Simplify 0 into 0 1.709 * [backup-simplify]: Simplify 0 into 0 1.709 * [backup-simplify]: Simplify 0 into 0 1.710 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.711 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.715 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 1.715 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.716 * [backup-simplify]: Simplify (- 0) into 0 1.716 * [backup-simplify]: Simplify (+ 0 0) into 0 1.717 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.721 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.722 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.724 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.724 * [taylor]: Taking taylor expansion of 0 in k 1.724 * [backup-simplify]: Simplify 0 into 0 1.724 * [backup-simplify]: Simplify 0 into 0 1.724 * [backup-simplify]: Simplify 0 into 0 1.724 * [backup-simplify]: Simplify 0 into 0 1.725 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.725 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.729 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 1.729 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.729 * [backup-simplify]: Simplify (- 0) into 0 1.729 * [backup-simplify]: Simplify (+ 0 0) into 0 1.730 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.731 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.732 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.734 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.734 * [taylor]: Taking taylor expansion of 0 in k 1.734 * [backup-simplify]: Simplify 0 into 0 1.734 * [backup-simplify]: Simplify 0 into 0 1.734 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 1.735 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 1.735 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.735 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.735 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.735 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.735 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.735 * [taylor]: Taking taylor expansion of 0.5 in k 1.735 * [backup-simplify]: Simplify 0.5 into 0.5 1.735 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.735 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.735 * [taylor]: Taking taylor expansion of k in k 1.735 * [backup-simplify]: Simplify 0 into 0 1.735 * [backup-simplify]: Simplify 1 into 1 1.735 * [backup-simplify]: Simplify (/ 1 1) into 1 1.736 * [taylor]: Taking taylor expansion of 1.0 in k 1.736 * [backup-simplify]: Simplify 1.0 into 1.0 1.736 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.736 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.736 * [taylor]: Taking taylor expansion of -2.0 in k 1.736 * [backup-simplify]: Simplify -2.0 into -2.0 1.736 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.736 * [taylor]: Taking taylor expansion of PI in k 1.736 * [backup-simplify]: Simplify PI into PI 1.736 * [taylor]: Taking taylor expansion of n in k 1.736 * [backup-simplify]: Simplify n into n 1.736 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.736 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.736 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.736 * [backup-simplify]: Simplify (+ 1 0) into 1 1.736 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.736 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.737 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 1.737 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.737 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.737 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.737 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.737 * [taylor]: Taking taylor expansion of 0.5 in n 1.737 * [backup-simplify]: Simplify 0.5 into 0.5 1.737 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.737 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.737 * [taylor]: Taking taylor expansion of k in n 1.737 * [backup-simplify]: Simplify k into k 1.737 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.737 * [taylor]: Taking taylor expansion of 1.0 in n 1.737 * [backup-simplify]: Simplify 1.0 into 1.0 1.737 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.737 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.737 * [taylor]: Taking taylor expansion of -2.0 in n 1.737 * [backup-simplify]: Simplify -2.0 into -2.0 1.737 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.737 * [taylor]: Taking taylor expansion of PI in n 1.737 * [backup-simplify]: Simplify PI into PI 1.737 * [taylor]: Taking taylor expansion of n in n 1.737 * [backup-simplify]: Simplify 0 into 0 1.737 * [backup-simplify]: Simplify 1 into 1 1.737 * [backup-simplify]: Simplify (/ PI 1) into PI 1.738 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.738 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.738 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.738 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.739 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.740 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.741 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.741 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.741 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.741 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.741 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.741 * [taylor]: Taking taylor expansion of 0.5 in n 1.741 * [backup-simplify]: Simplify 0.5 into 0.5 1.741 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.741 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.741 * [taylor]: Taking taylor expansion of k in n 1.741 * [backup-simplify]: Simplify k into k 1.741 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.741 * [taylor]: Taking taylor expansion of 1.0 in n 1.741 * [backup-simplify]: Simplify 1.0 into 1.0 1.741 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.741 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.741 * [taylor]: Taking taylor expansion of -2.0 in n 1.741 * [backup-simplify]: Simplify -2.0 into -2.0 1.741 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.741 * [taylor]: Taking taylor expansion of PI in n 1.741 * [backup-simplify]: Simplify PI into PI 1.741 * [taylor]: Taking taylor expansion of n in n 1.741 * [backup-simplify]: Simplify 0 into 0 1.741 * [backup-simplify]: Simplify 1 into 1 1.742 * [backup-simplify]: Simplify (/ PI 1) into PI 1.742 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.742 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.743 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.743 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.743 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.744 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 1.745 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.745 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 1.745 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 1.745 * [taylor]: Taking taylor expansion of 0.5 in k 1.745 * [backup-simplify]: Simplify 0.5 into 0.5 1.745 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 1.745 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.745 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.745 * [taylor]: Taking taylor expansion of k in k 1.745 * [backup-simplify]: Simplify 0 into 0 1.745 * [backup-simplify]: Simplify 1 into 1 1.745 * [backup-simplify]: Simplify (/ 1 1) into 1 1.745 * [taylor]: Taking taylor expansion of 1.0 in k 1.745 * [backup-simplify]: Simplify 1.0 into 1.0 1.745 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 1.746 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 1.746 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 1.746 * [taylor]: Taking taylor expansion of -2.0 in k 1.746 * [backup-simplify]: Simplify -2.0 into -2.0 1.746 * [taylor]: Taking taylor expansion of PI in k 1.746 * [backup-simplify]: Simplify PI into PI 1.746 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.746 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.747 * [taylor]: Taking taylor expansion of (log n) in k 1.747 * [taylor]: Taking taylor expansion of n in k 1.747 * [backup-simplify]: Simplify n into n 1.747 * [backup-simplify]: Simplify (log n) into (log n) 1.747 * [backup-simplify]: Simplify (+ 1 0) into 1 1.747 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.748 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.748 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.749 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 1.750 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.750 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 1.751 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.751 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.752 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.753 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.753 * [backup-simplify]: Simplify (+ 0 0) into 0 1.753 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.754 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.755 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.756 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.757 * [taylor]: Taking taylor expansion of 0 in k 1.757 * [backup-simplify]: Simplify 0 into 0 1.757 * [backup-simplify]: Simplify 0 into 0 1.757 * [backup-simplify]: Simplify 0 into 0 1.758 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.759 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.762 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 1.762 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.763 * [backup-simplify]: Simplify (+ 0 0) into 0 1.763 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.765 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.766 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.769 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 1.769 * [taylor]: Taking taylor expansion of 0 in k 1.769 * [backup-simplify]: Simplify 0 into 0 1.769 * [backup-simplify]: Simplify 0 into 0 1.769 * [backup-simplify]: Simplify 0 into 0 1.769 * [backup-simplify]: Simplify 0 into 0 1.770 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.771 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.776 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 1.776 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.777 * [backup-simplify]: Simplify (+ 0 0) into 0 1.778 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.779 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.781 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.783 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 1.783 * [taylor]: Taking taylor expansion of 0 in k 1.783 * [backup-simplify]: Simplify 0 into 0 1.783 * [backup-simplify]: Simplify 0 into 0 1.784 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 1.784 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 1.785 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.785 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.785 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.785 * [taylor]: Taking taylor expansion of 2.0 in n 1.785 * [backup-simplify]: Simplify 2.0 into 2.0 1.785 * [taylor]: Taking taylor expansion of (* n PI) in n 1.785 * [taylor]: Taking taylor expansion of n in n 1.785 * [backup-simplify]: Simplify 0 into 0 1.785 * [backup-simplify]: Simplify 1 into 1 1.785 * [taylor]: Taking taylor expansion of PI in n 1.785 * [backup-simplify]: Simplify PI into PI 1.785 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.785 * [taylor]: Taking taylor expansion of 2.0 in n 1.785 * [backup-simplify]: Simplify 2.0 into 2.0 1.785 * [taylor]: Taking taylor expansion of (* n PI) in n 1.785 * [taylor]: Taking taylor expansion of n in n 1.785 * [backup-simplify]: Simplify 0 into 0 1.785 * [backup-simplify]: Simplify 1 into 1 1.785 * [taylor]: Taking taylor expansion of PI in n 1.785 * [backup-simplify]: Simplify PI into PI 1.786 * [backup-simplify]: Simplify (* 0 PI) into 0 1.786 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.786 * [backup-simplify]: Simplify 0 into 0 1.788 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.789 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.789 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.790 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.790 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.790 * [backup-simplify]: Simplify 0 into 0 1.791 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.792 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.792 * [backup-simplify]: Simplify 0 into 0 1.792 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.793 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.793 * [backup-simplify]: Simplify 0 into 0 1.794 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.795 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.795 * [backup-simplify]: Simplify 0 into 0 1.796 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.797 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.797 * [backup-simplify]: Simplify 0 into 0 1.798 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.799 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.799 * [backup-simplify]: Simplify 0 into 0 1.799 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.799 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.800 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.800 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.800 * [taylor]: Taking taylor expansion of 2.0 in n 1.800 * [backup-simplify]: Simplify 2.0 into 2.0 1.800 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.800 * [taylor]: Taking taylor expansion of PI in n 1.800 * [backup-simplify]: Simplify PI into PI 1.800 * [taylor]: Taking taylor expansion of n in n 1.800 * [backup-simplify]: Simplify 0 into 0 1.800 * [backup-simplify]: Simplify 1 into 1 1.800 * [backup-simplify]: Simplify (/ PI 1) into PI 1.800 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.800 * [taylor]: Taking taylor expansion of 2.0 in n 1.800 * [backup-simplify]: Simplify 2.0 into 2.0 1.800 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.800 * [taylor]: Taking taylor expansion of PI in n 1.800 * [backup-simplify]: Simplify PI into PI 1.800 * [taylor]: Taking taylor expansion of n in n 1.800 * [backup-simplify]: Simplify 0 into 0 1.800 * [backup-simplify]: Simplify 1 into 1 1.800 * [backup-simplify]: Simplify (/ PI 1) into PI 1.801 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.801 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.802 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.802 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.802 * [backup-simplify]: Simplify 0 into 0 1.803 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.803 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.803 * [backup-simplify]: Simplify 0 into 0 1.804 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.805 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.805 * [backup-simplify]: Simplify 0 into 0 1.806 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.806 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.806 * [backup-simplify]: Simplify 0 into 0 1.807 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.808 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.808 * [backup-simplify]: Simplify 0 into 0 1.809 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.810 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.810 * [backup-simplify]: Simplify 0 into 0 1.810 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.810 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.811 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.811 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.811 * [taylor]: Taking taylor expansion of -2.0 in n 1.811 * [backup-simplify]: Simplify -2.0 into -2.0 1.811 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.811 * [taylor]: Taking taylor expansion of PI in n 1.811 * [backup-simplify]: Simplify PI into PI 1.811 * [taylor]: Taking taylor expansion of n in n 1.811 * [backup-simplify]: Simplify 0 into 0 1.811 * [backup-simplify]: Simplify 1 into 1 1.811 * [backup-simplify]: Simplify (/ PI 1) into PI 1.811 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.811 * [taylor]: Taking taylor expansion of -2.0 in n 1.811 * [backup-simplify]: Simplify -2.0 into -2.0 1.811 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.811 * [taylor]: Taking taylor expansion of PI in n 1.811 * [backup-simplify]: Simplify PI into PI 1.811 * [taylor]: Taking taylor expansion of n in n 1.811 * [backup-simplify]: Simplify 0 into 0 1.811 * [backup-simplify]: Simplify 1 into 1 1.811 * [backup-simplify]: Simplify (/ PI 1) into PI 1.812 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.812 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.813 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.813 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.813 * [backup-simplify]: Simplify 0 into 0 1.814 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.814 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.814 * [backup-simplify]: Simplify 0 into 0 1.815 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.816 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.816 * [backup-simplify]: Simplify 0 into 0 1.817 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.817 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.817 * [backup-simplify]: Simplify 0 into 0 1.818 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.819 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.819 * [backup-simplify]: Simplify 0 into 0 1.820 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.822 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.822 * [backup-simplify]: Simplify 0 into 0 1.826 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.826 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 1.827 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 1.827 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 1.827 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.827 * [taylor]: Taking taylor expansion of 1.0 in k 1.827 * [backup-simplify]: Simplify 1.0 into 1.0 1.827 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.827 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.827 * [taylor]: Taking taylor expansion of k in k 1.827 * [backup-simplify]: Simplify 0 into 0 1.827 * [backup-simplify]: Simplify 1 into 1 1.827 * [backup-simplify]: Simplify (/ 1 1) into 1 1.828 * [backup-simplify]: Simplify (sqrt 0) into 0 1.829 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.829 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k 1.829 * [taylor]: Taking taylor expansion of 1.0 in k 1.829 * [backup-simplify]: Simplify 1.0 into 1.0 1.829 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.829 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.829 * [taylor]: Taking taylor expansion of k in k 1.829 * [backup-simplify]: Simplify 0 into 0 1.829 * [backup-simplify]: Simplify 1 into 1 1.830 * [backup-simplify]: Simplify (/ 1 1) into 1 1.830 * [backup-simplify]: Simplify (sqrt 0) into 0 1.831 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.832 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.832 * [backup-simplify]: Simplify 0 into 0 1.833 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 1.833 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.834 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1.837 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.839 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 1.839 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.840 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.843 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.845 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 1.845 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.847 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 1.847 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 1.847 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 1.847 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.847 * [taylor]: Taking taylor expansion of 1.0 in k 1.847 * [backup-simplify]: Simplify 1.0 into 1.0 1.847 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.847 * [taylor]: Taking taylor expansion of k in k 1.847 * [backup-simplify]: Simplify 0 into 0 1.847 * [backup-simplify]: Simplify 1 into 1 1.847 * [backup-simplify]: Simplify (sqrt 0) into 0 1.849 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.849 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.849 * [taylor]: Taking taylor expansion of 1.0 in k 1.849 * [backup-simplify]: Simplify 1.0 into 1.0 1.849 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.849 * [taylor]: Taking taylor expansion of k in k 1.849 * [backup-simplify]: Simplify 0 into 0 1.849 * [backup-simplify]: Simplify 1 into 1 1.849 * [backup-simplify]: Simplify (sqrt 0) into 0 1.850 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.851 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.851 * [backup-simplify]: Simplify 0 into 0 1.852 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 1.852 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.855 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.856 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 1.857 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.860 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.862 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 1.862 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.864 * [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)))))))) 1.864 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 1.864 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 1.864 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.864 * [taylor]: Taking taylor expansion of 1.0 in k 1.864 * [backup-simplify]: Simplify 1.0 into 1.0 1.864 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.864 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.864 * [taylor]: Taking taylor expansion of -1 in k 1.864 * [backup-simplify]: Simplify -1 into -1 1.864 * [taylor]: Taking taylor expansion of k in k 1.864 * [backup-simplify]: Simplify 0 into 0 1.864 * [backup-simplify]: Simplify 1 into 1 1.865 * [backup-simplify]: Simplify (/ -1 1) into -1 1.865 * [backup-simplify]: Simplify (sqrt 0) into 0 1.866 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.866 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 1.866 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.866 * [taylor]: Taking taylor expansion of 1.0 in k 1.866 * [backup-simplify]: Simplify 1.0 into 1.0 1.866 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.866 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.866 * [taylor]: Taking taylor expansion of -1 in k 1.866 * [backup-simplify]: Simplify -1 into -1 1.866 * [taylor]: Taking taylor expansion of k in k 1.866 * [backup-simplify]: Simplify 0 into 0 1.866 * [backup-simplify]: Simplify 1 into 1 1.867 * [backup-simplify]: Simplify (/ -1 1) into -1 1.867 * [backup-simplify]: Simplify (sqrt 0) into 0 1.868 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.868 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 1.868 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.869 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1.870 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.872 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 1.872 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.873 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.875 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.877 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 1.878 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.878 * [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))))) 1.878 * * * * [progress]: [ 4 / 4 ] generating series at (2) 1.879 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) 1.879 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0 1.879 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 1.879 * [taylor]: Taking taylor expansion of 1.0 in n 1.879 * [backup-simplify]: Simplify 1.0 into 1.0 1.879 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 1.879 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 1.879 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.879 * [taylor]: Taking taylor expansion of k in n 1.879 * [backup-simplify]: Simplify k into k 1.879 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.879 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1.879 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.879 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1.879 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.879 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.879 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.879 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.879 * [taylor]: Taking taylor expansion of 0.5 in n 1.880 * [backup-simplify]: Simplify 0.5 into 0.5 1.880 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.880 * [taylor]: Taking taylor expansion of 1.0 in n 1.880 * [backup-simplify]: Simplify 1.0 into 1.0 1.880 * [taylor]: Taking taylor expansion of k in n 1.880 * [backup-simplify]: Simplify k into k 1.880 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.880 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.880 * [taylor]: Taking taylor expansion of 2.0 in n 1.880 * [backup-simplify]: Simplify 2.0 into 2.0 1.880 * [taylor]: Taking taylor expansion of (* n PI) in n 1.880 * [taylor]: Taking taylor expansion of n in n 1.880 * [backup-simplify]: Simplify 0 into 0 1.880 * [backup-simplify]: Simplify 1 into 1 1.880 * [taylor]: Taking taylor expansion of PI in n 1.880 * [backup-simplify]: Simplify PI into PI 1.880 * [backup-simplify]: Simplify (* 0 PI) into 0 1.880 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.881 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.882 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.883 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.883 * [backup-simplify]: Simplify (- k) into (- k) 1.883 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.883 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.884 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.884 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 1.885 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 1.885 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 1.885 * [taylor]: Taking taylor expansion of 1.0 in k 1.885 * [backup-simplify]: Simplify 1.0 into 1.0 1.885 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 1.885 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.885 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.885 * [taylor]: Taking taylor expansion of k in k 1.885 * [backup-simplify]: Simplify 0 into 0 1.885 * [backup-simplify]: Simplify 1 into 1 1.886 * [backup-simplify]: Simplify (/ 1 1) into 1 1.886 * [backup-simplify]: Simplify (sqrt 0) into 0 1.887 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.887 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.887 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.887 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.887 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.887 * [taylor]: Taking taylor expansion of 0.5 in k 1.887 * [backup-simplify]: Simplify 0.5 into 0.5 1.887 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.887 * [taylor]: Taking taylor expansion of 1.0 in k 1.887 * [backup-simplify]: Simplify 1.0 into 1.0 1.887 * [taylor]: Taking taylor expansion of k in k 1.887 * [backup-simplify]: Simplify 0 into 0 1.887 * [backup-simplify]: Simplify 1 into 1 1.887 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.887 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.887 * [taylor]: Taking taylor expansion of 2.0 in k 1.887 * [backup-simplify]: Simplify 2.0 into 2.0 1.887 * [taylor]: Taking taylor expansion of (* n PI) in k 1.887 * [taylor]: Taking taylor expansion of n in k 1.887 * [backup-simplify]: Simplify n into n 1.887 * [taylor]: Taking taylor expansion of PI in k 1.887 * [backup-simplify]: Simplify PI into PI 1.887 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.887 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.887 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.887 * [backup-simplify]: Simplify (- 0) into 0 1.888 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.888 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.888 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.888 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.888 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 1.888 * [taylor]: Taking taylor expansion of 1.0 in k 1.888 * [backup-simplify]: Simplify 1.0 into 1.0 1.888 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 1.888 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.888 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.888 * [taylor]: Taking taylor expansion of k in k 1.888 * [backup-simplify]: Simplify 0 into 0 1.888 * [backup-simplify]: Simplify 1 into 1 1.888 * [backup-simplify]: Simplify (/ 1 1) into 1 1.889 * [backup-simplify]: Simplify (sqrt 0) into 0 1.890 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.890 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.890 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.890 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.890 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.890 * [taylor]: Taking taylor expansion of 0.5 in k 1.890 * [backup-simplify]: Simplify 0.5 into 0.5 1.890 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.890 * [taylor]: Taking taylor expansion of 1.0 in k 1.890 * [backup-simplify]: Simplify 1.0 into 1.0 1.890 * [taylor]: Taking taylor expansion of k in k 1.890 * [backup-simplify]: Simplify 0 into 0 1.890 * [backup-simplify]: Simplify 1 into 1 1.890 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.890 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.890 * [taylor]: Taking taylor expansion of 2.0 in k 1.890 * [backup-simplify]: Simplify 2.0 into 2.0 1.890 * [taylor]: Taking taylor expansion of (* n PI) in k 1.890 * [taylor]: Taking taylor expansion of n in k 1.890 * [backup-simplify]: Simplify n into n 1.890 * [taylor]: Taking taylor expansion of PI in k 1.890 * [backup-simplify]: Simplify PI into PI 1.890 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.890 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.890 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.890 * [backup-simplify]: Simplify (- 0) into 0 1.891 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.891 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.891 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.891 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.891 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 1.891 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.891 * [taylor]: Taking taylor expansion of 0 in n 1.892 * [backup-simplify]: Simplify 0 into 0 1.892 * [backup-simplify]: Simplify 0 into 0 1.892 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 1.892 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 1.893 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 1.893 * [backup-simplify]: Simplify (- 1) into -1 1.893 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.894 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 1.895 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 1.895 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 1.896 * [backup-simplify]: Simplify (+ (* 0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 1.898 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 1.899 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n 1.899 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 1.899 * [taylor]: Taking taylor expansion of +nan.0 in n 1.899 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.899 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 1.899 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 1.899 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 1.899 * [taylor]: Taking taylor expansion of 0.5 in n 1.899 * [backup-simplify]: Simplify 0.5 into 0.5 1.899 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 1.899 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 1.899 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 1.899 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 1.899 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 1.899 * [taylor]: Taking taylor expansion of 1.0 in n 1.899 * [backup-simplify]: Simplify 1.0 into 1.0 1.899 * [taylor]: Taking taylor expansion of (log PI) in n 1.899 * [taylor]: Taking taylor expansion of PI in n 1.899 * [backup-simplify]: Simplify PI into PI 1.900 * [backup-simplify]: Simplify (log PI) into (log PI) 1.901 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 1.902 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 1.902 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 1.903 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 1.903 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 1.903 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 1.903 * [taylor]: Taking taylor expansion of 1.0 in n 1.903 * [backup-simplify]: Simplify 1.0 into 1.0 1.903 * [taylor]: Taking taylor expansion of (log n) in n 1.903 * [taylor]: Taking taylor expansion of n in n 1.903 * [backup-simplify]: Simplify 0 into 0 1.903 * [backup-simplify]: Simplify 1 into 1 1.903 * [backup-simplify]: Simplify (log 1) into 0 1.904 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1.904 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 1.904 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 1.904 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 1.904 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 1.904 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 1.904 * [taylor]: Taking taylor expansion of 1.0 in n 1.904 * [backup-simplify]: Simplify 1.0 into 1.0 1.904 * [taylor]: Taking taylor expansion of (log 2.0) in n 1.904 * [taylor]: Taking taylor expansion of 2.0 in n 1.904 * [backup-simplify]: Simplify 2.0 into 2.0 1.905 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 1.906 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 1.907 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 1.908 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 1.909 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.911 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 1.912 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 1.914 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 1.916 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 1.918 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) 1.919 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 1.919 * [backup-simplify]: Simplify 0 into 0 1.920 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1.921 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1.924 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0 1.924 * [backup-simplify]: Simplify (- 0) into 0 1.925 * [backup-simplify]: Simplify (+ 0 0) into 0 1.927 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 1.928 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 1.930 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 1.931 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1.935 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.938 * [backup-simplify]: Simplify (+ (* 0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5)))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 1.944 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) 1.944 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) in n 1.944 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))) in n 1.944 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n 1.944 * [taylor]: Taking taylor expansion of +nan.0 in n 1.944 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.944 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 1.944 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 1.944 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 1.944 * [taylor]: Taking taylor expansion of 0.5 in n 1.945 * [backup-simplify]: Simplify 0.5 into 0.5 1.945 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 1.945 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 1.945 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 1.945 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 1.945 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 1.945 * [taylor]: Taking taylor expansion of 1.0 in n 1.945 * [backup-simplify]: Simplify 1.0 into 1.0 1.945 * [taylor]: Taking taylor expansion of (log PI) in n 1.945 * [taylor]: Taking taylor expansion of PI in n 1.945 * [backup-simplify]: Simplify PI into PI 1.945 * [backup-simplify]: Simplify (log PI) into (log PI) 1.946 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 1.948 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 1.948 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 1.948 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 1.948 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 1.948 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 1.948 * [taylor]: Taking taylor expansion of 1.0 in n 1.948 * [backup-simplify]: Simplify 1.0 into 1.0 1.948 * [taylor]: Taking taylor expansion of (log n) in n 1.948 * [taylor]: Taking taylor expansion of n in n 1.948 * [backup-simplify]: Simplify 0 into 0 1.948 * [backup-simplify]: Simplify 1 into 1 1.949 * [backup-simplify]: Simplify (log 1) into 0 1.949 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1.949 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 1.949 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 1.949 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 1.949 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 1.949 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 1.949 * [taylor]: Taking taylor expansion of 1.0 in n 1.949 * [backup-simplify]: Simplify 1.0 into 1.0 1.949 * [taylor]: Taking taylor expansion of (log 2.0) in n 1.949 * [taylor]: Taking taylor expansion of 2.0 in n 1.950 * [backup-simplify]: Simplify 2.0 into 2.0 1.950 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 1.951 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 1.952 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 1.953 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0) 1.954 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.955 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)) 1.962 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0))) 1.963 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 1.963 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))) in n 1.963 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 1.963 * [taylor]: Taking taylor expansion of +nan.0 in n 1.963 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.963 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 1.963 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 1.963 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 1.963 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 1.963 * [taylor]: Taking taylor expansion of 0.5 in n 1.963 * [backup-simplify]: Simplify 0.5 into 0.5 1.963 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 1.964 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 1.964 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 1.964 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 1.964 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 1.964 * [taylor]: Taking taylor expansion of 1.0 in n 1.964 * [backup-simplify]: Simplify 1.0 into 1.0 1.964 * [taylor]: Taking taylor expansion of (log 2.0) in n 1.964 * [taylor]: Taking taylor expansion of 2.0 in n 1.964 * [backup-simplify]: Simplify 2.0 into 2.0 1.964 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 1.965 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 1.967 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 1.967 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 1.967 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 1.967 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 1.967 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 1.967 * [taylor]: Taking taylor expansion of 1.0 in n 1.967 * [backup-simplify]: Simplify 1.0 into 1.0 1.967 * [taylor]: Taking taylor expansion of (log PI) in n 1.967 * [taylor]: Taking taylor expansion of PI in n 1.967 * [backup-simplify]: Simplify PI into PI 1.968 * [backup-simplify]: Simplify (log PI) into (log PI) 1.969 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 1.970 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 1.970 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 1.970 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 1.970 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 1.970 * [taylor]: Taking taylor expansion of 1.0 in n 1.970 * [backup-simplify]: Simplify 1.0 into 1.0 1.970 * [taylor]: Taking taylor expansion of (log n) in n 1.970 * [taylor]: Taking taylor expansion of n in n 1.970 * [backup-simplify]: Simplify 0 into 0 1.970 * [backup-simplify]: Simplify 1 into 1 1.971 * [backup-simplify]: Simplify (log 1) into 0 1.971 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1.971 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 1.971 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 1.972 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 1.973 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.975 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 1.976 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 1.977 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 1.977 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.977 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.977 * [taylor]: Taking taylor expansion of 2.0 in n 1.978 * [backup-simplify]: Simplify 2.0 into 2.0 1.978 * [taylor]: Taking taylor expansion of (* n PI) in n 1.978 * [taylor]: Taking taylor expansion of n in n 1.978 * [backup-simplify]: Simplify 0 into 0 1.978 * [backup-simplify]: Simplify 1 into 1 1.978 * [taylor]: Taking taylor expansion of PI in n 1.978 * [backup-simplify]: Simplify PI into PI 1.978 * [backup-simplify]: Simplify (* 0 PI) into 0 1.979 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.980 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.982 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.983 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.984 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) 1.986 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.988 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 1.991 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 1.993 * [backup-simplify]: Simplify (- (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))) 1.999 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 2.005 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 2.012 * [backup-simplify]: Simplify (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 2.014 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 2.015 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 2.017 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 2.018 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.018 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.019 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 2.020 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.021 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 2.022 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 2.023 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 2.025 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 2.026 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 2.029 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1)))) 1) into 0 2.030 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)))) into 0 2.033 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0 2.035 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0 2.035 * [backup-simplify]: Simplify (- 0) into 0 2.035 * [backup-simplify]: Simplify 0 into 0 2.035 * [backup-simplify]: Simplify 0 into 0 2.036 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 2.037 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0 2.040 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0 2.041 * [backup-simplify]: Simplify (- 0) into 0 2.041 * [backup-simplify]: Simplify (+ 0 0) into 0 2.042 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 2.044 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 2.046 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.046 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.050 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.054 * [backup-simplify]: Simplify (+ (* 0 (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 2.060 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))) (+ (* 0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) 2.061 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n 2.061 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n 2.061 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n 2.061 * [taylor]: Taking taylor expansion of +nan.0 in n 2.061 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.061 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 2.061 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 2.061 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 2.061 * [taylor]: Taking taylor expansion of 0.5 in n 2.061 * [backup-simplify]: Simplify 0.5 into 0.5 2.061 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 2.061 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 2.061 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.061 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.061 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.061 * [taylor]: Taking taylor expansion of 1.0 in n 2.061 * [backup-simplify]: Simplify 1.0 into 1.0 2.061 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.061 * [taylor]: Taking taylor expansion of 2.0 in n 2.061 * [backup-simplify]: Simplify 2.0 into 2.0 2.061 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.062 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.063 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.063 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n 2.063 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.063 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.063 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.063 * [taylor]: Taking taylor expansion of 1.0 in n 2.063 * [backup-simplify]: Simplify 1.0 into 1.0 2.063 * [taylor]: Taking taylor expansion of (log n) in n 2.063 * [taylor]: Taking taylor expansion of n in n 2.063 * [backup-simplify]: Simplify 0 into 0 2.063 * [backup-simplify]: Simplify 1 into 1 2.063 * [backup-simplify]: Simplify (log 1) into 0 2.063 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.063 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.063 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.063 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.063 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.063 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.063 * [taylor]: Taking taylor expansion of 1.0 in n 2.064 * [backup-simplify]: Simplify 1.0 into 1.0 2.064 * [taylor]: Taking taylor expansion of (log PI) in n 2.064 * [taylor]: Taking taylor expansion of PI in n 2.064 * [backup-simplify]: Simplify PI into PI 2.064 * [backup-simplify]: Simplify (log PI) into (log PI) 2.064 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.065 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.066 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.067 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 2.067 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 2.068 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 2.069 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.069 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n 2.069 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n 2.069 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n 2.069 * [taylor]: Taking taylor expansion of +nan.0 in n 2.069 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.069 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n 2.069 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.069 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.069 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.069 * [taylor]: Taking taylor expansion of 0.5 in n 2.069 * [backup-simplify]: Simplify 0.5 into 0.5 2.069 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.069 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.069 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.069 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.069 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.069 * [taylor]: Taking taylor expansion of 1.0 in n 2.069 * [backup-simplify]: Simplify 1.0 into 1.0 2.069 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.069 * [taylor]: Taking taylor expansion of 2.0 in n 2.069 * [backup-simplify]: Simplify 2.0 into 2.0 2.070 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.070 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.071 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.071 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.071 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.071 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.071 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.071 * [taylor]: Taking taylor expansion of 1.0 in n 2.071 * [backup-simplify]: Simplify 1.0 into 1.0 2.071 * [taylor]: Taking taylor expansion of (log PI) in n 2.071 * [taylor]: Taking taylor expansion of PI in n 2.071 * [backup-simplify]: Simplify PI into PI 2.072 * [backup-simplify]: Simplify (log PI) into (log PI) 2.072 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.073 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.073 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.073 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.073 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.073 * [taylor]: Taking taylor expansion of 1.0 in n 2.073 * [backup-simplify]: Simplify 1.0 into 1.0 2.073 * [taylor]: Taking taylor expansion of (log n) in n 2.073 * [taylor]: Taking taylor expansion of n in n 2.073 * [backup-simplify]: Simplify 0 into 0 2.073 * [backup-simplify]: Simplify 1 into 1 2.073 * [backup-simplify]: Simplify (log 1) into 0 2.074 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.074 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.074 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.074 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.075 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 2.076 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 2.077 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 2.078 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.078 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.078 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.078 * [taylor]: Taking taylor expansion of 2.0 in n 2.078 * [backup-simplify]: Simplify 2.0 into 2.0 2.078 * [taylor]: Taking taylor expansion of (* n PI) in n 2.078 * [taylor]: Taking taylor expansion of n in n 2.078 * [backup-simplify]: Simplify 0 into 0 2.078 * [backup-simplify]: Simplify 1 into 1 2.078 * [taylor]: Taking taylor expansion of PI in n 2.078 * [backup-simplify]: Simplify PI into PI 2.078 * [backup-simplify]: Simplify (* 0 PI) into 0 2.078 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.079 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.081 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.082 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.082 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n 2.082 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n 2.082 * [taylor]: Taking taylor expansion of +nan.0 in n 2.082 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.082 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n 2.082 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.082 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.082 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.082 * [taylor]: Taking taylor expansion of 0.5 in n 2.082 * [backup-simplify]: Simplify 0.5 into 0.5 2.082 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.082 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.082 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.082 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.082 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.082 * [taylor]: Taking taylor expansion of 1.0 in n 2.082 * [backup-simplify]: Simplify 1.0 into 1.0 2.082 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.082 * [taylor]: Taking taylor expansion of 2.0 in n 2.082 * [backup-simplify]: Simplify 2.0 into 2.0 2.083 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.084 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.085 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.085 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.085 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.085 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.085 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.085 * [taylor]: Taking taylor expansion of 1.0 in n 2.085 * [backup-simplify]: Simplify 1.0 into 1.0 2.085 * [taylor]: Taking taylor expansion of (log PI) in n 2.085 * [taylor]: Taking taylor expansion of PI in n 2.085 * [backup-simplify]: Simplify PI into PI 2.086 * [backup-simplify]: Simplify (log PI) into (log PI) 2.087 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.088 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.088 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.088 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.088 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.088 * [taylor]: Taking taylor expansion of 1.0 in n 2.088 * [backup-simplify]: Simplify 1.0 into 1.0 2.088 * [taylor]: Taking taylor expansion of (log n) in n 2.088 * [taylor]: Taking taylor expansion of n in n 2.088 * [backup-simplify]: Simplify 0 into 0 2.088 * [backup-simplify]: Simplify 1 into 1 2.089 * [backup-simplify]: Simplify (log 1) into 0 2.089 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.089 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.089 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.090 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.097 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 2.099 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0)) 2.100 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0))) 2.102 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) 2.102 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 2.102 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.102 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.102 * [taylor]: Taking taylor expansion of 2.0 in n 2.102 * [backup-simplify]: Simplify 2.0 into 2.0 2.102 * [taylor]: Taking taylor expansion of (* n PI) in n 2.102 * [taylor]: Taking taylor expansion of n in n 2.102 * [backup-simplify]: Simplify 0 into 0 2.102 * [backup-simplify]: Simplify 1 into 1 2.102 * [taylor]: Taking taylor expansion of PI in n 2.102 * [backup-simplify]: Simplify PI into PI 2.102 * [backup-simplify]: Simplify (* 0 PI) into 0 2.103 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.104 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.106 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.107 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.108 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.110 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 2.112 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.113 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 2.114 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.115 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.116 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.118 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 2.119 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) 2.121 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) 2.122 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) 2.129 * [backup-simplify]: Simplify (+ (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)))))))))))) 2.138 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))) 2.147 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 2.157 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 2.166 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) 2.181 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) 2.182 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) 2.182 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0 2.182 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 2.182 * [taylor]: Taking taylor expansion of 1.0 in n 2.182 * [backup-simplify]: Simplify 1.0 into 1.0 2.182 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 2.182 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.182 * [taylor]: Taking taylor expansion of k in n 2.182 * [backup-simplify]: Simplify k into k 2.182 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.182 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.182 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.182 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.182 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.182 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.182 * [taylor]: Taking taylor expansion of 0.5 in n 2.182 * [backup-simplify]: Simplify 0.5 into 0.5 2.182 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.182 * [taylor]: Taking taylor expansion of 1.0 in n 2.182 * [backup-simplify]: Simplify 1.0 into 1.0 2.182 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.182 * [taylor]: Taking taylor expansion of k in n 2.182 * [backup-simplify]: Simplify k into k 2.182 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.182 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.182 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.182 * [taylor]: Taking taylor expansion of 2.0 in n 2.182 * [backup-simplify]: Simplify 2.0 into 2.0 2.182 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.182 * [taylor]: Taking taylor expansion of PI in n 2.182 * [backup-simplify]: Simplify PI into PI 2.183 * [taylor]: Taking taylor expansion of n in n 2.183 * [backup-simplify]: Simplify 0 into 0 2.183 * [backup-simplify]: Simplify 1 into 1 2.183 * [backup-simplify]: Simplify (/ PI 1) into PI 2.183 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.184 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.184 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.184 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.184 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.185 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.186 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.186 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.186 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 2.186 * [taylor]: Taking taylor expansion of 1.0 in k 2.186 * [backup-simplify]: Simplify 1.0 into 1.0 2.186 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 2.186 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.186 * [taylor]: Taking taylor expansion of k in k 2.186 * [backup-simplify]: Simplify 0 into 0 2.186 * [backup-simplify]: Simplify 1 into 1 2.187 * [backup-simplify]: Simplify (sqrt 0) into 0 2.191 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.191 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.191 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.191 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.191 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.191 * [taylor]: Taking taylor expansion of 0.5 in k 2.191 * [backup-simplify]: Simplify 0.5 into 0.5 2.191 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.191 * [taylor]: Taking taylor expansion of 1.0 in k 2.191 * [backup-simplify]: Simplify 1.0 into 1.0 2.191 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.191 * [taylor]: Taking taylor expansion of k in k 2.191 * [backup-simplify]: Simplify 0 into 0 2.191 * [backup-simplify]: Simplify 1 into 1 2.191 * [backup-simplify]: Simplify (/ 1 1) into 1 2.191 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.191 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.191 * [taylor]: Taking taylor expansion of 2.0 in k 2.191 * [backup-simplify]: Simplify 2.0 into 2.0 2.191 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.191 * [taylor]: Taking taylor expansion of PI in k 2.191 * [backup-simplify]: Simplify PI into PI 2.191 * [taylor]: Taking taylor expansion of n in k 2.191 * [backup-simplify]: Simplify n into n 2.191 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.192 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.192 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.192 * [backup-simplify]: Simplify (- 1) into -1 2.192 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.192 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.192 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.193 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.193 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 2.193 * [taylor]: Taking taylor expansion of 1.0 in k 2.193 * [backup-simplify]: Simplify 1.0 into 1.0 2.193 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 2.193 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.193 * [taylor]: Taking taylor expansion of k in k 2.193 * [backup-simplify]: Simplify 0 into 0 2.193 * [backup-simplify]: Simplify 1 into 1 2.193 * [backup-simplify]: Simplify (sqrt 0) into 0 2.194 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.194 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.194 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.194 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.194 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.194 * [taylor]: Taking taylor expansion of 0.5 in k 2.194 * [backup-simplify]: Simplify 0.5 into 0.5 2.194 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.194 * [taylor]: Taking taylor expansion of 1.0 in k 2.194 * [backup-simplify]: Simplify 1.0 into 1.0 2.194 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.194 * [taylor]: Taking taylor expansion of k in k 2.194 * [backup-simplify]: Simplify 0 into 0 2.194 * [backup-simplify]: Simplify 1 into 1 2.194 * [backup-simplify]: Simplify (/ 1 1) into 1 2.194 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.194 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.194 * [taylor]: Taking taylor expansion of 2.0 in k 2.194 * [backup-simplify]: Simplify 2.0 into 2.0 2.194 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.194 * [taylor]: Taking taylor expansion of PI in k 2.194 * [backup-simplify]: Simplify PI into PI 2.194 * [taylor]: Taking taylor expansion of n in k 2.194 * [backup-simplify]: Simplify n into n 2.194 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.194 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.195 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.195 * [backup-simplify]: Simplify (- 1) into -1 2.195 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.195 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.195 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.195 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 2.196 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 2.196 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.196 * [taylor]: Taking taylor expansion of 0 in n 2.196 * [backup-simplify]: Simplify 0 into 0 2.196 * [backup-simplify]: Simplify 0 into 0 2.196 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 2.197 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 2.197 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.197 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.197 * [taylor]: Taking taylor expansion of +nan.0 in n 2.197 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.197 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.197 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.197 * [taylor]: Taking taylor expansion of 0.5 in n 2.197 * [backup-simplify]: Simplify 0.5 into 0.5 2.197 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.197 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.197 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.197 * [taylor]: Taking taylor expansion of 2.0 in n 2.197 * [backup-simplify]: Simplify 2.0 into 2.0 2.197 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.197 * [taylor]: Taking taylor expansion of PI in n 2.197 * [backup-simplify]: Simplify PI into PI 2.197 * [taylor]: Taking taylor expansion of n in n 2.197 * [backup-simplify]: Simplify 0 into 0 2.197 * [backup-simplify]: Simplify 1 into 1 2.198 * [backup-simplify]: Simplify (/ PI 1) into PI 2.198 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.198 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.198 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.198 * [taylor]: Taking taylor expansion of 1.0 in n 2.199 * [backup-simplify]: Simplify 1.0 into 1.0 2.199 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.199 * [taylor]: Taking taylor expansion of k in n 2.199 * [backup-simplify]: Simplify k into k 2.199 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.199 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.200 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.200 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.200 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.201 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.202 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.202 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 2.203 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 2.204 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 2.204 * [backup-simplify]: Simplify 0 into 0 2.206 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.206 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 2.207 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 2.207 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.207 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.207 * [taylor]: Taking taylor expansion of +nan.0 in n 2.207 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.207 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.207 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.207 * [taylor]: Taking taylor expansion of 0.5 in n 2.207 * [backup-simplify]: Simplify 0.5 into 0.5 2.207 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.207 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.207 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.207 * [taylor]: Taking taylor expansion of 2.0 in n 2.207 * [backup-simplify]: Simplify 2.0 into 2.0 2.207 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.207 * [taylor]: Taking taylor expansion of PI in n 2.207 * [backup-simplify]: Simplify PI into PI 2.207 * [taylor]: Taking taylor expansion of n in n 2.207 * [backup-simplify]: Simplify 0 into 0 2.207 * [backup-simplify]: Simplify 1 into 1 2.208 * [backup-simplify]: Simplify (/ PI 1) into PI 2.208 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.209 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.209 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.209 * [taylor]: Taking taylor expansion of 1.0 in n 2.209 * [backup-simplify]: Simplify 1.0 into 1.0 2.209 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.209 * [taylor]: Taking taylor expansion of k in n 2.209 * [backup-simplify]: Simplify k into k 2.209 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.210 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.210 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.210 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.210 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.211 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.212 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.214 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 2.215 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 2.216 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 2.218 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.218 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.218 * [backup-simplify]: Simplify (- 0) into 0 2.219 * [backup-simplify]: Simplify (+ 0 0) into 0 2.219 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.220 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.222 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.223 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.225 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 2.227 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.229 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 2.229 * [backup-simplify]: Simplify (- 0) into 0 2.229 * [backup-simplify]: Simplify 0 into 0 2.229 * [backup-simplify]: Simplify 0 into 0 2.233 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.235 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 2.237 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) 2.237 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.237 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.237 * [taylor]: Taking taylor expansion of +nan.0 in n 2.237 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.237 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.237 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.237 * [taylor]: Taking taylor expansion of 0.5 in n 2.237 * [backup-simplify]: Simplify 0.5 into 0.5 2.237 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.237 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.237 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.237 * [taylor]: Taking taylor expansion of 2.0 in n 2.237 * [backup-simplify]: Simplify 2.0 into 2.0 2.237 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.237 * [taylor]: Taking taylor expansion of PI in n 2.237 * [backup-simplify]: Simplify PI into PI 2.237 * [taylor]: Taking taylor expansion of n in n 2.237 * [backup-simplify]: Simplify 0 into 0 2.237 * [backup-simplify]: Simplify 1 into 1 2.238 * [backup-simplify]: Simplify (/ PI 1) into PI 2.238 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.239 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.240 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.240 * [taylor]: Taking taylor expansion of 1.0 in n 2.240 * [backup-simplify]: Simplify 1.0 into 1.0 2.240 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.240 * [taylor]: Taking taylor expansion of k in n 2.240 * [backup-simplify]: Simplify k into k 2.240 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.241 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.241 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.242 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.243 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.244 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 2.246 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2.247 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 2.249 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 2.250 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 2.255 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) 2.257 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 2.257 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0 2.257 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 2.257 * [taylor]: Taking taylor expansion of 1.0 in n 2.257 * [backup-simplify]: Simplify 1.0 into 1.0 2.257 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 2.257 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.257 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.257 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.257 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.257 * [taylor]: Taking taylor expansion of 0.5 in n 2.257 * [backup-simplify]: Simplify 0.5 into 0.5 2.257 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.257 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.257 * [taylor]: Taking taylor expansion of k in n 2.257 * [backup-simplify]: Simplify k into k 2.257 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.257 * [taylor]: Taking taylor expansion of 1.0 in n 2.257 * [backup-simplify]: Simplify 1.0 into 1.0 2.257 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.257 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.257 * [taylor]: Taking taylor expansion of -2.0 in n 2.257 * [backup-simplify]: Simplify -2.0 into -2.0 2.257 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.257 * [taylor]: Taking taylor expansion of PI in n 2.257 * [backup-simplify]: Simplify PI into PI 2.257 * [taylor]: Taking taylor expansion of n in n 2.257 * [backup-simplify]: Simplify 0 into 0 2.257 * [backup-simplify]: Simplify 1 into 1 2.258 * [backup-simplify]: Simplify (/ PI 1) into PI 2.258 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.259 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.260 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.260 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.261 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.262 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.264 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.264 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.264 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.264 * [taylor]: Taking taylor expansion of -1 in n 2.264 * [backup-simplify]: Simplify -1 into -1 2.264 * [taylor]: Taking taylor expansion of k in n 2.264 * [backup-simplify]: Simplify k into k 2.264 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.264 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.264 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.264 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.265 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) 2.266 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.266 * [taylor]: Taking taylor expansion of 1.0 in k 2.266 * [backup-simplify]: Simplify 1.0 into 1.0 2.266 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.266 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.266 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.266 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.266 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.266 * [taylor]: Taking taylor expansion of 0.5 in k 2.266 * [backup-simplify]: Simplify 0.5 into 0.5 2.266 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.266 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.266 * [taylor]: Taking taylor expansion of k in k 2.266 * [backup-simplify]: Simplify 0 into 0 2.266 * [backup-simplify]: Simplify 1 into 1 2.266 * [backup-simplify]: Simplify (/ 1 1) into 1 2.266 * [taylor]: Taking taylor expansion of 1.0 in k 2.266 * [backup-simplify]: Simplify 1.0 into 1.0 2.266 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.266 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.267 * [taylor]: Taking taylor expansion of -2.0 in k 2.267 * [backup-simplify]: Simplify -2.0 into -2.0 2.267 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.267 * [taylor]: Taking taylor expansion of PI in k 2.267 * [backup-simplify]: Simplify PI into PI 2.267 * [taylor]: Taking taylor expansion of n in k 2.267 * [backup-simplify]: Simplify n into n 2.267 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.267 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.267 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.267 * [backup-simplify]: Simplify (+ 1 0) into 1 2.268 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.268 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.268 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.268 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.268 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.268 * [taylor]: Taking taylor expansion of -1 in k 2.268 * [backup-simplify]: Simplify -1 into -1 2.268 * [taylor]: Taking taylor expansion of k in k 2.269 * [backup-simplify]: Simplify 0 into 0 2.269 * [backup-simplify]: Simplify 1 into 1 2.269 * [backup-simplify]: Simplify (/ -1 1) into -1 2.269 * [backup-simplify]: Simplify (sqrt 0) into 0 2.271 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.271 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 2.271 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.271 * [taylor]: Taking taylor expansion of 1.0 in k 2.271 * [backup-simplify]: Simplify 1.0 into 1.0 2.271 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.271 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.271 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.271 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.271 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.271 * [taylor]: Taking taylor expansion of 0.5 in k 2.271 * [backup-simplify]: Simplify 0.5 into 0.5 2.271 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.272 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.272 * [taylor]: Taking taylor expansion of k in k 2.272 * [backup-simplify]: Simplify 0 into 0 2.272 * [backup-simplify]: Simplify 1 into 1 2.272 * [backup-simplify]: Simplify (/ 1 1) into 1 2.272 * [taylor]: Taking taylor expansion of 1.0 in k 2.272 * [backup-simplify]: Simplify 1.0 into 1.0 2.272 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.272 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.272 * [taylor]: Taking taylor expansion of -2.0 in k 2.272 * [backup-simplify]: Simplify -2.0 into -2.0 2.272 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.272 * [taylor]: Taking taylor expansion of PI in k 2.272 * [backup-simplify]: Simplify PI into PI 2.272 * [taylor]: Taking taylor expansion of n in k 2.272 * [backup-simplify]: Simplify n into n 2.272 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.273 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.273 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.273 * [backup-simplify]: Simplify (+ 1 0) into 1 2.274 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.274 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.274 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 2.274 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.274 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.274 * [taylor]: Taking taylor expansion of -1 in k 2.274 * [backup-simplify]: Simplify -1 into -1 2.274 * [taylor]: Taking taylor expansion of k in k 2.274 * [backup-simplify]: Simplify 0 into 0 2.274 * [backup-simplify]: Simplify 1 into 1 2.275 * [backup-simplify]: Simplify (/ -1 1) into -1 2.275 * [backup-simplify]: Simplify (sqrt 0) into 0 2.276 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.277 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 2.277 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 2.277 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.277 * [taylor]: Taking taylor expansion of +nan.0 in n 2.277 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.277 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.277 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.277 * [taylor]: Taking taylor expansion of 0.5 in n 2.278 * [backup-simplify]: Simplify 0.5 into 0.5 2.278 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.278 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.278 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.278 * [taylor]: Taking taylor expansion of k in n 2.278 * [backup-simplify]: Simplify k into k 2.278 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.278 * [taylor]: Taking taylor expansion of 1.0 in n 2.278 * [backup-simplify]: Simplify 1.0 into 1.0 2.278 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.278 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.278 * [taylor]: Taking taylor expansion of -2.0 in n 2.278 * [backup-simplify]: Simplify -2.0 into -2.0 2.278 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.278 * [taylor]: Taking taylor expansion of PI in n 2.278 * [backup-simplify]: Simplify PI into PI 2.278 * [taylor]: Taking taylor expansion of n in n 2.278 * [backup-simplify]: Simplify 0 into 0 2.278 * [backup-simplify]: Simplify 1 into 1 2.279 * [backup-simplify]: Simplify (/ PI 1) into PI 2.279 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.280 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.280 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.282 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.283 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.285 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.286 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.289 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 2.290 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 2.291 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.295 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.296 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 2.297 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 2.297 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 2.297 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.297 * [taylor]: Taking taylor expansion of +nan.0 in n 2.297 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.297 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.297 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.297 * [taylor]: Taking taylor expansion of 0.5 in n 2.297 * [backup-simplify]: Simplify 0.5 into 0.5 2.297 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.297 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.297 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.297 * [taylor]: Taking taylor expansion of k in n 2.297 * [backup-simplify]: Simplify k into k 2.297 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.298 * [taylor]: Taking taylor expansion of 1.0 in n 2.298 * [backup-simplify]: Simplify 1.0 into 1.0 2.298 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.298 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.298 * [taylor]: Taking taylor expansion of -2.0 in n 2.298 * [backup-simplify]: Simplify -2.0 into -2.0 2.298 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.298 * [taylor]: Taking taylor expansion of PI in n 2.298 * [backup-simplify]: Simplify PI into PI 2.298 * [taylor]: Taking taylor expansion of n in n 2.298 * [backup-simplify]: Simplify 0 into 0 2.298 * [backup-simplify]: Simplify 1 into 1 2.298 * [backup-simplify]: Simplify (/ PI 1) into PI 2.299 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.300 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.300 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.302 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.303 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.304 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.305 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.307 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 2.308 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 2.309 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 2.310 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.311 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.313 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.313 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.313 * [backup-simplify]: Simplify (+ 0 0) into 0 2.315 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.316 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.317 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 2.318 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.319 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 2.319 * [backup-simplify]: Simplify 0 into 0 2.320 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.322 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.323 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 2.323 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) 2.323 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 2.323 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.324 * [taylor]: Taking taylor expansion of +nan.0 in n 2.324 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.324 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.324 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.324 * [taylor]: Taking taylor expansion of 0.5 in n 2.324 * [backup-simplify]: Simplify 0.5 into 0.5 2.324 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.324 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.324 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.324 * [taylor]: Taking taylor expansion of k in n 2.324 * [backup-simplify]: Simplify k into k 2.324 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.324 * [taylor]: Taking taylor expansion of 1.0 in n 2.324 * [backup-simplify]: Simplify 1.0 into 1.0 2.324 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.324 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.324 * [taylor]: Taking taylor expansion of -2.0 in n 2.324 * [backup-simplify]: Simplify -2.0 into -2.0 2.324 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.324 * [taylor]: Taking taylor expansion of PI in n 2.324 * [backup-simplify]: Simplify PI into PI 2.324 * [taylor]: Taking taylor expansion of n in n 2.324 * [backup-simplify]: Simplify 0 into 0 2.324 * [backup-simplify]: Simplify 1 into 1 2.324 * [backup-simplify]: Simplify (/ PI 1) into PI 2.325 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.328 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.328 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.330 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.330 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.331 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 2.332 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.333 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 2.333 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 2.334 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 2.337 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 2.337 * * * [progress]: simplifying candidates 2.339 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (log 1.0) (log (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt 1)) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) 1) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 (sqrt 1)) (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) (/ 1 1) (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ 1.0 (sqrt (sqrt k))) (/ 1.0 1) (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (+ (log (/ 1.0 (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) 1) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 2.344 * * [simplify]: Extracting # 0 : cost 0 2.344 * * [simplify]: Extracting # 1 : cost 0 2.344 * * [simplify]: Extracting # 2 : cost 0 2.345 * * [simplify]: Extracting # 3 : cost 0 2.345 * * [simplify]: Extracting # 4 : cost 0 2.345 * * [simplify]: Extracting # 5 : cost 0 2.346 * * [simplify]: Extracting # 6 : cost 0 2.346 * * [simplify]: Extracting # 7 : cost 0 2.347 * * [simplify]: Extracting # 8 : cost 0 2.347 * * [simplify]: Extracting # 9 : cost 0 2.348 * * [simplify]: Extracting # 10 : cost 0 2.349 * * [simplify]: Extracting # 11 : cost 0 2.350 * * [simplify]: Extracting # 12 : cost 0 2.351 * * [simplify]: Extracting # 13 : cost 0 2.352 * * [simplify]: Extracting # 14 : cost 0 2.353 * * [simplify]: Extracting # 15 : cost 0 2.354 * * [simplify]: Extracting # 16 : cost 0 2.355 * * [simplify]: Extracting # 17 : cost 0 2.356 * * [simplify]: Extracting # 18 : cost 0 2.357 * * [simplify]: Extracting # 19 : cost 0 2.358 * * [simplify]: Extracting # 20 : cost 0 2.359 * * [simplify]: Extracting # 21 : cost 0 2.360 * * [simplify]: Extracting # 22 : cost 0 2.362 * * [simplify]: Extracting # 23 : cost 0 2.363 * * [simplify]: Extracting # 24 : cost 0 2.364 * * [simplify]: Extracting # 25 : cost 0 2.365 * * [simplify]: Extracting # 26 : cost 0 2.366 * * [simplify]: Extracting # 27 : cost 0 2.367 * * [simplify]: Extracting # 28 : cost 0 2.368 * * [simplify]: Extracting # 29 : cost 0 2.369 * * [simplify]: Extracting # 30 : cost 0 2.370 * * [simplify]: Extracting # 31 : cost 0 2.371 * * [simplify]: Extracting # 32 : cost 0 2.372 * * [simplify]: iteration 0 : 361 enodes (cost 2800 ) 2.512 * * [simplify]: Extracting # 0 : cost 0 2.513 * * [simplify]: Extracting # 1 : cost 0 2.515 * * [simplify]: Extracting # 2 : cost 0 2.516 * * [simplify]: Extracting # 3 : cost 0 2.518 * * [simplify]: Extracting # 4 : cost 0 2.524 * * [simplify]: Extracting # 5 : cost 0 2.526 * * [simplify]: iteration 1 : 1008 enodes (cost 2643 ) 3.214 * * [simplify]: Extracting # 0 : cost 0 3.224 * * [simplify]: Extracting # 1 : cost 0 3.230 * * [simplify]: Extracting # 2 : cost 0 3.237 * * [simplify]: Extracting # 3 : cost 0 3.242 * * [simplify]: Extracting # 4 : cost 0 3.248 * * [simplify]: Extracting # 5 : cost 0 3.257 * * [simplify]: iteration 2 : 4735 enodes (cost 2473 ) 4.922 * * [simplify]: Extracting # 0 : cost 0 4.929 * * [simplify]: Extracting # 1 : cost 0 4.935 * * [simplify]: Extracting # 2 : cost 0 4.944 * * [simplify]: Extracting # 3 : cost 0 4.956 * * [simplify]: iteration done: 5001 enodes (cost 2473 ) 4.958 * [simplify]: Simplified to: (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* n PI) (log (/ 1.0 (sqrt k))) (log (/ 1.0 (sqrt k))) (exp (/ 1.0 (sqrt k))) (/ (pow 1.0 3) (* k (sqrt k))) (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k)))) (cbrt (/ 1.0 (sqrt k))) (pow (/ 1.0 (sqrt k)) 3) (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))) (- 1.0) (- (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (/ (cbrt 1.0) (sqrt (cbrt k))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt k))) (* (cbrt 1.0) (cbrt 1.0)) (/ (cbrt 1.0) (sqrt k)) (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1.0) (cbrt (sqrt k))) (/ (sqrt 1.0) (fabs (cbrt k))) (/ (sqrt 1.0) (sqrt (cbrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))) (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt 1.0) (/ (sqrt 1.0) (sqrt k)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (cbrt (sqrt k))) (/ 1 (fabs (cbrt k))) (/ 1.0 (sqrt (cbrt k))) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))) 1 (/ 1.0 (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) 1.0) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1.0 (fabs (cbrt k))) (/ 1.0 (sqrt (sqrt k))) 1.0 (/ 1.0 (sqrt (sqrt k))) 1.0 (/ (sqrt k) (cbrt 1.0)) (/ (sqrt k) (sqrt 1.0)) (/ (sqrt k) 1.0) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (pow 1.0 3) (* k (sqrt k))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3)) (* (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (pow (/ 1.0 (sqrt k)) 3)) (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (pow (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (- (+ (+ (* (* 0.125 (pow k 2)) (+ (* (pow (log (* 2.0 PI)) 2) (pow (* (* 2.0 PI) n) 0.5)) (* (pow (* (* 2.0 PI) n) 0.5) (pow (log n) 2)))) (pow (* (* 2.0 PI) n) 0.5)) (* (* (* 0.25 (pow k 2)) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log n)))) (* 0.5 (* k (+ (* (pow (* (* 2.0 PI) n) 0.5) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log n)))))) (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (- (- (* +nan.0 k) (- (* +nan.0 (pow k 2)) +nan.0))) (+ (- (/ +nan.0 k) (/ +nan.0 (pow k 3))) (- (/ +nan.0 (pow k 2)))) (+ (- (/ +nan.0 (pow k 2))) (- (/ +nan.0 k) +nan.0)) (+ (- (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (- (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (+ (- (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)))) (+ (- (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5)))) (+ (- (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (* +nan.0 (- (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))) (+ (* (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (pow k 3)) (- +nan.0)) (* +nan.0 (- (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) k) (/ (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) k) k)))) (+ (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k))) (* +nan.0 (- (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))) 4.960 * * * [progress]: adding candidates to table 5.627 * * [progress]: iteration 2 / 4 5.627 * * * [progress]: picking best candidate 5.670 * * * * [pick]: Picked # 5.670 * * * [progress]: localizing error 5.685 * * * [progress]: generating rewritten candidates 5.685 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1 2) 5.712 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 2 1) 5.742 * * * * [progress]: [ 3 / 3 ] rewriting at (2) 5.769 * * * [progress]: generating series expansions 5.769 * * * * [progress]: [ 1 / 3 ] generating series at (2 1 2) 5.770 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 5.770 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 5.770 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 5.770 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 5.770 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 5.770 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 5.770 * [taylor]: Taking taylor expansion of 0.5 in k 5.770 * [backup-simplify]: Simplify 0.5 into 0.5 5.770 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 5.770 * [taylor]: Taking taylor expansion of 1.0 in k 5.770 * [backup-simplify]: Simplify 1.0 into 1.0 5.770 * [taylor]: Taking taylor expansion of k in k 5.770 * [backup-simplify]: Simplify 0 into 0 5.770 * [backup-simplify]: Simplify 1 into 1 5.770 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 5.770 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 5.770 * [taylor]: Taking taylor expansion of 2.0 in k 5.770 * [backup-simplify]: Simplify 2.0 into 2.0 5.770 * [taylor]: Taking taylor expansion of (* n PI) in k 5.770 * [taylor]: Taking taylor expansion of n in k 5.770 * [backup-simplify]: Simplify n into n 5.770 * [taylor]: Taking taylor expansion of PI in k 5.770 * [backup-simplify]: Simplify PI into PI 5.770 * [backup-simplify]: Simplify (* n PI) into (* n PI) 5.770 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 5.771 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 5.771 * [backup-simplify]: Simplify (- 0) into 0 5.771 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 5.772 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 5.772 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 5.772 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 5.772 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 5.772 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 5.772 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 5.772 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 5.772 * [taylor]: Taking taylor expansion of 0.5 in n 5.772 * [backup-simplify]: Simplify 0.5 into 0.5 5.772 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 5.772 * [taylor]: Taking taylor expansion of 1.0 in n 5.772 * [backup-simplify]: Simplify 1.0 into 1.0 5.772 * [taylor]: Taking taylor expansion of k in n 5.772 * [backup-simplify]: Simplify k into k 5.772 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 5.772 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 5.772 * [taylor]: Taking taylor expansion of 2.0 in n 5.772 * [backup-simplify]: Simplify 2.0 into 2.0 5.772 * [taylor]: Taking taylor expansion of (* n PI) in n 5.772 * [taylor]: Taking taylor expansion of n in n 5.772 * [backup-simplify]: Simplify 0 into 0 5.772 * [backup-simplify]: Simplify 1 into 1 5.772 * [taylor]: Taking taylor expansion of PI in n 5.772 * [backup-simplify]: Simplify PI into PI 5.772 * [backup-simplify]: Simplify (* 0 PI) into 0 5.773 * [backup-simplify]: Simplify (* 2.0 0) into 0 5.774 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 5.775 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 5.775 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.775 * [backup-simplify]: Simplify (- k) into (- k) 5.775 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 5.775 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 5.776 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.777 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 5.778 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 5.778 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 5.778 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 5.778 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 5.778 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 5.778 * [taylor]: Taking taylor expansion of 0.5 in n 5.778 * [backup-simplify]: Simplify 0.5 into 0.5 5.778 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 5.778 * [taylor]: Taking taylor expansion of 1.0 in n 5.778 * [backup-simplify]: Simplify 1.0 into 1.0 5.778 * [taylor]: Taking taylor expansion of k in n 5.778 * [backup-simplify]: Simplify k into k 5.778 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 5.778 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 5.778 * [taylor]: Taking taylor expansion of 2.0 in n 5.778 * [backup-simplify]: Simplify 2.0 into 2.0 5.778 * [taylor]: Taking taylor expansion of (* n PI) in n 5.778 * [taylor]: Taking taylor expansion of n in n 5.778 * [backup-simplify]: Simplify 0 into 0 5.778 * [backup-simplify]: Simplify 1 into 1 5.778 * [taylor]: Taking taylor expansion of PI in n 5.778 * [backup-simplify]: Simplify PI into PI 5.779 * [backup-simplify]: Simplify (* 0 PI) into 0 5.779 * [backup-simplify]: Simplify (* 2.0 0) into 0 5.780 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 5.781 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 5.782 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.782 * [backup-simplify]: Simplify (- k) into (- k) 5.782 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 5.782 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 5.783 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.783 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 5.784 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 5.784 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 5.784 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 5.784 * [taylor]: Taking taylor expansion of 0.5 in k 5.784 * [backup-simplify]: Simplify 0.5 into 0.5 5.784 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 5.784 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 5.784 * [taylor]: Taking taylor expansion of 1.0 in k 5.784 * [backup-simplify]: Simplify 1.0 into 1.0 5.784 * [taylor]: Taking taylor expansion of k in k 5.784 * [backup-simplify]: Simplify 0 into 0 5.784 * [backup-simplify]: Simplify 1 into 1 5.784 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 5.784 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 5.784 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 5.785 * [taylor]: Taking taylor expansion of 2.0 in k 5.785 * [backup-simplify]: Simplify 2.0 into 2.0 5.785 * [taylor]: Taking taylor expansion of PI in k 5.785 * [backup-simplify]: Simplify PI into PI 5.785 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.785 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.786 * [taylor]: Taking taylor expansion of (log n) in k 5.786 * [taylor]: Taking taylor expansion of n in k 5.786 * [backup-simplify]: Simplify n into n 5.786 * [backup-simplify]: Simplify (log n) into (log n) 5.786 * [backup-simplify]: Simplify (- 0) into 0 5.786 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 5.787 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 5.787 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 5.788 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 5.789 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 5.789 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 5.790 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 5.791 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 5.792 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 5.792 * [backup-simplify]: Simplify (- 0) into 0 5.792 * [backup-simplify]: Simplify (+ 0 0) into 0 5.793 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 5.794 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.794 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 5.795 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 5.795 * [taylor]: Taking taylor expansion of 0 in k 5.795 * [backup-simplify]: Simplify 0 into 0 5.796 * [backup-simplify]: Simplify 0 into 0 5.796 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 5.797 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 5.802 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 5.803 * [backup-simplify]: Simplify (+ 0 0) into 0 5.803 * [backup-simplify]: Simplify (- 1) into -1 5.803 * [backup-simplify]: Simplify (+ 0 -1) into -1 5.804 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 5.806 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 5.808 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 5.809 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 5.810 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 5.811 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 5.813 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 5.813 * [backup-simplify]: Simplify (- 0) into 0 5.813 * [backup-simplify]: Simplify (+ 0 0) into 0 5.814 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 5.815 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 5.816 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 5.817 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 5.817 * [taylor]: Taking taylor expansion of 0 in k 5.817 * [backup-simplify]: Simplify 0 into 0 5.817 * [backup-simplify]: Simplify 0 into 0 5.817 * [backup-simplify]: Simplify 0 into 0 5.818 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 5.820 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 5.821 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 5.821 * [backup-simplify]: Simplify (+ 0 0) into 0 5.821 * [backup-simplify]: Simplify (- 0) into 0 5.822 * [backup-simplify]: Simplify (+ 0 0) into 0 5.823 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 5.825 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 5.827 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 5.830 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 5.837 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 5.837 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 5.837 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 5.837 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 5.837 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 5.837 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 5.837 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 5.837 * [taylor]: Taking taylor expansion of 0.5 in k 5.837 * [backup-simplify]: Simplify 0.5 into 0.5 5.837 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 5.837 * [taylor]: Taking taylor expansion of 1.0 in k 5.837 * [backup-simplify]: Simplify 1.0 into 1.0 5.837 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.837 * [taylor]: Taking taylor expansion of k in k 5.837 * [backup-simplify]: Simplify 0 into 0 5.837 * [backup-simplify]: Simplify 1 into 1 5.838 * [backup-simplify]: Simplify (/ 1 1) into 1 5.838 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 5.838 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 5.838 * [taylor]: Taking taylor expansion of 2.0 in k 5.838 * [backup-simplify]: Simplify 2.0 into 2.0 5.838 * [taylor]: Taking taylor expansion of (/ PI n) in k 5.838 * [taylor]: Taking taylor expansion of PI in k 5.838 * [backup-simplify]: Simplify PI into PI 5.838 * [taylor]: Taking taylor expansion of n in k 5.838 * [backup-simplify]: Simplify n into n 5.838 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 5.838 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 5.838 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 5.838 * [backup-simplify]: Simplify (- 1) into -1 5.839 * [backup-simplify]: Simplify (+ 0 -1) into -1 5.839 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 5.839 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 5.839 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 5.839 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 5.839 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 5.839 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 5.839 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 5.839 * [taylor]: Taking taylor expansion of 0.5 in n 5.839 * [backup-simplify]: Simplify 0.5 into 0.5 5.839 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 5.839 * [taylor]: Taking taylor expansion of 1.0 in n 5.839 * [backup-simplify]: Simplify 1.0 into 1.0 5.839 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.839 * [taylor]: Taking taylor expansion of k in n 5.839 * [backup-simplify]: Simplify k into k 5.839 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.839 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 5.839 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 5.839 * [taylor]: Taking taylor expansion of 2.0 in n 5.839 * [backup-simplify]: Simplify 2.0 into 2.0 5.839 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.839 * [taylor]: Taking taylor expansion of PI in n 5.839 * [backup-simplify]: Simplify PI into PI 5.839 * [taylor]: Taking taylor expansion of n in n 5.839 * [backup-simplify]: Simplify 0 into 0 5.840 * [backup-simplify]: Simplify 1 into 1 5.840 * [backup-simplify]: Simplify (/ PI 1) into PI 5.840 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.841 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.841 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 5.841 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 5.841 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 5.842 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.843 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 5.843 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.844 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 5.844 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 5.844 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 5.844 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 5.844 * [taylor]: Taking taylor expansion of 0.5 in n 5.844 * [backup-simplify]: Simplify 0.5 into 0.5 5.844 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 5.844 * [taylor]: Taking taylor expansion of 1.0 in n 5.844 * [backup-simplify]: Simplify 1.0 into 1.0 5.844 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.844 * [taylor]: Taking taylor expansion of k in n 5.844 * [backup-simplify]: Simplify k into k 5.844 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.844 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 5.844 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 5.844 * [taylor]: Taking taylor expansion of 2.0 in n 5.844 * [backup-simplify]: Simplify 2.0 into 2.0 5.844 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.844 * [taylor]: Taking taylor expansion of PI in n 5.844 * [backup-simplify]: Simplify PI into PI 5.844 * [taylor]: Taking taylor expansion of n in n 5.844 * [backup-simplify]: Simplify 0 into 0 5.844 * [backup-simplify]: Simplify 1 into 1 5.844 * [backup-simplify]: Simplify (/ PI 1) into PI 5.845 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.845 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.845 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 5.845 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 5.845 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 5.846 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.847 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 5.848 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.848 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 5.848 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 5.848 * [taylor]: Taking taylor expansion of 0.5 in k 5.848 * [backup-simplify]: Simplify 0.5 into 0.5 5.848 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 5.848 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 5.848 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 5.848 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 5.848 * [taylor]: Taking taylor expansion of 2.0 in k 5.848 * [backup-simplify]: Simplify 2.0 into 2.0 5.848 * [taylor]: Taking taylor expansion of PI in k 5.848 * [backup-simplify]: Simplify PI into PI 5.849 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.849 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 5.849 * [taylor]: Taking taylor expansion of (log n) in k 5.849 * [taylor]: Taking taylor expansion of n in k 5.849 * [backup-simplify]: Simplify n into n 5.849 * [backup-simplify]: Simplify (log n) into (log n) 5.849 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 5.849 * [taylor]: Taking taylor expansion of 1.0 in k 5.849 * [backup-simplify]: Simplify 1.0 into 1.0 5.849 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.849 * [taylor]: Taking taylor expansion of k in k 5.850 * [backup-simplify]: Simplify 0 into 0 5.850 * [backup-simplify]: Simplify 1 into 1 5.850 * [backup-simplify]: Simplify (/ 1 1) into 1 5.850 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 5.850 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 5.851 * [backup-simplify]: Simplify (- 1) into -1 5.851 * [backup-simplify]: Simplify (+ 0 -1) into -1 5.852 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 5.852 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 5.853 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.854 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 5.855 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 5.855 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 5.856 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 5.856 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 5.856 * [backup-simplify]: Simplify (- 0) into 0 5.857 * [backup-simplify]: Simplify (+ 0 0) into 0 5.857 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 5.858 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.859 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 5.860 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 5.860 * [taylor]: Taking taylor expansion of 0 in k 5.860 * [backup-simplify]: Simplify 0 into 0 5.860 * [backup-simplify]: Simplify 0 into 0 5.860 * [backup-simplify]: Simplify 0 into 0 5.861 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.862 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 5.864 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 5.864 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 5.864 * [backup-simplify]: Simplify (- 0) into 0 5.864 * [backup-simplify]: Simplify (+ 0 0) into 0 5.865 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 5.866 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.867 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 5.868 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 5.868 * [taylor]: Taking taylor expansion of 0 in k 5.868 * [backup-simplify]: Simplify 0 into 0 5.868 * [backup-simplify]: Simplify 0 into 0 5.868 * [backup-simplify]: Simplify 0 into 0 5.868 * [backup-simplify]: Simplify 0 into 0 5.869 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.870 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 5.873 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 5.873 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 5.873 * [backup-simplify]: Simplify (- 0) into 0 5.874 * [backup-simplify]: Simplify (+ 0 0) into 0 5.874 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 5.875 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 5.876 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 5.878 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 5.878 * [taylor]: Taking taylor expansion of 0 in k 5.878 * [backup-simplify]: Simplify 0 into 0 5.878 * [backup-simplify]: Simplify 0 into 0 5.879 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 5.879 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 5.880 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 5.880 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 5.880 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 5.880 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 5.880 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 5.880 * [taylor]: Taking taylor expansion of 0.5 in k 5.880 * [backup-simplify]: Simplify 0.5 into 0.5 5.880 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 5.880 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.880 * [taylor]: Taking taylor expansion of k in k 5.880 * [backup-simplify]: Simplify 0 into 0 5.880 * [backup-simplify]: Simplify 1 into 1 5.880 * [backup-simplify]: Simplify (/ 1 1) into 1 5.880 * [taylor]: Taking taylor expansion of 1.0 in k 5.880 * [backup-simplify]: Simplify 1.0 into 1.0 5.880 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 5.880 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 5.880 * [taylor]: Taking taylor expansion of -2.0 in k 5.880 * [backup-simplify]: Simplify -2.0 into -2.0 5.880 * [taylor]: Taking taylor expansion of (/ PI n) in k 5.880 * [taylor]: Taking taylor expansion of PI in k 5.880 * [backup-simplify]: Simplify PI into PI 5.880 * [taylor]: Taking taylor expansion of n in k 5.880 * [backup-simplify]: Simplify n into n 5.880 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 5.880 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 5.880 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 5.881 * [backup-simplify]: Simplify (+ 1 0) into 1 5.881 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 5.881 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 5.881 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 5.881 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 5.881 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 5.881 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 5.881 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 5.881 * [taylor]: Taking taylor expansion of 0.5 in n 5.881 * [backup-simplify]: Simplify 0.5 into 0.5 5.881 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 5.881 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.881 * [taylor]: Taking taylor expansion of k in n 5.881 * [backup-simplify]: Simplify k into k 5.881 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.881 * [taylor]: Taking taylor expansion of 1.0 in n 5.881 * [backup-simplify]: Simplify 1.0 into 1.0 5.881 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 5.881 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.881 * [taylor]: Taking taylor expansion of -2.0 in n 5.881 * [backup-simplify]: Simplify -2.0 into -2.0 5.881 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.882 * [taylor]: Taking taylor expansion of PI in n 5.882 * [backup-simplify]: Simplify PI into PI 5.882 * [taylor]: Taking taylor expansion of n in n 5.882 * [backup-simplify]: Simplify 0 into 0 5.882 * [backup-simplify]: Simplify 1 into 1 5.882 * [backup-simplify]: Simplify (/ PI 1) into PI 5.882 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.883 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.883 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 5.883 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 5.884 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.885 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 5.885 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.885 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 5.885 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 5.885 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 5.885 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 5.885 * [taylor]: Taking taylor expansion of 0.5 in n 5.886 * [backup-simplify]: Simplify 0.5 into 0.5 5.886 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 5.886 * [taylor]: Taking taylor expansion of (/ 1 k) in n 5.886 * [taylor]: Taking taylor expansion of k in n 5.886 * [backup-simplify]: Simplify k into k 5.886 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 5.886 * [taylor]: Taking taylor expansion of 1.0 in n 5.886 * [backup-simplify]: Simplify 1.0 into 1.0 5.886 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 5.886 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.886 * [taylor]: Taking taylor expansion of -2.0 in n 5.886 * [backup-simplify]: Simplify -2.0 into -2.0 5.886 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.886 * [taylor]: Taking taylor expansion of PI in n 5.886 * [backup-simplify]: Simplify PI into PI 5.886 * [taylor]: Taking taylor expansion of n in n 5.886 * [backup-simplify]: Simplify 0 into 0 5.886 * [backup-simplify]: Simplify 1 into 1 5.886 * [backup-simplify]: Simplify (/ PI 1) into PI 5.886 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.887 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.887 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 5.887 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 5.888 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.889 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 5.890 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.890 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 5.890 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 5.890 * [taylor]: Taking taylor expansion of 0.5 in k 5.890 * [backup-simplify]: Simplify 0.5 into 0.5 5.890 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 5.890 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 5.890 * [taylor]: Taking taylor expansion of (/ 1 k) in k 5.890 * [taylor]: Taking taylor expansion of k in k 5.890 * [backup-simplify]: Simplify 0 into 0 5.890 * [backup-simplify]: Simplify 1 into 1 5.890 * [backup-simplify]: Simplify (/ 1 1) into 1 5.890 * [taylor]: Taking taylor expansion of 1.0 in k 5.890 * [backup-simplify]: Simplify 1.0 into 1.0 5.890 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 5.890 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 5.890 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 5.890 * [taylor]: Taking taylor expansion of -2.0 in k 5.890 * [backup-simplify]: Simplify -2.0 into -2.0 5.890 * [taylor]: Taking taylor expansion of PI in k 5.890 * [backup-simplify]: Simplify PI into PI 5.891 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.891 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 5.891 * [taylor]: Taking taylor expansion of (log n) in k 5.891 * [taylor]: Taking taylor expansion of n in k 5.891 * [backup-simplify]: Simplify n into n 5.891 * [backup-simplify]: Simplify (log n) into (log n) 5.892 * [backup-simplify]: Simplify (+ 1 0) into 1 5.892 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 5.898 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 5.899 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 5.900 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 5.900 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.901 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 5.902 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 5.902 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 5.903 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 5.903 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 5.904 * [backup-simplify]: Simplify (+ 0 0) into 0 5.904 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 5.906 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.907 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 5.909 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 5.909 * [taylor]: Taking taylor expansion of 0 in k 5.909 * [backup-simplify]: Simplify 0 into 0 5.909 * [backup-simplify]: Simplify 0 into 0 5.909 * [backup-simplify]: Simplify 0 into 0 5.910 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.912 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 5.916 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 5.916 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 5.916 * [backup-simplify]: Simplify (+ 0 0) into 0 5.917 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 5.919 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.920 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 5.923 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 5.923 * [taylor]: Taking taylor expansion of 0 in k 5.923 * [backup-simplify]: Simplify 0 into 0 5.923 * [backup-simplify]: Simplify 0 into 0 5.923 * [backup-simplify]: Simplify 0 into 0 5.923 * [backup-simplify]: Simplify 0 into 0 5.925 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.926 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 5.931 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 5.932 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 5.932 * [backup-simplify]: Simplify (+ 0 0) into 0 5.933 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 5.935 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 5.937 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 5.940 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 5.940 * [taylor]: Taking taylor expansion of 0 in k 5.940 * [backup-simplify]: Simplify 0 into 0 5.940 * [backup-simplify]: Simplify 0 into 0 5.941 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 5.941 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 2 1) 5.942 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 5.942 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 5.942 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 5.942 * [taylor]: Taking taylor expansion of 2.0 in n 5.942 * [backup-simplify]: Simplify 2.0 into 2.0 5.942 * [taylor]: Taking taylor expansion of (* n PI) in n 5.942 * [taylor]: Taking taylor expansion of n in n 5.942 * [backup-simplify]: Simplify 0 into 0 5.942 * [backup-simplify]: Simplify 1 into 1 5.942 * [taylor]: Taking taylor expansion of PI in n 5.942 * [backup-simplify]: Simplify PI into PI 5.942 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 5.942 * [taylor]: Taking taylor expansion of 2.0 in n 5.942 * [backup-simplify]: Simplify 2.0 into 2.0 5.942 * [taylor]: Taking taylor expansion of (* n PI) in n 5.942 * [taylor]: Taking taylor expansion of n in n 5.942 * [backup-simplify]: Simplify 0 into 0 5.942 * [backup-simplify]: Simplify 1 into 1 5.943 * [taylor]: Taking taylor expansion of PI in n 5.943 * [backup-simplify]: Simplify PI into PI 5.943 * [backup-simplify]: Simplify (* 0 PI) into 0 5.944 * [backup-simplify]: Simplify (* 2.0 0) into 0 5.944 * [backup-simplify]: Simplify 0 into 0 5.945 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 5.947 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 5.947 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.948 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 5.949 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 5.949 * [backup-simplify]: Simplify 0 into 0 5.950 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 5.951 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 5.951 * [backup-simplify]: Simplify 0 into 0 5.953 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 5.954 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 5.954 * [backup-simplify]: Simplify 0 into 0 5.956 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 5.957 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 5.957 * [backup-simplify]: Simplify 0 into 0 5.959 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 5.961 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 5.961 * [backup-simplify]: Simplify 0 into 0 5.963 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 5.965 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 5.965 * [backup-simplify]: Simplify 0 into 0 5.966 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 5.967 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 5.967 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 5.967 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 5.967 * [taylor]: Taking taylor expansion of 2.0 in n 5.967 * [backup-simplify]: Simplify 2.0 into 2.0 5.967 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.967 * [taylor]: Taking taylor expansion of PI in n 5.967 * [backup-simplify]: Simplify PI into PI 5.967 * [taylor]: Taking taylor expansion of n in n 5.967 * [backup-simplify]: Simplify 0 into 0 5.967 * [backup-simplify]: Simplify 1 into 1 5.967 * [backup-simplify]: Simplify (/ PI 1) into PI 5.968 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 5.968 * [taylor]: Taking taylor expansion of 2.0 in n 5.968 * [backup-simplify]: Simplify 2.0 into 2.0 5.968 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.968 * [taylor]: Taking taylor expansion of PI in n 5.968 * [backup-simplify]: Simplify PI into PI 5.968 * [taylor]: Taking taylor expansion of n in n 5.968 * [backup-simplify]: Simplify 0 into 0 5.968 * [backup-simplify]: Simplify 1 into 1 5.968 * [backup-simplify]: Simplify (/ PI 1) into PI 5.969 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.969 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 5.970 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 5.971 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 5.971 * [backup-simplify]: Simplify 0 into 0 5.972 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.973 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 5.973 * [backup-simplify]: Simplify 0 into 0 5.975 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.976 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 5.976 * [backup-simplify]: Simplify 0 into 0 5.977 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.978 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 5.978 * [backup-simplify]: Simplify 0 into 0 5.979 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.981 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 5.981 * [backup-simplify]: Simplify 0 into 0 5.982 * [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 5.984 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 5.984 * [backup-simplify]: Simplify 0 into 0 5.985 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 5.985 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 5.985 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 5.985 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.985 * [taylor]: Taking taylor expansion of -2.0 in n 5.985 * [backup-simplify]: Simplify -2.0 into -2.0 5.986 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.986 * [taylor]: Taking taylor expansion of PI in n 5.986 * [backup-simplify]: Simplify PI into PI 5.986 * [taylor]: Taking taylor expansion of n in n 5.986 * [backup-simplify]: Simplify 0 into 0 5.986 * [backup-simplify]: Simplify 1 into 1 5.986 * [backup-simplify]: Simplify (/ PI 1) into PI 5.986 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 5.986 * [taylor]: Taking taylor expansion of -2.0 in n 5.986 * [backup-simplify]: Simplify -2.0 into -2.0 5.986 * [taylor]: Taking taylor expansion of (/ PI n) in n 5.986 * [taylor]: Taking taylor expansion of PI in n 5.986 * [backup-simplify]: Simplify PI into PI 5.986 * [taylor]: Taking taylor expansion of n in n 5.986 * [backup-simplify]: Simplify 0 into 0 5.986 * [backup-simplify]: Simplify 1 into 1 5.987 * [backup-simplify]: Simplify (/ PI 1) into PI 5.987 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.988 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 5.989 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 5.989 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 5.990 * [backup-simplify]: Simplify 0 into 0 5.990 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.991 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 5.991 * [backup-simplify]: Simplify 0 into 0 5.993 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.994 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 5.994 * [backup-simplify]: Simplify 0 into 0 5.995 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.996 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 5.996 * [backup-simplify]: Simplify 0 into 0 5.997 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 5.999 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 5.999 * [backup-simplify]: Simplify 0 into 0 6.000 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.002 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.002 * [backup-simplify]: Simplify 0 into 0 6.003 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 6.003 * * * * [progress]: [ 3 / 3 ] generating series at (2) 6.004 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) 6.004 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (n k) around 0 6.004 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 6.004 * [taylor]: Taking taylor expansion of 1.0 in k 6.004 * [backup-simplify]: Simplify 1.0 into 1.0 6.004 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 6.004 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 6.004 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.004 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.004 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 6.004 * [taylor]: Taking taylor expansion of 0.5 in k 6.004 * [backup-simplify]: Simplify 0.5 into 0.5 6.004 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.004 * [taylor]: Taking taylor expansion of 1.0 in k 6.004 * [backup-simplify]: Simplify 1.0 into 1.0 6.004 * [taylor]: Taking taylor expansion of k in k 6.004 * [backup-simplify]: Simplify 0 into 0 6.004 * [backup-simplify]: Simplify 1 into 1 6.004 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.004 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.004 * [taylor]: Taking taylor expansion of 2.0 in k 6.004 * [backup-simplify]: Simplify 2.0 into 2.0 6.004 * [taylor]: Taking taylor expansion of (* n PI) in k 6.004 * [taylor]: Taking taylor expansion of n in k 6.005 * [backup-simplify]: Simplify n into n 6.005 * [taylor]: Taking taylor expansion of PI in k 6.005 * [backup-simplify]: Simplify PI into PI 6.005 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.005 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.005 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.005 * [backup-simplify]: Simplify (- 0) into 0 6.006 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.006 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 6.006 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 6.006 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 6.006 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.006 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.007 * [taylor]: Taking taylor expansion of k in k 6.007 * [backup-simplify]: Simplify 0 into 0 6.007 * [backup-simplify]: Simplify 1 into 1 6.007 * [backup-simplify]: Simplify (/ 1 1) into 1 6.007 * [backup-simplify]: Simplify (sqrt 0) into 0 6.009 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.009 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 6.009 * [taylor]: Taking taylor expansion of 1.0 in n 6.009 * [backup-simplify]: Simplify 1.0 into 1.0 6.009 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 6.009 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 6.009 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.009 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.009 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 6.009 * [taylor]: Taking taylor expansion of 0.5 in n 6.009 * [backup-simplify]: Simplify 0.5 into 0.5 6.009 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.009 * [taylor]: Taking taylor expansion of 1.0 in n 6.009 * [backup-simplify]: Simplify 1.0 into 1.0 6.009 * [taylor]: Taking taylor expansion of k in n 6.009 * [backup-simplify]: Simplify k into k 6.009 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.009 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.009 * [taylor]: Taking taylor expansion of 2.0 in n 6.009 * [backup-simplify]: Simplify 2.0 into 2.0 6.009 * [taylor]: Taking taylor expansion of (* n PI) in n 6.009 * [taylor]: Taking taylor expansion of n in n 6.009 * [backup-simplify]: Simplify 0 into 0 6.010 * [backup-simplify]: Simplify 1 into 1 6.010 * [taylor]: Taking taylor expansion of PI in n 6.010 * [backup-simplify]: Simplify PI into PI 6.010 * [backup-simplify]: Simplify (* 0 PI) into 0 6.011 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.012 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.014 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.015 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.015 * [backup-simplify]: Simplify (- k) into (- k) 6.015 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.015 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 6.016 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.018 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 6.019 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 6.019 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 6.019 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.019 * [taylor]: Taking taylor expansion of k in n 6.019 * [backup-simplify]: Simplify k into k 6.019 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.019 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 6.019 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.019 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 6.020 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 6.020 * [taylor]: Taking taylor expansion of 1.0 in n 6.020 * [backup-simplify]: Simplify 1.0 into 1.0 6.020 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 6.020 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 6.020 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.020 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.020 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 6.020 * [taylor]: Taking taylor expansion of 0.5 in n 6.020 * [backup-simplify]: Simplify 0.5 into 0.5 6.020 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.020 * [taylor]: Taking taylor expansion of 1.0 in n 6.020 * [backup-simplify]: Simplify 1.0 into 1.0 6.020 * [taylor]: Taking taylor expansion of k in n 6.020 * [backup-simplify]: Simplify k into k 6.020 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.020 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.020 * [taylor]: Taking taylor expansion of 2.0 in n 6.020 * [backup-simplify]: Simplify 2.0 into 2.0 6.020 * [taylor]: Taking taylor expansion of (* n PI) in n 6.020 * [taylor]: Taking taylor expansion of n in n 6.020 * [backup-simplify]: Simplify 0 into 0 6.020 * [backup-simplify]: Simplify 1 into 1 6.020 * [taylor]: Taking taylor expansion of PI in n 6.020 * [backup-simplify]: Simplify PI into PI 6.021 * [backup-simplify]: Simplify (* 0 PI) into 0 6.021 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.023 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.025 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.026 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.026 * [backup-simplify]: Simplify (- k) into (- k) 6.026 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.026 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 6.028 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.029 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 6.030 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 6.030 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 6.030 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.030 * [taylor]: Taking taylor expansion of k in n 6.030 * [backup-simplify]: Simplify k into k 6.030 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.030 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 6.031 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.031 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 6.032 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) into (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) 6.034 * [backup-simplify]: Simplify (* 1.0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))) into (* 1.0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))) 6.034 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))) in k 6.034 * [taylor]: Taking taylor expansion of 1.0 in k 6.034 * [backup-simplify]: Simplify 1.0 into 1.0 6.034 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) in k 6.034 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.034 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.034 * [taylor]: Taking taylor expansion of k in k 6.034 * [backup-simplify]: Simplify 0 into 0 6.034 * [backup-simplify]: Simplify 1 into 1 6.034 * [backup-simplify]: Simplify (/ 1 1) into 1 6.035 * [backup-simplify]: Simplify (sqrt 0) into 0 6.036 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.036 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 6.036 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 6.036 * [taylor]: Taking taylor expansion of 0.5 in k 6.036 * [backup-simplify]: Simplify 0.5 into 0.5 6.036 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 6.036 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.036 * [taylor]: Taking taylor expansion of 1.0 in k 6.037 * [backup-simplify]: Simplify 1.0 into 1.0 6.037 * [taylor]: Taking taylor expansion of k in k 6.037 * [backup-simplify]: Simplify 0 into 0 6.037 * [backup-simplify]: Simplify 1 into 1 6.037 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 6.037 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.037 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.037 * [taylor]: Taking taylor expansion of 2.0 in k 6.037 * [backup-simplify]: Simplify 2.0 into 2.0 6.037 * [taylor]: Taking taylor expansion of PI in k 6.037 * [backup-simplify]: Simplify PI into PI 6.037 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.038 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.038 * [taylor]: Taking taylor expansion of (log n) in k 6.038 * [taylor]: Taking taylor expansion of n in k 6.039 * [backup-simplify]: Simplify n into n 6.039 * [backup-simplify]: Simplify (log n) into (log n) 6.039 * [backup-simplify]: Simplify (- 0) into 0 6.039 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.041 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 6.042 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 6.043 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 6.044 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 6.045 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) into 0 6.046 * [backup-simplify]: Simplify (* 1.0 0) into 0 6.046 * [backup-simplify]: Simplify 0 into 0 6.047 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.056 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.057 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.058 * [backup-simplify]: Simplify (- 0) into 0 6.058 * [backup-simplify]: Simplify (+ 0 0) into 0 6.058 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 6.059 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.060 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 6.061 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.062 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0 6.063 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))))) into 0 6.063 * [taylor]: Taking taylor expansion of 0 in k 6.063 * [backup-simplify]: Simplify 0 into 0 6.064 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.065 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.066 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.066 * [backup-simplify]: Simplify (+ 0 0) into 0 6.066 * [backup-simplify]: Simplify (- 1) into -1 6.066 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.067 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 6.069 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 6.071 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 6.074 * [backup-simplify]: Simplify (+ (* 0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 6.075 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 6.075 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 6.076 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.076 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 6.077 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.077 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.079 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 6.080 * [backup-simplify]: Simplify (- 0) into 0 6.080 * [backup-simplify]: Simplify (+ 0 0) into 0 6.081 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 6.082 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.083 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.084 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.085 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 6.087 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))))) into 0 6.087 * [taylor]: Taking taylor expansion of 0 in k 6.087 * [backup-simplify]: Simplify 0 into 0 6.087 * [backup-simplify]: Simplify 0 into 0 6.087 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.089 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 6.090 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.091 * [backup-simplify]: Simplify (+ 0 0) into 0 6.091 * [backup-simplify]: Simplify (- 0) into 0 6.091 * [backup-simplify]: Simplify (+ 0 0) into 0 6.092 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.094 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.096 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 6.097 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 6.099 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.106 * [backup-simplify]: Simplify (+ (* 0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))) (+ (* +nan.0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))) 6.114 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))) 6.119 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))) 6.120 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.121 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 6.122 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.124 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 6.130 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 6.130 * [backup-simplify]: Simplify (- 0) into 0 6.131 * [backup-simplify]: Simplify (+ 0 0) into 0 6.132 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0 6.134 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.136 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.138 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.141 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0 6.143 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))))))) into 0 6.143 * [taylor]: Taking taylor expansion of 0 in k 6.143 * [backup-simplify]: Simplify 0 into 0 6.143 * [backup-simplify]: Simplify 0 into 0 6.143 * [backup-simplify]: Simplify 0 into 0 6.145 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.150 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 6.154 * [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 6.154 * [backup-simplify]: Simplify (+ 0 0) into 0 6.155 * [backup-simplify]: Simplify (- 0) into 0 6.155 * [backup-simplify]: Simplify (+ 0 0) into 0 6.157 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.160 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))))) into 0 6.168 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n))) (* 0.020833333333333332 (pow (log n) 3))))))) 6.169 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.173 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.194 * [backup-simplify]: Simplify (+ (* 0 (* -1 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n))) (* 0.020833333333333332 (pow (log n) 3)))))))) (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))) (+ (* +nan.0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))) 6.206 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) (+ (* 0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))))))))) 6.216 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))))))))) 6.238 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (pow k 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))))))))) 6.239 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) (sqrt (/ 1 k))) into (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) 6.240 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (n k) around 0 6.240 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 6.240 * [taylor]: Taking taylor expansion of 1.0 in k 6.240 * [backup-simplify]: Simplify 1.0 into 1.0 6.240 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 6.240 * [taylor]: Taking taylor expansion of (sqrt k) in k 6.240 * [taylor]: Taking taylor expansion of k in k 6.240 * [backup-simplify]: Simplify 0 into 0 6.240 * [backup-simplify]: Simplify 1 into 1 6.240 * [backup-simplify]: Simplify (sqrt 0) into 0 6.241 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.241 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 6.241 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.241 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.241 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 6.241 * [taylor]: Taking taylor expansion of 0.5 in k 6.241 * [backup-simplify]: Simplify 0.5 into 0.5 6.241 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.241 * [taylor]: Taking taylor expansion of 1.0 in k 6.241 * [backup-simplify]: Simplify 1.0 into 1.0 6.241 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.241 * [taylor]: Taking taylor expansion of k in k 6.241 * [backup-simplify]: Simplify 0 into 0 6.241 * [backup-simplify]: Simplify 1 into 1 6.241 * [backup-simplify]: Simplify (/ 1 1) into 1 6.241 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.241 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.241 * [taylor]: Taking taylor expansion of 2.0 in k 6.241 * [backup-simplify]: Simplify 2.0 into 2.0 6.241 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.241 * [taylor]: Taking taylor expansion of PI in k 6.241 * [backup-simplify]: Simplify PI into PI 6.241 * [taylor]: Taking taylor expansion of n in k 6.241 * [backup-simplify]: Simplify n into n 6.241 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.242 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.242 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.242 * [backup-simplify]: Simplify (- 1) into -1 6.242 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.242 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 6.242 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 6.243 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 6.243 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 6.243 * [taylor]: Taking taylor expansion of 1.0 in n 6.243 * [backup-simplify]: Simplify 1.0 into 1.0 6.243 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 6.243 * [taylor]: Taking taylor expansion of (sqrt k) in n 6.243 * [taylor]: Taking taylor expansion of k in n 6.243 * [backup-simplify]: Simplify k into k 6.243 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 6.243 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 6.243 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 6.243 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.243 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.243 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 6.243 * [taylor]: Taking taylor expansion of 0.5 in n 6.243 * [backup-simplify]: Simplify 0.5 into 0.5 6.243 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.243 * [taylor]: Taking taylor expansion of 1.0 in n 6.243 * [backup-simplify]: Simplify 1.0 into 1.0 6.243 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.243 * [taylor]: Taking taylor expansion of k in n 6.243 * [backup-simplify]: Simplify k into k 6.243 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.243 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.243 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.243 * [taylor]: Taking taylor expansion of 2.0 in n 6.243 * [backup-simplify]: Simplify 2.0 into 2.0 6.243 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.243 * [taylor]: Taking taylor expansion of PI in n 6.243 * [backup-simplify]: Simplify PI into PI 6.243 * [taylor]: Taking taylor expansion of n in n 6.243 * [backup-simplify]: Simplify 0 into 0 6.243 * [backup-simplify]: Simplify 1 into 1 6.244 * [backup-simplify]: Simplify (/ PI 1) into PI 6.244 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.244 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.245 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.245 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.245 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.246 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.246 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.247 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.247 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 6.247 * [taylor]: Taking taylor expansion of 1.0 in n 6.247 * [backup-simplify]: Simplify 1.0 into 1.0 6.247 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 6.247 * [taylor]: Taking taylor expansion of (sqrt k) in n 6.247 * [taylor]: Taking taylor expansion of k in n 6.247 * [backup-simplify]: Simplify k into k 6.247 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 6.247 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 6.247 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 6.247 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.247 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.247 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 6.247 * [taylor]: Taking taylor expansion of 0.5 in n 6.247 * [backup-simplify]: Simplify 0.5 into 0.5 6.247 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.247 * [taylor]: Taking taylor expansion of 1.0 in n 6.247 * [backup-simplify]: Simplify 1.0 into 1.0 6.247 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.247 * [taylor]: Taking taylor expansion of k in n 6.247 * [backup-simplify]: Simplify k into k 6.247 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.248 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.248 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.248 * [taylor]: Taking taylor expansion of 2.0 in n 6.248 * [backup-simplify]: Simplify 2.0 into 2.0 6.248 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.248 * [taylor]: Taking taylor expansion of PI in n 6.248 * [backup-simplify]: Simplify PI into PI 6.248 * [taylor]: Taking taylor expansion of n in n 6.248 * [backup-simplify]: Simplify 0 into 0 6.248 * [backup-simplify]: Simplify 1 into 1 6.248 * [backup-simplify]: Simplify (/ PI 1) into PI 6.248 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.249 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.249 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.249 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.249 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.250 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.251 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.251 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.252 * [backup-simplify]: Simplify (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) 6.253 * [backup-simplify]: Simplify (* 1.0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (* 1.0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 6.253 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) in k 6.253 * [taylor]: Taking taylor expansion of 1.0 in k 6.253 * [backup-simplify]: Simplify 1.0 into 1.0 6.253 * [taylor]: Taking taylor expansion of (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) in k 6.253 * [taylor]: Taking taylor expansion of (sqrt k) in k 6.253 * [taylor]: Taking taylor expansion of k in k 6.253 * [backup-simplify]: Simplify 0 into 0 6.253 * [backup-simplify]: Simplify 1 into 1 6.253 * [backup-simplify]: Simplify (sqrt 0) into 0 6.254 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.254 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 6.254 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 6.254 * [taylor]: Taking taylor expansion of 0.5 in k 6.254 * [backup-simplify]: Simplify 0.5 into 0.5 6.254 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 6.254 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.254 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.254 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.254 * [taylor]: Taking taylor expansion of 2.0 in k 6.254 * [backup-simplify]: Simplify 2.0 into 2.0 6.254 * [taylor]: Taking taylor expansion of PI in k 6.254 * [backup-simplify]: Simplify PI into PI 6.255 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.255 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.255 * [taylor]: Taking taylor expansion of (log n) in k 6.255 * [taylor]: Taking taylor expansion of n in k 6.255 * [backup-simplify]: Simplify n into n 6.256 * [backup-simplify]: Simplify (log n) into (log n) 6.256 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.256 * [taylor]: Taking taylor expansion of 1.0 in k 6.256 * [backup-simplify]: Simplify 1.0 into 1.0 6.256 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.256 * [taylor]: Taking taylor expansion of k in k 6.256 * [backup-simplify]: Simplify 0 into 0 6.256 * [backup-simplify]: Simplify 1 into 1 6.256 * [backup-simplify]: Simplify (/ 1 1) into 1 6.256 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.257 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.257 * [backup-simplify]: Simplify (- 1) into -1 6.257 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.258 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.258 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 6.259 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.260 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into 0 6.260 * [backup-simplify]: Simplify (* 1.0 0) into 0 6.260 * [backup-simplify]: Simplify 0 into 0 6.261 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.261 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.262 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.262 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.262 * [backup-simplify]: Simplify (- 0) into 0 6.263 * [backup-simplify]: Simplify (+ 0 0) into 0 6.263 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.264 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.265 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.267 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.268 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 6.270 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0 6.270 * [taylor]: Taking taylor expansion of 0 in k 6.270 * [backup-simplify]: Simplify 0 into 0 6.270 * [backup-simplify]: Simplify 0 into 0 6.272 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 6.274 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 6.275 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 6.276 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.277 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.280 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 6.280 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.281 * [backup-simplify]: Simplify (- 0) into 0 6.281 * [backup-simplify]: Simplify (+ 0 0) into 0 6.281 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.282 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.283 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.285 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.285 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 6.286 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0 6.288 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into 0 6.288 * [taylor]: Taking taylor expansion of 0 in k 6.288 * [backup-simplify]: Simplify 0 into 0 6.288 * [backup-simplify]: Simplify 0 into 0 6.288 * [backup-simplify]: Simplify 0 into 0 6.295 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.297 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 6.298 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 6.299 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 6.300 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.301 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.304 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 6.304 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.304 * [backup-simplify]: Simplify (- 0) into 0 6.304 * [backup-simplify]: Simplify (+ 0 0) into 0 6.305 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 6.306 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.307 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 6.309 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.309 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 6.310 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into 0 6.312 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))))) into 0 6.312 * [taylor]: Taking taylor expansion of 0 in k 6.312 * [backup-simplify]: Simplify 0 into 0 6.312 * [backup-simplify]: Simplify 0 into 0 6.312 * [backup-simplify]: Simplify 0 into 0 6.312 * [backup-simplify]: Simplify 0 into 0 6.316 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.319 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 6.323 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 6.324 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) 6.329 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) 6.330 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) (sqrt (/ 1 (- k)))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) 6.330 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (n k) around 0 6.330 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 6.330 * [taylor]: Taking taylor expansion of 1.0 in k 6.330 * [backup-simplify]: Simplify 1.0 into 1.0 6.330 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 6.330 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 6.330 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.330 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.330 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 6.330 * [taylor]: Taking taylor expansion of 0.5 in k 6.330 * [backup-simplify]: Simplify 0.5 into 0.5 6.330 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.330 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.330 * [taylor]: Taking taylor expansion of k in k 6.330 * [backup-simplify]: Simplify 0 into 0 6.330 * [backup-simplify]: Simplify 1 into 1 6.331 * [backup-simplify]: Simplify (/ 1 1) into 1 6.331 * [taylor]: Taking taylor expansion of 1.0 in k 6.331 * [backup-simplify]: Simplify 1.0 into 1.0 6.331 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.331 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.331 * [taylor]: Taking taylor expansion of -2.0 in k 6.331 * [backup-simplify]: Simplify -2.0 into -2.0 6.331 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.331 * [taylor]: Taking taylor expansion of PI in k 6.331 * [backup-simplify]: Simplify PI into PI 6.331 * [taylor]: Taking taylor expansion of n in k 6.331 * [backup-simplify]: Simplify n into n 6.331 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.331 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.331 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.332 * [backup-simplify]: Simplify (+ 1 0) into 1 6.332 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 6.332 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 6.333 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 6.333 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 6.333 * [taylor]: Taking taylor expansion of (/ -1 k) in k 6.333 * [taylor]: Taking taylor expansion of -1 in k 6.333 * [backup-simplify]: Simplify -1 into -1 6.333 * [taylor]: Taking taylor expansion of k in k 6.333 * [backup-simplify]: Simplify 0 into 0 6.333 * [backup-simplify]: Simplify 1 into 1 6.333 * [backup-simplify]: Simplify (/ -1 1) into -1 6.334 * [backup-simplify]: Simplify (sqrt 0) into 0 6.335 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 6.336 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) 6.336 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 6.336 * [taylor]: Taking taylor expansion of 1.0 in n 6.336 * [backup-simplify]: Simplify 1.0 into 1.0 6.336 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 6.336 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 6.336 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.336 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.336 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 6.336 * [taylor]: Taking taylor expansion of 0.5 in n 6.336 * [backup-simplify]: Simplify 0.5 into 0.5 6.336 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.336 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.336 * [taylor]: Taking taylor expansion of k in n 6.336 * [backup-simplify]: Simplify k into k 6.336 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.336 * [taylor]: Taking taylor expansion of 1.0 in n 6.336 * [backup-simplify]: Simplify 1.0 into 1.0 6.336 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.336 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.336 * [taylor]: Taking taylor expansion of -2.0 in n 6.336 * [backup-simplify]: Simplify -2.0 into -2.0 6.336 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.336 * [taylor]: Taking taylor expansion of PI in n 6.336 * [backup-simplify]: Simplify PI into PI 6.336 * [taylor]: Taking taylor expansion of n in n 6.336 * [backup-simplify]: Simplify 0 into 0 6.336 * [backup-simplify]: Simplify 1 into 1 6.337 * [backup-simplify]: Simplify (/ PI 1) into PI 6.337 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.338 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.338 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.339 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 6.340 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.341 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.342 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.342 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 6.342 * [taylor]: Taking taylor expansion of (/ -1 k) in n 6.342 * [taylor]: Taking taylor expansion of -1 in n 6.342 * [backup-simplify]: Simplify -1 into -1 6.342 * [taylor]: Taking taylor expansion of k in n 6.342 * [backup-simplify]: Simplify k into k 6.342 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 6.343 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 6.343 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 6.343 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 6.344 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) 6.344 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 6.344 * [taylor]: Taking taylor expansion of 1.0 in n 6.344 * [backup-simplify]: Simplify 1.0 into 1.0 6.344 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 6.344 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 6.344 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.344 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.344 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 6.344 * [taylor]: Taking taylor expansion of 0.5 in n 6.344 * [backup-simplify]: Simplify 0.5 into 0.5 6.344 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.344 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.344 * [taylor]: Taking taylor expansion of k in n 6.344 * [backup-simplify]: Simplify k into k 6.344 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.345 * [taylor]: Taking taylor expansion of 1.0 in n 6.345 * [backup-simplify]: Simplify 1.0 into 1.0 6.345 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.345 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.345 * [taylor]: Taking taylor expansion of -2.0 in n 6.345 * [backup-simplify]: Simplify -2.0 into -2.0 6.345 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.345 * [taylor]: Taking taylor expansion of PI in n 6.345 * [backup-simplify]: Simplify PI into PI 6.345 * [taylor]: Taking taylor expansion of n in n 6.345 * [backup-simplify]: Simplify 0 into 0 6.345 * [backup-simplify]: Simplify 1 into 1 6.345 * [backup-simplify]: Simplify (/ PI 1) into PI 6.346 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.347 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.347 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.347 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 6.348 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.350 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 6.351 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.351 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 6.351 * [taylor]: Taking taylor expansion of (/ -1 k) in n 6.351 * [taylor]: Taking taylor expansion of -1 in n 6.351 * [backup-simplify]: Simplify -1 into -1 6.351 * [taylor]: Taking taylor expansion of k in n 6.351 * [backup-simplify]: Simplify k into k 6.351 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 6.351 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 6.351 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 6.351 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 6.353 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) 6.354 * [backup-simplify]: Simplify (* 1.0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))) into (* 1.0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))) 6.354 * [taylor]: Taking taylor expansion of (* 1.0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))) in k 6.354 * [taylor]: Taking taylor expansion of 1.0 in k 6.354 * [backup-simplify]: Simplify 1.0 into 1.0 6.354 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) in k 6.354 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 6.354 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 6.354 * [taylor]: Taking taylor expansion of 0.5 in k 6.354 * [backup-simplify]: Simplify 0.5 into 0.5 6.354 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 6.354 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.354 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.354 * [taylor]: Taking taylor expansion of k in k 6.354 * [backup-simplify]: Simplify 0 into 0 6.354 * [backup-simplify]: Simplify 1 into 1 6.355 * [backup-simplify]: Simplify (/ 1 1) into 1 6.355 * [taylor]: Taking taylor expansion of 1.0 in k 6.355 * [backup-simplify]: Simplify 1.0 into 1.0 6.355 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 6.355 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 6.355 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 6.355 * [taylor]: Taking taylor expansion of -2.0 in k 6.355 * [backup-simplify]: Simplify -2.0 into -2.0 6.355 * [taylor]: Taking taylor expansion of PI in k 6.355 * [backup-simplify]: Simplify PI into PI 6.355 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.356 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.356 * [taylor]: Taking taylor expansion of (log n) in k 6.356 * [taylor]: Taking taylor expansion of n in k 6.356 * [backup-simplify]: Simplify n into n 6.357 * [backup-simplify]: Simplify (log n) into (log n) 6.357 * [backup-simplify]: Simplify (+ 1 0) into 1 6.357 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.358 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 6.359 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 6.360 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 6.361 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.362 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 6.362 * [taylor]: Taking taylor expansion of (/ -1 k) in k 6.362 * [taylor]: Taking taylor expansion of -1 in k 6.362 * [backup-simplify]: Simplify -1 into -1 6.362 * [taylor]: Taking taylor expansion of k in k 6.362 * [backup-simplify]: Simplify 0 into 0 6.362 * [backup-simplify]: Simplify 1 into 1 6.362 * [backup-simplify]: Simplify (/ -1 1) into -1 6.362 * [backup-simplify]: Simplify (sqrt 0) into 0 6.364 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 6.365 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 6.366 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 6.368 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) 6.369 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.369 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.370 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 6.370 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.370 * [backup-simplify]: Simplify (+ 0 0) into 0 6.371 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 6.371 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.372 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 6.373 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.374 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0 6.375 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))))) into 0 6.375 * [taylor]: Taking taylor expansion of 0 in k 6.375 * [backup-simplify]: Simplify 0 into 0 6.375 * [backup-simplify]: Simplify 0 into 0 6.376 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 6.378 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.379 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 6.381 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 6.381 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 6.382 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.383 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.384 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 6.385 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.385 * [backup-simplify]: Simplify (+ 0 0) into 0 6.385 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 6.386 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.387 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 6.389 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 6.389 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.389 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 6.390 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0 6.392 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))))) into 0 6.392 * [taylor]: Taking taylor expansion of 0 in k 6.392 * [backup-simplify]: Simplify 0 into 0 6.392 * [backup-simplify]: Simplify 0 into 0 6.392 * [backup-simplify]: Simplify 0 into 0 6.392 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.395 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.398 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 6.402 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 6.404 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) 6.408 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 6.408 * * * [progress]: simplifying candidates 6.420 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (log 1.0) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k))) (- (+ (log 1.0) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k))) (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k))) (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k))) (- (+ (log 1.0) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k))) (- (log (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k))) (log (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (exp (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (/ (* (* (* 1.0 1.0) 1.0) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) (/ (* (* (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (* (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (- (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (- (sqrt k)) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k))) (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))) (/ 1.0 (sqrt (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (/ 1.0 (sqrt 1)) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (/ 1.0 (sqrt (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (/ 1.0 1) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (* (cbrt k) (cbrt k)))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt 1)) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (- (+ (* +nan.0 (* (pow k 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2)))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))))) 6.427 * * [simplify]: Extracting # 0 : cost 0 6.427 * * [simplify]: Extracting # 1 : cost 0 6.428 * * [simplify]: Extracting # 2 : cost 0 6.428 * * [simplify]: Extracting # 3 : cost 0 6.429 * * [simplify]: Extracting # 4 : cost 0 6.430 * * [simplify]: Extracting # 5 : cost 0 6.430 * * [simplify]: Extracting # 6 : cost 0 6.431 * * [simplify]: Extracting # 7 : cost 0 6.432 * * [simplify]: Extracting # 8 : cost 0 6.432 * * [simplify]: Extracting # 9 : cost 0 6.432 * * [simplify]: Extracting # 10 : cost 0 6.433 * * [simplify]: Extracting # 11 : cost 0 6.433 * * [simplify]: Extracting # 12 : cost 0 6.433 * * [simplify]: Extracting # 13 : cost 0 6.434 * * [simplify]: Extracting # 14 : cost 0 6.434 * * [simplify]: Extracting # 15 : cost 0 6.434 * * [simplify]: Extracting # 16 : cost 0 6.435 * * [simplify]: Extracting # 17 : cost 0 6.435 * * [simplify]: Extracting # 18 : cost 0 6.435 * * [simplify]: Extracting # 19 : cost 0 6.436 * * [simplify]: Extracting # 20 : cost 0 6.436 * * [simplify]: Extracting # 21 : cost 0 6.436 * * [simplify]: Extracting # 22 : cost 0 6.437 * * [simplify]: Extracting # 23 : cost 0 6.437 * * [simplify]: Extracting # 24 : cost 0 6.437 * * [simplify]: Extracting # 25 : cost 0 6.438 * * [simplify]: Extracting # 26 : cost 0 6.438 * * [simplify]: Extracting # 27 : cost 0 6.438 * * [simplify]: Extracting # 28 : cost 0 6.439 * * [simplify]: Extracting # 29 : cost 0 6.439 * * [simplify]: Extracting # 30 : cost 0 6.439 * * [simplify]: iteration 0 : 264 enodes (cost 1828 ) 6.535 * * [simplify]: Extracting # 0 : cost 0 6.537 * * [simplify]: Extracting # 1 : cost 0 6.539 * * [simplify]: Extracting # 2 : cost 0 6.540 * * [simplify]: Extracting # 3 : cost 0 6.541 * * [simplify]: Extracting # 4 : cost 0 6.542 * * [simplify]: Extracting # 5 : cost 0 6.543 * * [simplify]: Extracting # 6 : cost 0 6.544 * * [simplify]: Extracting # 7 : cost 0 6.545 * * [simplify]: Extracting # 8 : cost 0 6.546 * * [simplify]: Extracting # 9 : cost 0 6.547 * * [simplify]: Extracting # 10 : cost 0 6.548 * * [simplify]: Extracting # 11 : cost 0 6.549 * * [simplify]: iteration 1 : 749 enodes (cost 1703 ) 7.376 * * [simplify]: Extracting # 0 : cost 0 7.380 * * [simplify]: Extracting # 1 : cost 0 7.385 * * [simplify]: Extracting # 2 : cost 0 7.398 * * [simplify]: Extracting # 3 : cost 0 7.407 * * [simplify]: Extracting # 4 : cost 0 7.414 * * [simplify]: Extracting # 5 : cost 0 7.422 * * [simplify]: Extracting # 6 : cost 0 7.429 * * [simplify]: iteration 2 : 3493 enodes (cost 1533 ) 8.676 * * [simplify]: Extracting # 0 : cost 0 8.683 * * [simplify]: Extracting # 1 : cost 0 8.690 * * [simplify]: Extracting # 2 : cost 0 8.697 * * [simplify]: iteration done: 5000 enodes (cost 1531 ) 8.698 * [simplify]: Simplified to: (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* 2.0 (* n PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* PI (* 2.0 n)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* PI (* 2.0 n)) (* PI (* 2.0 n)) (pow (* PI (* 2.0 n)) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* PI (* 2.0 n)) (* PI (* 2.0 n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (pow n 3) (pow 2.0 3)) (pow PI 3)) (pow (* PI (* 2.0 n)) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* PI (* 2.0 n)) 3) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* n PI) (log (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (log (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (log (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (log (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (log (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (log (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (log (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (exp (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (/ (/ (pow (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) k) (sqrt k)) (/ (/ (pow (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 3) k) (sqrt k)) (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (pow (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) 3) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (- (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (- (sqrt k)) (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k))) (/ 1.0 (fabs (cbrt k))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))) (/ 1.0 (sqrt (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) 1.0 (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (/ 1.0 (sqrt (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) 1.0 (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k)) (/ 1 (sqrt k)) (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (fabs (cbrt k))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (+ (* (* 0.125 (pow k 2)) (+ (* (pow (* (* 2.0 PI) n) 0.5) (pow (log (* 2.0 PI)) 2)) (* (pow (* (* 2.0 PI) n) 0.5) (pow (log n) 2)))) (- (+ (* (* (pow k 2) (* (pow (* (* 2.0 PI) n) 0.5) (* (log (* 2.0 PI)) (log n)))) 0.25) (pow (* (* 2.0 PI) n) 0.5)) (* 0.5 (* k (+ (* (pow (* (* 2.0 PI) n) 0.5) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log n))))))) (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* PI (* 2.0 n)) (* PI (* 2.0 n)) (* PI (* 2.0 n)) (+ (+ (- (* (* (* +nan.0 (pow k 2)) (log n)) (pow (* (* 2.0 PI) n) 0.5)) (* (* (pow k 2) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) +nan.0))) (- (* (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (* k +nan.0)) (+ (- (* (* (pow (* (* 2.0 PI) n) 0.5) (pow (log (* 2.0 PI)) 2)) (* +nan.0 (pow k 2))) (* (pow (* (* 2.0 PI) n) 0.5) (* +nan.0 k))) (+ (- (* (* (* (* +nan.0 (pow k 2)) (log n)) (pow (* (* 2.0 PI) n) 0.5)) (log (* 2.0 PI))) (* +nan.0 (* (pow (* (* 2.0 PI) n) 0.5) (* k (log (* 2.0 PI)))))) (* +nan.0 (- (* (pow (* (* 2.0 PI) n) 0.5) (* (pow (log n) 2) (pow k 2))) (pow (* (* 2.0 PI) n) 0.5))))))) (* (* +nan.0 (pow k 2)) (- (pow (* (* 2.0 PI) n) 0.5)))) (+ (* (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (pow k 3)) (- +nan.0)) (* +nan.0 (- (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) k) (/ (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (pow k 2))))) (+ (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k))) (* +nan.0 (- (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))) 8.698 * * * [progress]: adding candidates to table 9.075 * * [progress]: iteration 3 / 4 9.075 * * * [progress]: picking best candidate 9.118 * * * * [pick]: Picked # 9.118 * * * [progress]: localizing error 9.155 * * * [progress]: generating rewritten candidates 9.156 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 2 2) 9.210 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 1) 9.253 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 2) 9.327 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 2 2 1) 9.361 * * * [progress]: generating series expansions 9.361 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 2 2) 9.362 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 9.362 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 9.362 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 9.362 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 9.362 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 9.362 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 9.362 * [taylor]: Taking taylor expansion of 0.25 in k 9.362 * [backup-simplify]: Simplify 0.25 into 0.25 9.362 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.362 * [taylor]: Taking taylor expansion of 1.0 in k 9.362 * [backup-simplify]: Simplify 1.0 into 1.0 9.362 * [taylor]: Taking taylor expansion of k in k 9.362 * [backup-simplify]: Simplify 0 into 0 9.362 * [backup-simplify]: Simplify 1 into 1 9.362 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 9.362 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 9.362 * [taylor]: Taking taylor expansion of 2.0 in k 9.362 * [backup-simplify]: Simplify 2.0 into 2.0 9.362 * [taylor]: Taking taylor expansion of (* n PI) in k 9.362 * [taylor]: Taking taylor expansion of n in k 9.362 * [backup-simplify]: Simplify n into n 9.362 * [taylor]: Taking taylor expansion of PI in k 9.362 * [backup-simplify]: Simplify PI into PI 9.362 * [backup-simplify]: Simplify (* n PI) into (* n PI) 9.362 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 9.362 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 9.363 * [backup-simplify]: Simplify (- 0) into 0 9.363 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.363 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 9.364 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 9.364 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 9.364 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 9.364 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.364 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.364 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 9.364 * [taylor]: Taking taylor expansion of 0.25 in n 9.364 * [backup-simplify]: Simplify 0.25 into 0.25 9.364 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.364 * [taylor]: Taking taylor expansion of 1.0 in n 9.364 * [backup-simplify]: Simplify 1.0 into 1.0 9.364 * [taylor]: Taking taylor expansion of k in n 9.364 * [backup-simplify]: Simplify k into k 9.364 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.364 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.364 * [taylor]: Taking taylor expansion of 2.0 in n 9.364 * [backup-simplify]: Simplify 2.0 into 2.0 9.364 * [taylor]: Taking taylor expansion of (* n PI) in n 9.364 * [taylor]: Taking taylor expansion of n in n 9.364 * [backup-simplify]: Simplify 0 into 0 9.364 * [backup-simplify]: Simplify 1 into 1 9.364 * [taylor]: Taking taylor expansion of PI in n 9.364 * [backup-simplify]: Simplify PI into PI 9.364 * [backup-simplify]: Simplify (* 0 PI) into 0 9.365 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.366 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.367 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.367 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.367 * [backup-simplify]: Simplify (- k) into (- k) 9.367 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.367 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 9.368 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.369 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 9.370 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 9.370 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 9.370 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.370 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.370 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 9.370 * [taylor]: Taking taylor expansion of 0.25 in n 9.370 * [backup-simplify]: Simplify 0.25 into 0.25 9.370 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.370 * [taylor]: Taking taylor expansion of 1.0 in n 9.370 * [backup-simplify]: Simplify 1.0 into 1.0 9.370 * [taylor]: Taking taylor expansion of k in n 9.370 * [backup-simplify]: Simplify k into k 9.370 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.370 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.370 * [taylor]: Taking taylor expansion of 2.0 in n 9.370 * [backup-simplify]: Simplify 2.0 into 2.0 9.370 * [taylor]: Taking taylor expansion of (* n PI) in n 9.370 * [taylor]: Taking taylor expansion of n in n 9.370 * [backup-simplify]: Simplify 0 into 0 9.370 * [backup-simplify]: Simplify 1 into 1 9.370 * [taylor]: Taking taylor expansion of PI in n 9.370 * [backup-simplify]: Simplify PI into PI 9.370 * [backup-simplify]: Simplify (* 0 PI) into 0 9.371 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.372 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.373 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.373 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.373 * [backup-simplify]: Simplify (- k) into (- k) 9.373 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.373 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 9.374 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.375 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 9.376 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 9.376 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 9.376 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 9.376 * [taylor]: Taking taylor expansion of 0.25 in k 9.377 * [backup-simplify]: Simplify 0.25 into 0.25 9.377 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 9.377 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.377 * [taylor]: Taking taylor expansion of 1.0 in k 9.377 * [backup-simplify]: Simplify 1.0 into 1.0 9.377 * [taylor]: Taking taylor expansion of k in k 9.377 * [backup-simplify]: Simplify 0 into 0 9.377 * [backup-simplify]: Simplify 1 into 1 9.377 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 9.377 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.377 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.377 * [taylor]: Taking taylor expansion of 2.0 in k 9.377 * [backup-simplify]: Simplify 2.0 into 2.0 9.377 * [taylor]: Taking taylor expansion of PI in k 9.377 * [backup-simplify]: Simplify PI into PI 9.377 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.379 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.379 * [taylor]: Taking taylor expansion of (log n) in k 9.379 * [taylor]: Taking taylor expansion of n in k 9.379 * [backup-simplify]: Simplify n into n 9.379 * [backup-simplify]: Simplify (log n) into (log n) 9.380 * [backup-simplify]: Simplify (- 0) into 0 9.380 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.380 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 9.381 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 9.382 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 9.383 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 9.383 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 9.384 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.385 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.386 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.386 * [backup-simplify]: Simplify (- 0) into 0 9.386 * [backup-simplify]: Simplify (+ 0 0) into 0 9.386 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 9.387 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.388 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 9.389 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.389 * [taylor]: Taking taylor expansion of 0 in k 9.389 * [backup-simplify]: Simplify 0 into 0 9.389 * [backup-simplify]: Simplify 0 into 0 9.390 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.391 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.391 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 9.392 * [backup-simplify]: Simplify (+ 0 0) into 0 9.392 * [backup-simplify]: Simplify (- 1) into -1 9.392 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.393 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 9.394 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 9.397 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 9.399 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 9.399 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.400 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.402 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 9.402 * [backup-simplify]: Simplify (- 0) into 0 9.402 * [backup-simplify]: Simplify (+ 0 0) into 0 9.403 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 9.404 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.405 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.406 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.406 * [taylor]: Taking taylor expansion of 0 in k 9.406 * [backup-simplify]: Simplify 0 into 0 9.406 * [backup-simplify]: Simplify 0 into 0 9.406 * [backup-simplify]: Simplify 0 into 0 9.407 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.409 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 9.410 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 9.410 * [backup-simplify]: Simplify (+ 0 0) into 0 9.410 * [backup-simplify]: Simplify (- 0) into 0 9.411 * [backup-simplify]: Simplify (+ 0 0) into 0 9.412 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.415 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 9.419 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 9.434 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 9.445 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 9.446 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 9.446 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 9.446 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 9.446 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 9.446 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 9.446 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 9.446 * [taylor]: Taking taylor expansion of 0.25 in k 9.446 * [backup-simplify]: Simplify 0.25 into 0.25 9.446 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.446 * [taylor]: Taking taylor expansion of 1.0 in k 9.446 * [backup-simplify]: Simplify 1.0 into 1.0 9.446 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.446 * [taylor]: Taking taylor expansion of k in k 9.446 * [backup-simplify]: Simplify 0 into 0 9.446 * [backup-simplify]: Simplify 1 into 1 9.447 * [backup-simplify]: Simplify (/ 1 1) into 1 9.447 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 9.447 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 9.447 * [taylor]: Taking taylor expansion of 2.0 in k 9.447 * [backup-simplify]: Simplify 2.0 into 2.0 9.447 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.447 * [taylor]: Taking taylor expansion of PI in k 9.447 * [backup-simplify]: Simplify PI into PI 9.447 * [taylor]: Taking taylor expansion of n in k 9.447 * [backup-simplify]: Simplify n into n 9.447 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.447 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 9.447 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 9.448 * [backup-simplify]: Simplify (- 1) into -1 9.448 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.449 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 9.449 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 9.449 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 9.449 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.449 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.449 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.449 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.449 * [taylor]: Taking taylor expansion of 0.25 in n 9.449 * [backup-simplify]: Simplify 0.25 into 0.25 9.449 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.449 * [taylor]: Taking taylor expansion of 1.0 in n 9.449 * [backup-simplify]: Simplify 1.0 into 1.0 9.449 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.449 * [taylor]: Taking taylor expansion of k in n 9.449 * [backup-simplify]: Simplify k into k 9.449 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.450 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.450 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.450 * [taylor]: Taking taylor expansion of 2.0 in n 9.450 * [backup-simplify]: Simplify 2.0 into 2.0 9.450 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.450 * [taylor]: Taking taylor expansion of PI in n 9.450 * [backup-simplify]: Simplify PI into PI 9.450 * [taylor]: Taking taylor expansion of n in n 9.450 * [backup-simplify]: Simplify 0 into 0 9.450 * [backup-simplify]: Simplify 1 into 1 9.450 * [backup-simplify]: Simplify (/ PI 1) into PI 9.451 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.452 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.452 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.452 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.452 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.454 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.455 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 9.456 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 9.456 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.456 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.456 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.456 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.456 * [taylor]: Taking taylor expansion of 0.25 in n 9.456 * [backup-simplify]: Simplify 0.25 into 0.25 9.456 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.457 * [taylor]: Taking taylor expansion of 1.0 in n 9.457 * [backup-simplify]: Simplify 1.0 into 1.0 9.457 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.457 * [taylor]: Taking taylor expansion of k in n 9.457 * [backup-simplify]: Simplify k into k 9.457 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.457 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.457 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.457 * [taylor]: Taking taylor expansion of 2.0 in n 9.457 * [backup-simplify]: Simplify 2.0 into 2.0 9.457 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.457 * [taylor]: Taking taylor expansion of PI in n 9.457 * [backup-simplify]: Simplify PI into PI 9.457 * [taylor]: Taking taylor expansion of n in n 9.457 * [backup-simplify]: Simplify 0 into 0 9.457 * [backup-simplify]: Simplify 1 into 1 9.457 * [backup-simplify]: Simplify (/ PI 1) into PI 9.458 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.459 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.459 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.459 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.459 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.461 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.462 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 9.463 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 9.463 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 9.464 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 9.464 * [taylor]: Taking taylor expansion of 0.25 in k 9.464 * [backup-simplify]: Simplify 0.25 into 0.25 9.464 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 9.464 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 9.464 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.464 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.464 * [taylor]: Taking taylor expansion of 2.0 in k 9.464 * [backup-simplify]: Simplify 2.0 into 2.0 9.464 * [taylor]: Taking taylor expansion of PI in k 9.464 * [backup-simplify]: Simplify PI into PI 9.464 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.466 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.466 * [taylor]: Taking taylor expansion of (log n) in k 9.466 * [taylor]: Taking taylor expansion of n in k 9.466 * [backup-simplify]: Simplify n into n 9.466 * [backup-simplify]: Simplify (log n) into (log n) 9.466 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.466 * [taylor]: Taking taylor expansion of 1.0 in k 9.466 * [backup-simplify]: Simplify 1.0 into 1.0 9.466 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.466 * [taylor]: Taking taylor expansion of k in k 9.466 * [backup-simplify]: Simplify 0 into 0 9.466 * [backup-simplify]: Simplify 1 into 1 9.466 * [backup-simplify]: Simplify (/ 1 1) into 1 9.466 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.468 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 9.468 * [backup-simplify]: Simplify (- 1) into -1 9.469 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.470 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 9.471 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 9.472 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 9.473 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 9.474 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.475 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.477 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.477 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.478 * [backup-simplify]: Simplify (- 0) into 0 9.478 * [backup-simplify]: Simplify (+ 0 0) into 0 9.479 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 9.480 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.481 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 9.483 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.483 * [taylor]: Taking taylor expansion of 0 in k 9.483 * [backup-simplify]: Simplify 0 into 0 9.483 * [backup-simplify]: Simplify 0 into 0 9.483 * [backup-simplify]: Simplify 0 into 0 9.485 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.486 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.489 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 9.490 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.490 * [backup-simplify]: Simplify (- 0) into 0 9.490 * [backup-simplify]: Simplify (+ 0 0) into 0 9.492 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 9.493 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.495 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 9.498 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.498 * [taylor]: Taking taylor expansion of 0 in k 9.498 * [backup-simplify]: Simplify 0 into 0 9.498 * [backup-simplify]: Simplify 0 into 0 9.498 * [backup-simplify]: Simplify 0 into 0 9.498 * [backup-simplify]: Simplify 0 into 0 9.499 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.500 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.507 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 9.507 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.508 * [backup-simplify]: Simplify (- 0) into 0 9.508 * [backup-simplify]: Simplify (+ 0 0) into 0 9.509 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 9.511 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.513 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 9.516 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 9.516 * [taylor]: Taking taylor expansion of 0 in k 9.516 * [backup-simplify]: Simplify 0 into 0 9.516 * [backup-simplify]: Simplify 0 into 0 9.517 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 9.518 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 9.518 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 9.518 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 9.518 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 9.518 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 9.518 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 9.518 * [taylor]: Taking taylor expansion of 0.25 in k 9.518 * [backup-simplify]: Simplify 0.25 into 0.25 9.518 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.518 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.518 * [taylor]: Taking taylor expansion of k in k 9.518 * [backup-simplify]: Simplify 0 into 0 9.518 * [backup-simplify]: Simplify 1 into 1 9.519 * [backup-simplify]: Simplify (/ 1 1) into 1 9.519 * [taylor]: Taking taylor expansion of 1.0 in k 9.519 * [backup-simplify]: Simplify 1.0 into 1.0 9.519 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 9.519 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 9.519 * [taylor]: Taking taylor expansion of -2.0 in k 9.519 * [backup-simplify]: Simplify -2.0 into -2.0 9.519 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.519 * [taylor]: Taking taylor expansion of PI in k 9.519 * [backup-simplify]: Simplify PI into PI 9.519 * [taylor]: Taking taylor expansion of n in k 9.519 * [backup-simplify]: Simplify n into n 9.519 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.519 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 9.520 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 9.520 * [backup-simplify]: Simplify (+ 1 0) into 1 9.520 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 9.521 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 9.521 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 9.521 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.521 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.521 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.521 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.521 * [taylor]: Taking taylor expansion of 0.25 in n 9.521 * [backup-simplify]: Simplify 0.25 into 0.25 9.521 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.521 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.521 * [taylor]: Taking taylor expansion of k in n 9.521 * [backup-simplify]: Simplify k into k 9.521 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.521 * [taylor]: Taking taylor expansion of 1.0 in n 9.521 * [backup-simplify]: Simplify 1.0 into 1.0 9.521 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.521 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.521 * [taylor]: Taking taylor expansion of -2.0 in n 9.521 * [backup-simplify]: Simplify -2.0 into -2.0 9.521 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.521 * [taylor]: Taking taylor expansion of PI in n 9.521 * [backup-simplify]: Simplify PI into PI 9.521 * [taylor]: Taking taylor expansion of n in n 9.521 * [backup-simplify]: Simplify 0 into 0 9.521 * [backup-simplify]: Simplify 1 into 1 9.522 * [backup-simplify]: Simplify (/ PI 1) into PI 9.522 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.523 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.523 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.524 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.525 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.526 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 9.527 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 9.527 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.527 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.528 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.528 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.528 * [taylor]: Taking taylor expansion of 0.25 in n 9.528 * [backup-simplify]: Simplify 0.25 into 0.25 9.528 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.528 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.528 * [taylor]: Taking taylor expansion of k in n 9.528 * [backup-simplify]: Simplify k into k 9.528 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.528 * [taylor]: Taking taylor expansion of 1.0 in n 9.528 * [backup-simplify]: Simplify 1.0 into 1.0 9.528 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.528 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.528 * [taylor]: Taking taylor expansion of -2.0 in n 9.528 * [backup-simplify]: Simplify -2.0 into -2.0 9.528 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.528 * [taylor]: Taking taylor expansion of PI in n 9.528 * [backup-simplify]: Simplify PI into PI 9.528 * [taylor]: Taking taylor expansion of n in n 9.528 * [backup-simplify]: Simplify 0 into 0 9.528 * [backup-simplify]: Simplify 1 into 1 9.529 * [backup-simplify]: Simplify (/ PI 1) into PI 9.529 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.530 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.530 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.530 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.532 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.533 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 9.534 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 9.535 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 9.535 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 9.535 * [taylor]: Taking taylor expansion of 0.25 in k 9.535 * [backup-simplify]: Simplify 0.25 into 0.25 9.535 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 9.535 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.535 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.535 * [taylor]: Taking taylor expansion of k in k 9.535 * [backup-simplify]: Simplify 0 into 0 9.535 * [backup-simplify]: Simplify 1 into 1 9.535 * [backup-simplify]: Simplify (/ 1 1) into 1 9.535 * [taylor]: Taking taylor expansion of 1.0 in k 9.535 * [backup-simplify]: Simplify 1.0 into 1.0 9.535 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 9.535 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 9.535 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 9.535 * [taylor]: Taking taylor expansion of -2.0 in k 9.535 * [backup-simplify]: Simplify -2.0 into -2.0 9.535 * [taylor]: Taking taylor expansion of PI in k 9.536 * [backup-simplify]: Simplify PI into PI 9.536 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.537 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.537 * [taylor]: Taking taylor expansion of (log n) in k 9.537 * [taylor]: Taking taylor expansion of n in k 9.537 * [backup-simplify]: Simplify n into n 9.537 * [backup-simplify]: Simplify (log n) into (log n) 9.538 * [backup-simplify]: Simplify (+ 1 0) into 1 9.538 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.539 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 9.540 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 9.541 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 9.543 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 9.544 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 9.545 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.546 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.547 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 9.548 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.548 * [backup-simplify]: Simplify (+ 0 0) into 0 9.549 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 9.550 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.551 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 9.553 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.554 * [taylor]: Taking taylor expansion of 0 in k 9.554 * [backup-simplify]: Simplify 0 into 0 9.554 * [backup-simplify]: Simplify 0 into 0 9.554 * [backup-simplify]: Simplify 0 into 0 9.555 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.556 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.560 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 9.560 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.560 * [backup-simplify]: Simplify (+ 0 0) into 0 9.561 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 9.563 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.565 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 9.567 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.567 * [taylor]: Taking taylor expansion of 0 in k 9.567 * [backup-simplify]: Simplify 0 into 0 9.567 * [backup-simplify]: Simplify 0 into 0 9.567 * [backup-simplify]: Simplify 0 into 0 9.568 * [backup-simplify]: Simplify 0 into 0 9.569 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.570 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.576 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 9.576 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.577 * [backup-simplify]: Simplify (+ 0 0) into 0 9.578 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 9.580 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.582 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 9.592 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 9.592 * [taylor]: Taking taylor expansion of 0 in k 9.593 * [backup-simplify]: Simplify 0 into 0 9.593 * [backup-simplify]: Simplify 0 into 0 9.594 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 9.594 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 1) 9.595 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 9.595 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 9.595 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 9.595 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 9.595 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 9.595 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 9.595 * [taylor]: Taking taylor expansion of 0.25 in k 9.595 * [backup-simplify]: Simplify 0.25 into 0.25 9.596 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.596 * [taylor]: Taking taylor expansion of 1.0 in k 9.596 * [backup-simplify]: Simplify 1.0 into 1.0 9.596 * [taylor]: Taking taylor expansion of k in k 9.596 * [backup-simplify]: Simplify 0 into 0 9.596 * [backup-simplify]: Simplify 1 into 1 9.596 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 9.596 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 9.596 * [taylor]: Taking taylor expansion of 2.0 in k 9.596 * [backup-simplify]: Simplify 2.0 into 2.0 9.596 * [taylor]: Taking taylor expansion of (* n PI) in k 9.596 * [taylor]: Taking taylor expansion of n in k 9.596 * [backup-simplify]: Simplify n into n 9.596 * [taylor]: Taking taylor expansion of PI in k 9.596 * [backup-simplify]: Simplify PI into PI 9.596 * [backup-simplify]: Simplify (* n PI) into (* n PI) 9.596 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 9.596 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 9.597 * [backup-simplify]: Simplify (- 0) into 0 9.597 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.597 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 9.598 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 9.598 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 9.598 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 9.598 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.598 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.598 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 9.598 * [taylor]: Taking taylor expansion of 0.25 in n 9.598 * [backup-simplify]: Simplify 0.25 into 0.25 9.598 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.598 * [taylor]: Taking taylor expansion of 1.0 in n 9.598 * [backup-simplify]: Simplify 1.0 into 1.0 9.598 * [taylor]: Taking taylor expansion of k in n 9.598 * [backup-simplify]: Simplify k into k 9.598 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.598 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.598 * [taylor]: Taking taylor expansion of 2.0 in n 9.598 * [backup-simplify]: Simplify 2.0 into 2.0 9.598 * [taylor]: Taking taylor expansion of (* n PI) in n 9.598 * [taylor]: Taking taylor expansion of n in n 9.598 * [backup-simplify]: Simplify 0 into 0 9.598 * [backup-simplify]: Simplify 1 into 1 9.598 * [taylor]: Taking taylor expansion of PI in n 9.598 * [backup-simplify]: Simplify PI into PI 9.599 * [backup-simplify]: Simplify (* 0 PI) into 0 9.599 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.601 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.602 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.603 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.603 * [backup-simplify]: Simplify (- k) into (- k) 9.603 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.603 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 9.605 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.606 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 9.607 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 9.607 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 9.608 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.608 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.608 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 9.608 * [taylor]: Taking taylor expansion of 0.25 in n 9.608 * [backup-simplify]: Simplify 0.25 into 0.25 9.608 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.608 * [taylor]: Taking taylor expansion of 1.0 in n 9.608 * [backup-simplify]: Simplify 1.0 into 1.0 9.608 * [taylor]: Taking taylor expansion of k in n 9.608 * [backup-simplify]: Simplify k into k 9.608 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.608 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.608 * [taylor]: Taking taylor expansion of 2.0 in n 9.608 * [backup-simplify]: Simplify 2.0 into 2.0 9.608 * [taylor]: Taking taylor expansion of (* n PI) in n 9.608 * [taylor]: Taking taylor expansion of n in n 9.608 * [backup-simplify]: Simplify 0 into 0 9.608 * [backup-simplify]: Simplify 1 into 1 9.608 * [taylor]: Taking taylor expansion of PI in n 9.608 * [backup-simplify]: Simplify PI into PI 9.608 * [backup-simplify]: Simplify (* 0 PI) into 0 9.609 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.610 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.612 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.613 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.613 * [backup-simplify]: Simplify (- k) into (- k) 9.613 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.613 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 9.614 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.615 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 9.617 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 9.617 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 9.617 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 9.617 * [taylor]: Taking taylor expansion of 0.25 in k 9.617 * [backup-simplify]: Simplify 0.25 into 0.25 9.617 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 9.617 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.617 * [taylor]: Taking taylor expansion of 1.0 in k 9.617 * [backup-simplify]: Simplify 1.0 into 1.0 9.617 * [taylor]: Taking taylor expansion of k in k 9.617 * [backup-simplify]: Simplify 0 into 0 9.617 * [backup-simplify]: Simplify 1 into 1 9.617 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 9.617 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.617 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.617 * [taylor]: Taking taylor expansion of 2.0 in k 9.617 * [backup-simplify]: Simplify 2.0 into 2.0 9.617 * [taylor]: Taking taylor expansion of PI in k 9.617 * [backup-simplify]: Simplify PI into PI 9.618 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.619 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.619 * [taylor]: Taking taylor expansion of (log n) in k 9.619 * [taylor]: Taking taylor expansion of n in k 9.619 * [backup-simplify]: Simplify n into n 9.619 * [backup-simplify]: Simplify (log n) into (log n) 9.619 * [backup-simplify]: Simplify (- 0) into 0 9.620 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.621 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 9.622 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 9.623 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 9.624 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 9.625 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 9.626 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.627 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.629 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.629 * [backup-simplify]: Simplify (- 0) into 0 9.630 * [backup-simplify]: Simplify (+ 0 0) into 0 9.630 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 9.632 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.633 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 9.635 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.635 * [taylor]: Taking taylor expansion of 0 in k 9.635 * [backup-simplify]: Simplify 0 into 0 9.635 * [backup-simplify]: Simplify 0 into 0 9.637 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.639 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.640 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 9.640 * [backup-simplify]: Simplify (+ 0 0) into 0 9.641 * [backup-simplify]: Simplify (- 1) into -1 9.641 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.643 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 9.645 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 9.649 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 9.652 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 9.653 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.654 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.658 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 9.658 * [backup-simplify]: Simplify (- 0) into 0 9.659 * [backup-simplify]: Simplify (+ 0 0) into 0 9.660 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 9.661 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.663 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.666 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.666 * [taylor]: Taking taylor expansion of 0 in k 9.666 * [backup-simplify]: Simplify 0 into 0 9.666 * [backup-simplify]: Simplify 0 into 0 9.666 * [backup-simplify]: Simplify 0 into 0 9.667 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.670 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 9.672 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 9.673 * [backup-simplify]: Simplify (+ 0 0) into 0 9.673 * [backup-simplify]: Simplify (- 0) into 0 9.673 * [backup-simplify]: Simplify (+ 0 0) into 0 9.675 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.678 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 9.681 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 9.684 * [backup-simplify]: Simplify (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 9.690 * [backup-simplify]: Simplify (+ (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 9.691 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 9.691 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 9.691 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 9.691 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 9.691 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 9.691 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 9.691 * [taylor]: Taking taylor expansion of 0.25 in k 9.691 * [backup-simplify]: Simplify 0.25 into 0.25 9.691 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.691 * [taylor]: Taking taylor expansion of 1.0 in k 9.691 * [backup-simplify]: Simplify 1.0 into 1.0 9.691 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.691 * [taylor]: Taking taylor expansion of k in k 9.691 * [backup-simplify]: Simplify 0 into 0 9.691 * [backup-simplify]: Simplify 1 into 1 9.691 * [backup-simplify]: Simplify (/ 1 1) into 1 9.691 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 9.691 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 9.691 * [taylor]: Taking taylor expansion of 2.0 in k 9.691 * [backup-simplify]: Simplify 2.0 into 2.0 9.692 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.692 * [taylor]: Taking taylor expansion of PI in k 9.692 * [backup-simplify]: Simplify PI into PI 9.692 * [taylor]: Taking taylor expansion of n in k 9.692 * [backup-simplify]: Simplify n into n 9.692 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.692 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 9.692 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 9.692 * [backup-simplify]: Simplify (- 1) into -1 9.692 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.693 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 9.693 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 9.693 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 9.693 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.693 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.693 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.693 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.693 * [taylor]: Taking taylor expansion of 0.25 in n 9.693 * [backup-simplify]: Simplify 0.25 into 0.25 9.693 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.693 * [taylor]: Taking taylor expansion of 1.0 in n 9.693 * [backup-simplify]: Simplify 1.0 into 1.0 9.693 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.693 * [taylor]: Taking taylor expansion of k in n 9.693 * [backup-simplify]: Simplify k into k 9.693 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.693 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.693 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.693 * [taylor]: Taking taylor expansion of 2.0 in n 9.693 * [backup-simplify]: Simplify 2.0 into 2.0 9.693 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.693 * [taylor]: Taking taylor expansion of PI in n 9.693 * [backup-simplify]: Simplify PI into PI 9.693 * [taylor]: Taking taylor expansion of n in n 9.693 * [backup-simplify]: Simplify 0 into 0 9.693 * [backup-simplify]: Simplify 1 into 1 9.693 * [backup-simplify]: Simplify (/ PI 1) into PI 9.694 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.694 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.694 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.695 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.695 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.695 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.696 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 9.697 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 9.697 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.697 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.697 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.697 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.697 * [taylor]: Taking taylor expansion of 0.25 in n 9.697 * [backup-simplify]: Simplify 0.25 into 0.25 9.697 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.697 * [taylor]: Taking taylor expansion of 1.0 in n 9.697 * [backup-simplify]: Simplify 1.0 into 1.0 9.697 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.697 * [taylor]: Taking taylor expansion of k in n 9.697 * [backup-simplify]: Simplify k into k 9.697 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.697 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.697 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.697 * [taylor]: Taking taylor expansion of 2.0 in n 9.697 * [backup-simplify]: Simplify 2.0 into 2.0 9.697 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.697 * [taylor]: Taking taylor expansion of PI in n 9.697 * [backup-simplify]: Simplify PI into PI 9.697 * [taylor]: Taking taylor expansion of n in n 9.697 * [backup-simplify]: Simplify 0 into 0 9.697 * [backup-simplify]: Simplify 1 into 1 9.698 * [backup-simplify]: Simplify (/ PI 1) into PI 9.698 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.699 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.699 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.699 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.699 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.700 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.701 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 9.701 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 9.701 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 9.701 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 9.701 * [taylor]: Taking taylor expansion of 0.25 in k 9.702 * [backup-simplify]: Simplify 0.25 into 0.25 9.702 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 9.702 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 9.702 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.702 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.702 * [taylor]: Taking taylor expansion of 2.0 in k 9.702 * [backup-simplify]: Simplify 2.0 into 2.0 9.702 * [taylor]: Taking taylor expansion of PI in k 9.702 * [backup-simplify]: Simplify PI into PI 9.702 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.703 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.703 * [taylor]: Taking taylor expansion of (log n) in k 9.703 * [taylor]: Taking taylor expansion of n in k 9.703 * [backup-simplify]: Simplify n into n 9.703 * [backup-simplify]: Simplify (log n) into (log n) 9.703 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.703 * [taylor]: Taking taylor expansion of 1.0 in k 9.703 * [backup-simplify]: Simplify 1.0 into 1.0 9.703 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.703 * [taylor]: Taking taylor expansion of k in k 9.703 * [backup-simplify]: Simplify 0 into 0 9.703 * [backup-simplify]: Simplify 1 into 1 9.703 * [backup-simplify]: Simplify (/ 1 1) into 1 9.703 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.704 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 9.704 * [backup-simplify]: Simplify (- 1) into -1 9.705 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.706 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 9.707 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 9.708 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 9.710 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 9.711 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.712 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.714 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.714 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.714 * [backup-simplify]: Simplify (- 0) into 0 9.715 * [backup-simplify]: Simplify (+ 0 0) into 0 9.715 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 9.717 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.718 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 9.720 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.720 * [taylor]: Taking taylor expansion of 0 in k 9.720 * [backup-simplify]: Simplify 0 into 0 9.720 * [backup-simplify]: Simplify 0 into 0 9.720 * [backup-simplify]: Simplify 0 into 0 9.721 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.722 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.726 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 9.726 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.727 * [backup-simplify]: Simplify (- 0) into 0 9.727 * [backup-simplify]: Simplify (+ 0 0) into 0 9.737 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 9.739 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.740 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 9.743 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.743 * [taylor]: Taking taylor expansion of 0 in k 9.743 * [backup-simplify]: Simplify 0 into 0 9.743 * [backup-simplify]: Simplify 0 into 0 9.743 * [backup-simplify]: Simplify 0 into 0 9.743 * [backup-simplify]: Simplify 0 into 0 9.744 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.745 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.752 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 9.752 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.752 * [backup-simplify]: Simplify (- 0) into 0 9.753 * [backup-simplify]: Simplify (+ 0 0) into 0 9.754 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 9.756 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.758 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 9.760 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 9.760 * [taylor]: Taking taylor expansion of 0 in k 9.760 * [backup-simplify]: Simplify 0 into 0 9.760 * [backup-simplify]: Simplify 0 into 0 9.761 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 9.762 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 9.762 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 9.762 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 9.762 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 9.762 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 9.762 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 9.762 * [taylor]: Taking taylor expansion of 0.25 in k 9.762 * [backup-simplify]: Simplify 0.25 into 0.25 9.762 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.762 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.762 * [taylor]: Taking taylor expansion of k in k 9.762 * [backup-simplify]: Simplify 0 into 0 9.762 * [backup-simplify]: Simplify 1 into 1 9.762 * [backup-simplify]: Simplify (/ 1 1) into 1 9.762 * [taylor]: Taking taylor expansion of 1.0 in k 9.762 * [backup-simplify]: Simplify 1.0 into 1.0 9.762 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 9.762 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 9.762 * [taylor]: Taking taylor expansion of -2.0 in k 9.762 * [backup-simplify]: Simplify -2.0 into -2.0 9.762 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.762 * [taylor]: Taking taylor expansion of PI in k 9.762 * [backup-simplify]: Simplify PI into PI 9.762 * [taylor]: Taking taylor expansion of n in k 9.762 * [backup-simplify]: Simplify n into n 9.762 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.763 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 9.763 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 9.763 * [backup-simplify]: Simplify (+ 1 0) into 1 9.763 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 9.763 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 9.763 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 9.763 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.763 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.763 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.763 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.763 * [taylor]: Taking taylor expansion of 0.25 in n 9.763 * [backup-simplify]: Simplify 0.25 into 0.25 9.764 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.764 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.764 * [taylor]: Taking taylor expansion of k in n 9.764 * [backup-simplify]: Simplify k into k 9.764 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.764 * [taylor]: Taking taylor expansion of 1.0 in n 9.764 * [backup-simplify]: Simplify 1.0 into 1.0 9.764 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.764 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.764 * [taylor]: Taking taylor expansion of -2.0 in n 9.764 * [backup-simplify]: Simplify -2.0 into -2.0 9.764 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.764 * [taylor]: Taking taylor expansion of PI in n 9.764 * [backup-simplify]: Simplify PI into PI 9.764 * [taylor]: Taking taylor expansion of n in n 9.764 * [backup-simplify]: Simplify 0 into 0 9.764 * [backup-simplify]: Simplify 1 into 1 9.764 * [backup-simplify]: Simplify (/ PI 1) into PI 9.764 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.765 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.765 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.765 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.766 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.767 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 9.768 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 9.768 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 9.768 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 9.768 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 9.768 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 9.768 * [taylor]: Taking taylor expansion of 0.25 in n 9.768 * [backup-simplify]: Simplify 0.25 into 0.25 9.768 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 9.768 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.768 * [taylor]: Taking taylor expansion of k in n 9.768 * [backup-simplify]: Simplify k into k 9.768 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.768 * [taylor]: Taking taylor expansion of 1.0 in n 9.768 * [backup-simplify]: Simplify 1.0 into 1.0 9.768 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 9.768 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 9.768 * [taylor]: Taking taylor expansion of -2.0 in n 9.768 * [backup-simplify]: Simplify -2.0 into -2.0 9.768 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.768 * [taylor]: Taking taylor expansion of PI in n 9.768 * [backup-simplify]: Simplify PI into PI 9.768 * [taylor]: Taking taylor expansion of n in n 9.768 * [backup-simplify]: Simplify 0 into 0 9.768 * [backup-simplify]: Simplify 1 into 1 9.768 * [backup-simplify]: Simplify (/ PI 1) into PI 9.769 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.769 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.769 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 9.769 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 9.770 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.771 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 9.772 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 9.772 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 9.772 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 9.772 * [taylor]: Taking taylor expansion of 0.25 in k 9.772 * [backup-simplify]: Simplify 0.25 into 0.25 9.772 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 9.772 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 9.772 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.772 * [taylor]: Taking taylor expansion of k in k 9.772 * [backup-simplify]: Simplify 0 into 0 9.772 * [backup-simplify]: Simplify 1 into 1 9.772 * [backup-simplify]: Simplify (/ 1 1) into 1 9.772 * [taylor]: Taking taylor expansion of 1.0 in k 9.772 * [backup-simplify]: Simplify 1.0 into 1.0 9.772 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 9.772 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 9.772 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 9.772 * [taylor]: Taking taylor expansion of -2.0 in k 9.772 * [backup-simplify]: Simplify -2.0 into -2.0 9.772 * [taylor]: Taking taylor expansion of PI in k 9.772 * [backup-simplify]: Simplify PI into PI 9.773 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 9.773 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 9.773 * [taylor]: Taking taylor expansion of (log n) in k 9.773 * [taylor]: Taking taylor expansion of n in k 9.773 * [backup-simplify]: Simplify n into n 9.773 * [backup-simplify]: Simplify (log n) into (log n) 9.774 * [backup-simplify]: Simplify (+ 1 0) into 1 9.774 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.774 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 9.775 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 9.776 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 9.777 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 9.777 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 9.778 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.778 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 9.779 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 9.780 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.780 * [backup-simplify]: Simplify (+ 0 0) into 0 9.780 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 9.781 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.782 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 9.783 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.783 * [taylor]: Taking taylor expansion of 0 in k 9.783 * [backup-simplify]: Simplify 0 into 0 9.783 * [backup-simplify]: Simplify 0 into 0 9.783 * [backup-simplify]: Simplify 0 into 0 9.784 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.784 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.786 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 9.786 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.786 * [backup-simplify]: Simplify (+ 0 0) into 0 9.787 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 9.788 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.789 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 9.790 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.790 * [taylor]: Taking taylor expansion of 0 in k 9.790 * [backup-simplify]: Simplify 0 into 0 9.790 * [backup-simplify]: Simplify 0 into 0 9.790 * [backup-simplify]: Simplify 0 into 0 9.790 * [backup-simplify]: Simplify 0 into 0 9.791 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.792 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 9.799 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 9.799 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 9.799 * [backup-simplify]: Simplify (+ 0 0) into 0 9.801 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 9.802 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 9.804 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 9.807 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 9.807 * [taylor]: Taking taylor expansion of 0 in k 9.807 * [backup-simplify]: Simplify 0 into 0 9.807 * [backup-simplify]: Simplify 0 into 0 9.809 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 9.809 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 2) 9.811 * [backup-simplify]: Simplify (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) into (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) 9.811 * [approximate]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in (n k) around 0 9.811 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in k 9.811 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 9.811 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 9.811 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 9.811 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 9.811 * [taylor]: Taking taylor expansion of 0.25 in k 9.811 * [backup-simplify]: Simplify 0.25 into 0.25 9.811 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.811 * [taylor]: Taking taylor expansion of 1.0 in k 9.811 * [backup-simplify]: Simplify 1.0 into 1.0 9.811 * [taylor]: Taking taylor expansion of k in k 9.811 * [backup-simplify]: Simplify 0 into 0 9.811 * [backup-simplify]: Simplify 1 into 1 9.811 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 9.811 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 9.811 * [taylor]: Taking taylor expansion of 2.0 in k 9.811 * [backup-simplify]: Simplify 2.0 into 2.0 9.811 * [taylor]: Taking taylor expansion of (* n PI) in k 9.811 * [taylor]: Taking taylor expansion of n in k 9.811 * [backup-simplify]: Simplify n into n 9.811 * [taylor]: Taking taylor expansion of PI in k 9.811 * [backup-simplify]: Simplify PI into PI 9.811 * [backup-simplify]: Simplify (* n PI) into (* n PI) 9.812 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 9.812 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 9.812 * [backup-simplify]: Simplify (- 0) into 0 9.812 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.813 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 9.813 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 9.813 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 9.813 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in n 9.813 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 9.813 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.813 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.813 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 9.813 * [taylor]: Taking taylor expansion of 0.25 in n 9.813 * [backup-simplify]: Simplify 0.25 into 0.25 9.813 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.814 * [taylor]: Taking taylor expansion of 1.0 in n 9.814 * [backup-simplify]: Simplify 1.0 into 1.0 9.814 * [taylor]: Taking taylor expansion of k in n 9.814 * [backup-simplify]: Simplify k into k 9.814 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.814 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.814 * [taylor]: Taking taylor expansion of 2.0 in n 9.814 * [backup-simplify]: Simplify 2.0 into 2.0 9.814 * [taylor]: Taking taylor expansion of (* n PI) in n 9.814 * [taylor]: Taking taylor expansion of n in n 9.814 * [backup-simplify]: Simplify 0 into 0 9.814 * [backup-simplify]: Simplify 1 into 1 9.814 * [taylor]: Taking taylor expansion of PI in n 9.814 * [backup-simplify]: Simplify PI into PI 9.814 * [backup-simplify]: Simplify (* 0 PI) into 0 9.815 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.816 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.818 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.819 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.819 * [backup-simplify]: Simplify (- k) into (- k) 9.820 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.820 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 9.821 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.822 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 9.824 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 9.824 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in n 9.824 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 9.824 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 9.824 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 9.824 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 9.824 * [taylor]: Taking taylor expansion of 0.25 in n 9.824 * [backup-simplify]: Simplify 0.25 into 0.25 9.824 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 9.824 * [taylor]: Taking taylor expansion of 1.0 in n 9.824 * [backup-simplify]: Simplify 1.0 into 1.0 9.824 * [taylor]: Taking taylor expansion of k in n 9.824 * [backup-simplify]: Simplify k into k 9.824 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 9.824 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 9.824 * [taylor]: Taking taylor expansion of 2.0 in n 9.824 * [backup-simplify]: Simplify 2.0 into 2.0 9.824 * [taylor]: Taking taylor expansion of (* n PI) in n 9.824 * [taylor]: Taking taylor expansion of n in n 9.824 * [backup-simplify]: Simplify 0 into 0 9.824 * [backup-simplify]: Simplify 1 into 1 9.824 * [taylor]: Taking taylor expansion of PI in n 9.824 * [backup-simplify]: Simplify PI into PI 9.825 * [backup-simplify]: Simplify (* 0 PI) into 0 9.825 * [backup-simplify]: Simplify (* 2.0 0) into 0 9.827 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 9.828 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 9.829 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.829 * [backup-simplify]: Simplify (- k) into (- k) 9.829 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 9.830 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 9.831 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.832 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 9.833 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 9.836 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) into (pow (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2) 9.836 * [taylor]: Taking taylor expansion of (pow (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2) in k 9.836 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 9.836 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 9.836 * [taylor]: Taking taylor expansion of 0.25 in k 9.836 * [backup-simplify]: Simplify 0.25 into 0.25 9.836 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 9.836 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 9.836 * [taylor]: Taking taylor expansion of 1.0 in k 9.836 * [backup-simplify]: Simplify 1.0 into 1.0 9.836 * [taylor]: Taking taylor expansion of k in k 9.836 * [backup-simplify]: Simplify 0 into 0 9.836 * [backup-simplify]: Simplify 1 into 1 9.836 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 9.836 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.836 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.836 * [taylor]: Taking taylor expansion of 2.0 in k 9.836 * [backup-simplify]: Simplify 2.0 into 2.0 9.836 * [taylor]: Taking taylor expansion of PI in k 9.836 * [backup-simplify]: Simplify PI into PI 9.837 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.838 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.838 * [taylor]: Taking taylor expansion of (log n) in k 9.838 * [taylor]: Taking taylor expansion of n in k 9.838 * [backup-simplify]: Simplify n into n 9.838 * [backup-simplify]: Simplify (log n) into (log n) 9.839 * [backup-simplify]: Simplify (- 0) into 0 9.839 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 9.840 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 9.841 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 9.842 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 9.844 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 9.846 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) into (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) 9.847 * [backup-simplify]: Simplify (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) into (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) 9.848 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 9.849 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 9.851 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.852 * [backup-simplify]: Simplify (- 0) into 0 9.852 * [backup-simplify]: Simplify (+ 0 0) into 0 9.852 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 9.854 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.855 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 9.857 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.860 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))) into 0 9.860 * [taylor]: Taking taylor expansion of 0 in k 9.860 * [backup-simplify]: Simplify 0 into 0 9.860 * [backup-simplify]: Simplify 0 into 0 9.861 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.863 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.864 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 9.864 * [backup-simplify]: Simplify (+ 0 0) into 0 9.864 * [backup-simplify]: Simplify (- 1) into -1 9.865 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.866 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 9.877 * [backup-simplify]: Simplify (+ (* 0.25 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 9.881 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) 9.889 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.5 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))) (* 0.5 (* (log (* 2.0 PI)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))))) 9.893 * [backup-simplify]: Simplify (- (+ (* 0.5 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))) (* 0.5 (* (log (* 2.0 PI)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))))) into (- (+ (* 0.5 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))) (* 0.5 (* (log (* 2.0 PI)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))))) 9.895 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 9.896 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 9.900 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 9.900 * [backup-simplify]: Simplify (- 0) into 0 9.901 * [backup-simplify]: Simplify (+ 0 0) into 0 9.901 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 9.903 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 9.904 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.907 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 9.909 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))))) into 0 9.909 * [taylor]: Taking taylor expansion of 0 in k 9.909 * [backup-simplify]: Simplify 0 into 0 9.909 * [backup-simplify]: Simplify 0 into 0 9.909 * [backup-simplify]: Simplify 0 into 0 9.910 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.912 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 9.913 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 9.913 * [backup-simplify]: Simplify (+ 0 0) into 0 9.913 * [backup-simplify]: Simplify (- 0) into 0 9.914 * [backup-simplify]: Simplify (+ 0 0) into 0 9.915 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 9.916 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 9.919 * [backup-simplify]: Simplify (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) 9.930 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (+ (* (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))))) (* -1 (* (+ (* 0.25 (log (* 2.0 PI))) (* 0.25 (log n))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* (* (+ (* 0.03125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.03125 (pow (log n) 2)) (* 0.0625 (* (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) into (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))) (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))) (* 0.125 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))) 9.935 * [backup-simplify]: Simplify (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))) (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))) (* 0.125 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))) into (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))) (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))) (* 0.125 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))) 9.946 * [backup-simplify]: Simplify (+ (* (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))) (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))) (* 0.125 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))) (pow (* k 1) 2)) (+ (* (- (+ (* 0.5 (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))) (* 0.5 (* (log (* 2.0 PI)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))))) (* k 1)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2))) into (- (+ (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))))) (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2)))) (* 0.125 (* (pow k 2) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2)))) (* 0.5 (* k (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))))) 9.948 * [backup-simplify]: Simplify (* (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) (pow (* (* 2.0 PI) (/ 1 n)) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2))) into (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) 9.948 * [approximate]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in (n k) around 0 9.948 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in k 9.948 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 9.948 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 9.948 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 9.948 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 9.948 * [taylor]: Taking taylor expansion of 0.25 in k 9.948 * [backup-simplify]: Simplify 0.25 into 0.25 9.948 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.948 * [taylor]: Taking taylor expansion of 1.0 in k 9.948 * [backup-simplify]: Simplify 1.0 into 1.0 9.948 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.948 * [taylor]: Taking taylor expansion of k in k 9.948 * [backup-simplify]: Simplify 0 into 0 9.948 * [backup-simplify]: Simplify 1 into 1 9.949 * [backup-simplify]: Simplify (/ 1 1) into 1 9.949 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 9.949 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 9.949 * [taylor]: Taking taylor expansion of 2.0 in k 9.949 * [backup-simplify]: Simplify 2.0 into 2.0 9.949 * [taylor]: Taking taylor expansion of (/ PI n) in k 9.949 * [taylor]: Taking taylor expansion of PI in k 9.949 * [backup-simplify]: Simplify PI into PI 9.949 * [taylor]: Taking taylor expansion of n in k 9.949 * [backup-simplify]: Simplify n into n 9.949 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 9.949 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 9.949 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 9.950 * [backup-simplify]: Simplify (- 1) into -1 9.950 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.951 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 9.951 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 9.951 * [backup-simplify]: Simplify (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.25 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 9.951 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in n 9.951 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.951 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.951 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.951 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.951 * [taylor]: Taking taylor expansion of 0.25 in n 9.951 * [backup-simplify]: Simplify 0.25 into 0.25 9.951 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.951 * [taylor]: Taking taylor expansion of 1.0 in n 9.951 * [backup-simplify]: Simplify 1.0 into 1.0 9.951 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.951 * [taylor]: Taking taylor expansion of k in n 9.951 * [backup-simplify]: Simplify k into k 9.952 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.952 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.952 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.952 * [taylor]: Taking taylor expansion of 2.0 in n 9.952 * [backup-simplify]: Simplify 2.0 into 2.0 9.952 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.952 * [taylor]: Taking taylor expansion of PI in n 9.952 * [backup-simplify]: Simplify PI into PI 9.952 * [taylor]: Taking taylor expansion of n in n 9.952 * [backup-simplify]: Simplify 0 into 0 9.952 * [backup-simplify]: Simplify 1 into 1 9.953 * [backup-simplify]: Simplify (/ PI 1) into PI 9.953 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.954 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.954 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.954 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.955 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.956 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.958 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 9.959 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 9.959 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in n 9.959 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 9.959 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 9.959 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 9.959 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 9.959 * [taylor]: Taking taylor expansion of 0.25 in n 9.959 * [backup-simplify]: Simplify 0.25 into 0.25 9.959 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 9.959 * [taylor]: Taking taylor expansion of 1.0 in n 9.959 * [backup-simplify]: Simplify 1.0 into 1.0 9.959 * [taylor]: Taking taylor expansion of (/ 1 k) in n 9.960 * [taylor]: Taking taylor expansion of k in n 9.960 * [backup-simplify]: Simplify k into k 9.960 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 9.960 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 9.960 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 9.960 * [taylor]: Taking taylor expansion of 2.0 in n 9.960 * [backup-simplify]: Simplify 2.0 into 2.0 9.960 * [taylor]: Taking taylor expansion of (/ PI n) in n 9.960 * [taylor]: Taking taylor expansion of PI in n 9.960 * [backup-simplify]: Simplify PI into PI 9.960 * [taylor]: Taking taylor expansion of n in n 9.960 * [backup-simplify]: Simplify 0 into 0 9.960 * [backup-simplify]: Simplify 1 into 1 9.961 * [backup-simplify]: Simplify (/ PI 1) into PI 9.961 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.963 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.963 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 9.963 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 9.963 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 9.964 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.966 * [backup-simplify]: Simplify (* (* 0.25 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 9.967 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 9.969 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) 9.969 * [taylor]: Taking taylor expansion of (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) in k 9.969 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 9.969 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 9.969 * [taylor]: Taking taylor expansion of 0.25 in k 9.969 * [backup-simplify]: Simplify 0.25 into 0.25 9.969 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 9.969 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 9.969 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 9.969 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 9.969 * [taylor]: Taking taylor expansion of 2.0 in k 9.969 * [backup-simplify]: Simplify 2.0 into 2.0 9.969 * [taylor]: Taking taylor expansion of PI in k 9.969 * [backup-simplify]: Simplify PI into PI 9.969 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 9.970 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 9.970 * [taylor]: Taking taylor expansion of (log n) in k 9.970 * [taylor]: Taking taylor expansion of n in k 9.970 * [backup-simplify]: Simplify n into n 9.970 * [backup-simplify]: Simplify (log n) into (log n) 9.970 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 9.970 * [taylor]: Taking taylor expansion of 1.0 in k 9.970 * [backup-simplify]: Simplify 1.0 into 1.0 9.970 * [taylor]: Taking taylor expansion of (/ 1 k) in k 9.970 * [taylor]: Taking taylor expansion of k in k 9.970 * [backup-simplify]: Simplify 0 into 0 9.970 * [backup-simplify]: Simplify 1 into 1 9.971 * [backup-simplify]: Simplify (/ 1 1) into 1 9.971 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 9.971 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 9.972 * [backup-simplify]: Simplify (- 1) into -1 9.972 * [backup-simplify]: Simplify (+ 0 -1) into -1 9.973 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 9.973 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 9.974 * [backup-simplify]: Simplify (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 9.976 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) 9.977 * [backup-simplify]: Simplify (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) into (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) 9.978 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 9.978 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 9.979 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 9.979 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 9.980 * [backup-simplify]: Simplify (- 0) into 0 9.980 * [backup-simplify]: Simplify (+ 0 0) into 0 9.980 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 9.982 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 9.982 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 9.984 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 9.985 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (* 0 (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 9.985 * [taylor]: Taking taylor expansion of 0 in k 9.985 * [backup-simplify]: Simplify 0 into 0 9.985 * [backup-simplify]: Simplify 0 into 0 9.987 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (* 0 (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 9.988 * [backup-simplify]: Simplify 0 into 0 9.989 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 9.989 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 9.999 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 9.999 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.000 * [backup-simplify]: Simplify (- 0) into 0 10.000 * [backup-simplify]: Simplify (+ 0 0) into 0 10.001 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 10.001 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.002 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 10.004 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 10.006 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0 10.006 * [taylor]: Taking taylor expansion of 0 in k 10.006 * [backup-simplify]: Simplify 0 into 0 10.006 * [backup-simplify]: Simplify 0 into 0 10.006 * [backup-simplify]: Simplify 0 into 0 10.007 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0 10.007 * [backup-simplify]: Simplify 0 into 0 10.008 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.009 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.012 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 10.013 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.013 * [backup-simplify]: Simplify (- 0) into 0 10.013 * [backup-simplify]: Simplify (+ 0 0) into 0 10.014 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 10.015 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.016 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 10.018 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 10.020 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into 0 10.020 * [taylor]: Taking taylor expansion of 0 in k 10.020 * [backup-simplify]: Simplify 0 into 0 10.020 * [backup-simplify]: Simplify 0 into 0 10.021 * [backup-simplify]: Simplify (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) 2) into (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 2) 10.022 * [backup-simplify]: Simplify (* (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2))) into (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) 10.022 * [approximate]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in (n k) around 0 10.022 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in k 10.022 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 10.022 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 10.022 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 10.022 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 10.022 * [taylor]: Taking taylor expansion of 0.25 in k 10.022 * [backup-simplify]: Simplify 0.25 into 0.25 10.022 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 10.022 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.022 * [taylor]: Taking taylor expansion of k in k 10.022 * [backup-simplify]: Simplify 0 into 0 10.022 * [backup-simplify]: Simplify 1 into 1 10.022 * [backup-simplify]: Simplify (/ 1 1) into 1 10.022 * [taylor]: Taking taylor expansion of 1.0 in k 10.022 * [backup-simplify]: Simplify 1.0 into 1.0 10.022 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 10.022 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 10.022 * [taylor]: Taking taylor expansion of -2.0 in k 10.022 * [backup-simplify]: Simplify -2.0 into -2.0 10.022 * [taylor]: Taking taylor expansion of (/ PI n) in k 10.022 * [taylor]: Taking taylor expansion of PI in k 10.022 * [backup-simplify]: Simplify PI into PI 10.022 * [taylor]: Taking taylor expansion of n in k 10.022 * [backup-simplify]: Simplify n into n 10.022 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 10.022 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 10.022 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 10.023 * [backup-simplify]: Simplify (+ 1 0) into 1 10.023 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 10.023 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 10.023 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 10.023 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in n 10.023 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 10.023 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 10.023 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 10.023 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 10.023 * [taylor]: Taking taylor expansion of 0.25 in n 10.023 * [backup-simplify]: Simplify 0.25 into 0.25 10.023 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 10.023 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.023 * [taylor]: Taking taylor expansion of k in n 10.023 * [backup-simplify]: Simplify k into k 10.024 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.024 * [taylor]: Taking taylor expansion of 1.0 in n 10.024 * [backup-simplify]: Simplify 1.0 into 1.0 10.024 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 10.024 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.024 * [taylor]: Taking taylor expansion of -2.0 in n 10.024 * [backup-simplify]: Simplify -2.0 into -2.0 10.024 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.024 * [taylor]: Taking taylor expansion of PI in n 10.024 * [backup-simplify]: Simplify PI into PI 10.024 * [taylor]: Taking taylor expansion of n in n 10.024 * [backup-simplify]: Simplify 0 into 0 10.024 * [backup-simplify]: Simplify 1 into 1 10.024 * [backup-simplify]: Simplify (/ PI 1) into PI 10.024 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.025 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.025 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 10.025 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 10.026 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.027 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 10.027 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 10.027 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in n 10.027 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 10.028 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 10.028 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 10.028 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 10.028 * [taylor]: Taking taylor expansion of 0.25 in n 10.028 * [backup-simplify]: Simplify 0.25 into 0.25 10.028 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 10.028 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.028 * [taylor]: Taking taylor expansion of k in n 10.028 * [backup-simplify]: Simplify k into k 10.028 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.028 * [taylor]: Taking taylor expansion of 1.0 in n 10.028 * [backup-simplify]: Simplify 1.0 into 1.0 10.028 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 10.028 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.028 * [taylor]: Taking taylor expansion of -2.0 in n 10.028 * [backup-simplify]: Simplify -2.0 into -2.0 10.028 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.028 * [taylor]: Taking taylor expansion of PI in n 10.028 * [backup-simplify]: Simplify PI into PI 10.028 * [taylor]: Taking taylor expansion of n in n 10.028 * [backup-simplify]: Simplify 0 into 0 10.028 * [backup-simplify]: Simplify 1 into 1 10.029 * [backup-simplify]: Simplify (/ PI 1) into PI 10.029 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.030 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.030 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 10.031 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 10.032 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.033 * [backup-simplify]: Simplify (* (* 0.25 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 10.035 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 10.037 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (pow (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) 10.037 * [taylor]: Taking taylor expansion of (pow (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) in k 10.037 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 10.037 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 10.037 * [taylor]: Taking taylor expansion of 0.25 in k 10.037 * [backup-simplify]: Simplify 0.25 into 0.25 10.038 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 10.038 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 10.038 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.038 * [taylor]: Taking taylor expansion of k in k 10.038 * [backup-simplify]: Simplify 0 into 0 10.038 * [backup-simplify]: Simplify 1 into 1 10.038 * [backup-simplify]: Simplify (/ 1 1) into 1 10.038 * [taylor]: Taking taylor expansion of 1.0 in k 10.038 * [backup-simplify]: Simplify 1.0 into 1.0 10.038 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 10.038 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 10.038 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 10.038 * [taylor]: Taking taylor expansion of -2.0 in k 10.038 * [backup-simplify]: Simplify -2.0 into -2.0 10.038 * [taylor]: Taking taylor expansion of PI in k 10.038 * [backup-simplify]: Simplify PI into PI 10.039 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.040 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.040 * [taylor]: Taking taylor expansion of (log n) in k 10.040 * [taylor]: Taking taylor expansion of n in k 10.040 * [backup-simplify]: Simplify n into n 10.040 * [backup-simplify]: Simplify (log n) into (log n) 10.041 * [backup-simplify]: Simplify (+ 1 0) into 1 10.041 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 10.042 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 10.043 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 10.044 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 10.045 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 10.048 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (pow (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) 10.049 * [backup-simplify]: Simplify (pow (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) into (pow (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) 10.050 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.051 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 10.053 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 10.053 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 10.054 * [backup-simplify]: Simplify (+ 0 0) into 0 10.054 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 10.056 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.057 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 10.059 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.061 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (* 0 (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 10.061 * [taylor]: Taking taylor expansion of 0 in k 10.061 * [backup-simplify]: Simplify 0 into 0 10.062 * [backup-simplify]: Simplify 0 into 0 10.065 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (* 0 (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 10.065 * [backup-simplify]: Simplify 0 into 0 10.066 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.067 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.069 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 10.069 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.070 * [backup-simplify]: Simplify (+ 0 0) into 0 10.070 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 10.071 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.072 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 10.073 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 10.075 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) into 0 10.075 * [taylor]: Taking taylor expansion of 0 in k 10.075 * [backup-simplify]: Simplify 0 into 0 10.075 * [backup-simplify]: Simplify 0 into 0 10.075 * [backup-simplify]: Simplify 0 into 0 10.077 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) into 0 10.077 * [backup-simplify]: Simplify 0 into 0 10.077 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.078 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.081 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 10.082 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.082 * [backup-simplify]: Simplify (+ 0 0) into 0 10.083 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 10.083 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.085 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 10.086 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 10.088 * [backup-simplify]: Simplify (+ (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))) into 0 10.088 * [taylor]: Taking taylor expansion of 0 in k 10.088 * [backup-simplify]: Simplify 0 into 0 10.088 * [backup-simplify]: Simplify 0 into 0 10.089 * [backup-simplify]: Simplify (pow (exp (* 0.25 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) 2) into (pow (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2) 10.089 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 2 2 1) 10.089 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 10.089 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 10.089 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.089 * [taylor]: Taking taylor expansion of 2.0 in n 10.089 * [backup-simplify]: Simplify 2.0 into 2.0 10.090 * [taylor]: Taking taylor expansion of (* n PI) in n 10.090 * [taylor]: Taking taylor expansion of n in n 10.090 * [backup-simplify]: Simplify 0 into 0 10.090 * [backup-simplify]: Simplify 1 into 1 10.090 * [taylor]: Taking taylor expansion of PI in n 10.090 * [backup-simplify]: Simplify PI into PI 10.090 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.090 * [taylor]: Taking taylor expansion of 2.0 in n 10.090 * [backup-simplify]: Simplify 2.0 into 2.0 10.090 * [taylor]: Taking taylor expansion of (* n PI) in n 10.090 * [taylor]: Taking taylor expansion of n in n 10.090 * [backup-simplify]: Simplify 0 into 0 10.090 * [backup-simplify]: Simplify 1 into 1 10.090 * [taylor]: Taking taylor expansion of PI in n 10.090 * [backup-simplify]: Simplify PI into PI 10.090 * [backup-simplify]: Simplify (* 0 PI) into 0 10.090 * [backup-simplify]: Simplify (* 2.0 0) into 0 10.090 * [backup-simplify]: Simplify 0 into 0 10.091 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.092 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 10.092 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.093 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 10.094 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 10.094 * [backup-simplify]: Simplify 0 into 0 10.094 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 10.095 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 10.095 * [backup-simplify]: Simplify 0 into 0 10.096 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 10.097 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 10.097 * [backup-simplify]: Simplify 0 into 0 10.098 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 10.098 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 10.099 * [backup-simplify]: Simplify 0 into 0 10.099 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 10.101 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 10.101 * [backup-simplify]: Simplify 0 into 0 10.103 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 10.113 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 10.113 * [backup-simplify]: Simplify 0 into 0 10.113 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 10.114 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 10.114 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 10.114 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 10.114 * [taylor]: Taking taylor expansion of 2.0 in n 10.114 * [backup-simplify]: Simplify 2.0 into 2.0 10.114 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.114 * [taylor]: Taking taylor expansion of PI in n 10.114 * [backup-simplify]: Simplify PI into PI 10.114 * [taylor]: Taking taylor expansion of n in n 10.114 * [backup-simplify]: Simplify 0 into 0 10.114 * [backup-simplify]: Simplify 1 into 1 10.114 * [backup-simplify]: Simplify (/ PI 1) into PI 10.114 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 10.114 * [taylor]: Taking taylor expansion of 2.0 in n 10.114 * [backup-simplify]: Simplify 2.0 into 2.0 10.114 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.114 * [taylor]: Taking taylor expansion of PI in n 10.114 * [backup-simplify]: Simplify PI into PI 10.114 * [taylor]: Taking taylor expansion of n in n 10.114 * [backup-simplify]: Simplify 0 into 0 10.114 * [backup-simplify]: Simplify 1 into 1 10.115 * [backup-simplify]: Simplify (/ PI 1) into PI 10.115 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.115 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.116 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.116 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 10.116 * [backup-simplify]: Simplify 0 into 0 10.117 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.117 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.117 * [backup-simplify]: Simplify 0 into 0 10.118 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.119 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.119 * [backup-simplify]: Simplify 0 into 0 10.119 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.120 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 10.120 * [backup-simplify]: Simplify 0 into 0 10.121 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.122 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 10.122 * [backup-simplify]: Simplify 0 into 0 10.122 * [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 10.123 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 10.124 * [backup-simplify]: Simplify 0 into 0 10.124 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 10.124 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 10.124 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 10.124 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.124 * [taylor]: Taking taylor expansion of -2.0 in n 10.124 * [backup-simplify]: Simplify -2.0 into -2.0 10.124 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.124 * [taylor]: Taking taylor expansion of PI in n 10.124 * [backup-simplify]: Simplify PI into PI 10.124 * [taylor]: Taking taylor expansion of n in n 10.124 * [backup-simplify]: Simplify 0 into 0 10.124 * [backup-simplify]: Simplify 1 into 1 10.125 * [backup-simplify]: Simplify (/ PI 1) into PI 10.125 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.125 * [taylor]: Taking taylor expansion of -2.0 in n 10.125 * [backup-simplify]: Simplify -2.0 into -2.0 10.125 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.125 * [taylor]: Taking taylor expansion of PI in n 10.125 * [backup-simplify]: Simplify PI into PI 10.125 * [taylor]: Taking taylor expansion of n in n 10.125 * [backup-simplify]: Simplify 0 into 0 10.125 * [backup-simplify]: Simplify 1 into 1 10.125 * [backup-simplify]: Simplify (/ PI 1) into PI 10.126 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.126 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.126 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.127 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 10.127 * [backup-simplify]: Simplify 0 into 0 10.127 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.128 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.128 * [backup-simplify]: Simplify 0 into 0 10.129 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.129 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.129 * [backup-simplify]: Simplify 0 into 0 10.130 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.131 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 10.131 * [backup-simplify]: Simplify 0 into 0 10.131 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.132 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 10.132 * [backup-simplify]: Simplify 0 into 0 10.133 * [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 10.134 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 10.134 * [backup-simplify]: Simplify 0 into 0 10.134 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 10.134 * * * [progress]: simplifying candidates 10.138 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (exp (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))) (cbrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (log (* 2.0 PI)) (log n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (* 1 (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (sqrt (/ (- 1.0 k) 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ 1 1) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) (sqrt 2))) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)) 1)) (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 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k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n))))) (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2)))) (* 0.125 (* (pow k 2) (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (pow (log n) 2))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2)))) (* 0.5 (* k (* (pow (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 2) (log n)))))) (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 2) (pow (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 10.144 * * [simplify]: Extracting # 0 : cost 0 10.145 * * [simplify]: Extracting # 1 : cost 0 10.145 * * [simplify]: Extracting # 2 : cost 0 10.145 * * [simplify]: Extracting # 3 : cost 0 10.146 * * [simplify]: Extracting # 4 : cost 0 10.146 * * [simplify]: Extracting # 5 : cost 0 10.146 * * [simplify]: Extracting # 6 : cost 0 10.147 * * [simplify]: Extracting # 7 : cost 0 10.147 * * [simplify]: Extracting # 8 : cost 0 10.148 * * [simplify]: Extracting # 9 : cost 0 10.148 * * [simplify]: Extracting # 10 : cost 0 10.149 * * [simplify]: Extracting # 11 : cost 0 10.149 * * [simplify]: Extracting # 12 : cost 0 10.149 * * [simplify]: Extracting # 13 : cost 0 10.150 * * [simplify]: iteration 0 : 313 enodes (cost 5306 ) 10.279 * * [simplify]: Extracting # 0 : cost 0 10.282 * * [simplify]: Extracting # 1 : cost 0 10.285 * * [simplify]: Extracting # 2 : cost 0 10.287 * * [simplify]: Extracting # 3 : cost 0 10.290 * * [simplify]: Extracting # 4 : cost 0 10.293 * * [simplify]: Extracting # 5 : cost 0 10.304 * * [simplify]: Extracting # 6 : cost 0 10.306 * * [simplify]: iteration 1 : 1017 enodes (cost 4459 ) 10.817 * * [simplify]: Extracting # 0 : cost 0 10.829 * * [simplify]: Extracting # 1 : cost 0 10.842 * * [simplify]: Extracting # 2 : cost 0 10.849 * * [simplify]: Extracting # 3 : cost 0 10.861 * * [simplify]: Extracting # 4 : cost 0 10.871 * * [simplify]: Extracting # 5 : cost 0 10.883 * * [simplify]: Extracting # 6 : cost 0 10.896 * * [simplify]: iteration done: 5000 enodes (cost 3965 ) 10.900 * [simplify]: Simplified to: (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (/ (/ (- 1.0 k) 2.0) 2) (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ k 2.0) 2)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (/ (- 1.0 k) 2.0) 2)) (cbrt (/ (/ (- 1.0 k) 2.0) 2)))) (pow (* (* 2.0 PI) n) (sqrt (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (/ (- 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1.0 2.0) 2))) (* (pow (* (* 2.0 PI) n) (/ (/ 1.0 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (log (* n (* 2.0 PI))) (log (* n (* 2.0 PI))) (log (* n (* 2.0 PI))) (exp (* (* 2.0 PI) n)) (pow (* n (* 2.0 PI)) 3) (pow (* n (* 2.0 PI)) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* n (* 2.0 PI)) 3) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* n PI) (+ (+ (* 0.03125 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* n (* 2.0 PI)) 0.25))) (pow (* n (* 2.0 PI)) 0.25)) (- (+ (* (* (* 0.0625 (pow k 2)) (* (pow (* n (* 2.0 PI)) 0.25) (log n))) (log (* 2.0 PI))) (* (* k (* k (pow (* n (* 2.0 PI)) 0.25))) (* (pow (log n) 2) 0.03125))) (* (* 0.25 k) (+ (* (pow (* n (* 2.0 PI)) 0.25) (log n)) (* (log (* 2.0 PI)) (pow (* n (* 2.0 PI)) 0.25)))))) (pow (pow (* n (* 2.0 PI)) 0.25) (- 1.0 k)) (pow (exp 0.25) (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))) (+ (+ (* 0.03125 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* n (* 2.0 PI)) 0.25))) (pow (* n (* 2.0 PI)) 0.25)) (- (+ (* (* (* 0.0625 (pow k 2)) (* (pow (* n (* 2.0 PI)) 0.25) (log n))) (log (* 2.0 PI))) (* (* k (* k (pow (* n (* 2.0 PI)) 0.25))) (* (pow (log n) 2) 0.03125))) (* (* 0.25 k) (+ (* (pow (* n (* 2.0 PI)) 0.25) (log n)) (* (log (* 2.0 PI)) (pow (* n (* 2.0 PI)) 0.25)))))) (pow (pow (* n (* 2.0 PI)) 0.25) (- 1.0 k)) (pow (exp 0.25) (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))) (+ (+ (* (* (* (log (* 2.0 PI)) (log n)) (pow (pow (* n (* 2.0 PI)) 0.25) 2)) (* (pow k 2) 0.25)) (* 0.125 (* (pow k 2) (+ (* (pow (pow (* n (* 2.0 PI)) 0.25) 2) (pow (log (* 2.0 PI)) 2)) (* (pow (pow (* n (* 2.0 PI)) 0.25) 2) (pow (log n) 2)))))) (- (pow (pow (* n (* 2.0 PI)) 0.25) 2) (* (* k (+ (* (log (* 2.0 PI)) (pow (pow (* n (* 2.0 PI)) 0.25) 2)) (* (pow (pow (* n (* 2.0 PI)) 0.25) 2) (log n)))) 0.5))) (pow (pow (pow (* n (* 2.0 PI)) 0.25) (- 1.0 k)) 2) (pow (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (* n (* 2.0 PI)) 10.903 * * * [progress]: adding candidates to table 12.164 * * [progress]: iteration 4 / 4 12.164 * * * [progress]: picking best candidate 12.181 * * * * [pick]: Picked # 12.181 * * * [progress]: localizing error 12.211 * * * [progress]: generating rewritten candidates 12.211 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1 2) 12.234 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1 2) 12.264 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1 2 1) 12.286 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1 2 1) 12.330 * * * [progress]: generating series expansions 12.330 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1 2) 12.331 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 12.331 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 12.331 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 12.331 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 12.331 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 12.331 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 12.331 * [taylor]: Taking taylor expansion of 0.5 in k 12.331 * [backup-simplify]: Simplify 0.5 into 0.5 12.331 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.331 * [taylor]: Taking taylor expansion of 1.0 in k 12.331 * [backup-simplify]: Simplify 1.0 into 1.0 12.332 * [taylor]: Taking taylor expansion of k in k 12.332 * [backup-simplify]: Simplify 0 into 0 12.332 * [backup-simplify]: Simplify 1 into 1 12.332 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 12.332 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 12.332 * [taylor]: Taking taylor expansion of 2.0 in k 12.332 * [backup-simplify]: Simplify 2.0 into 2.0 12.332 * [taylor]: Taking taylor expansion of (* n PI) in k 12.332 * [taylor]: Taking taylor expansion of n in k 12.332 * [backup-simplify]: Simplify n into n 12.332 * [taylor]: Taking taylor expansion of PI in k 12.332 * [backup-simplify]: Simplify PI into PI 12.332 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.332 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 12.332 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 12.333 * [backup-simplify]: Simplify (- 0) into 0 12.333 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.334 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 12.334 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 12.334 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 12.334 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 12.334 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.334 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.334 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.334 * [taylor]: Taking taylor expansion of 0.5 in n 12.334 * [backup-simplify]: Simplify 0.5 into 0.5 12.334 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.334 * [taylor]: Taking taylor expansion of 1.0 in n 12.334 * [backup-simplify]: Simplify 1.0 into 1.0 12.334 * [taylor]: Taking taylor expansion of k in n 12.334 * [backup-simplify]: Simplify k into k 12.334 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.334 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.334 * [taylor]: Taking taylor expansion of 2.0 in n 12.334 * [backup-simplify]: Simplify 2.0 into 2.0 12.334 * [taylor]: Taking taylor expansion of (* n PI) in n 12.334 * [taylor]: Taking taylor expansion of n in n 12.334 * [backup-simplify]: Simplify 0 into 0 12.334 * [backup-simplify]: Simplify 1 into 1 12.334 * [taylor]: Taking taylor expansion of PI in n 12.335 * [backup-simplify]: Simplify PI into PI 12.335 * [backup-simplify]: Simplify (* 0 PI) into 0 12.336 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.337 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.339 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.340 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.340 * [backup-simplify]: Simplify (- k) into (- k) 12.340 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.340 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.342 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.343 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.344 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.345 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 12.345 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.345 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.345 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.345 * [taylor]: Taking taylor expansion of 0.5 in n 12.345 * [backup-simplify]: Simplify 0.5 into 0.5 12.345 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.345 * [taylor]: Taking taylor expansion of 1.0 in n 12.345 * [backup-simplify]: Simplify 1.0 into 1.0 12.345 * [taylor]: Taking taylor expansion of k in n 12.345 * [backup-simplify]: Simplify k into k 12.345 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.345 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.345 * [taylor]: Taking taylor expansion of 2.0 in n 12.345 * [backup-simplify]: Simplify 2.0 into 2.0 12.345 * [taylor]: Taking taylor expansion of (* n PI) in n 12.345 * [taylor]: Taking taylor expansion of n in n 12.345 * [backup-simplify]: Simplify 0 into 0 12.345 * [backup-simplify]: Simplify 1 into 1 12.345 * [taylor]: Taking taylor expansion of PI in n 12.345 * [backup-simplify]: Simplify PI into PI 12.346 * [backup-simplify]: Simplify (* 0 PI) into 0 12.346 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.348 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.350 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.351 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.351 * [backup-simplify]: Simplify (- k) into (- k) 12.351 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.351 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.353 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.354 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.356 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.356 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 12.356 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 12.356 * [taylor]: Taking taylor expansion of 0.5 in k 12.356 * [backup-simplify]: Simplify 0.5 into 0.5 12.356 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 12.356 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.356 * [taylor]: Taking taylor expansion of 1.0 in k 12.356 * [backup-simplify]: Simplify 1.0 into 1.0 12.356 * [taylor]: Taking taylor expansion of k in k 12.356 * [backup-simplify]: Simplify 0 into 0 12.356 * [backup-simplify]: Simplify 1 into 1 12.356 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 12.356 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.356 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.356 * [taylor]: Taking taylor expansion of 2.0 in k 12.356 * [backup-simplify]: Simplify 2.0 into 2.0 12.356 * [taylor]: Taking taylor expansion of PI in k 12.356 * [backup-simplify]: Simplify PI into PI 12.357 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.358 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.358 * [taylor]: Taking taylor expansion of (log n) in k 12.358 * [taylor]: Taking taylor expansion of n in k 12.359 * [backup-simplify]: Simplify n into n 12.359 * [backup-simplify]: Simplify (log n) into (log n) 12.359 * [backup-simplify]: Simplify (- 0) into 0 12.360 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.361 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 12.362 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 12.363 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 12.365 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 12.366 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 12.367 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.368 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.370 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.371 * [backup-simplify]: Simplify (- 0) into 0 12.371 * [backup-simplify]: Simplify (+ 0 0) into 0 12.372 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 12.373 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.374 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 12.377 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.377 * [taylor]: Taking taylor expansion of 0 in k 12.377 * [backup-simplify]: Simplify 0 into 0 12.377 * [backup-simplify]: Simplify 0 into 0 12.378 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.380 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.381 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.382 * [backup-simplify]: Simplify (+ 0 0) into 0 12.382 * [backup-simplify]: Simplify (- 1) into -1 12.383 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.384 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 12.387 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 12.389 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 12.391 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 12.392 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.393 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.394 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.395 * [backup-simplify]: Simplify (- 0) into 0 12.395 * [backup-simplify]: Simplify (+ 0 0) into 0 12.396 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 12.397 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.398 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.399 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.399 * [taylor]: Taking taylor expansion of 0 in k 12.399 * [backup-simplify]: Simplify 0 into 0 12.399 * [backup-simplify]: Simplify 0 into 0 12.399 * [backup-simplify]: Simplify 0 into 0 12.400 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.402 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.403 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 12.403 * [backup-simplify]: Simplify (+ 0 0) into 0 12.403 * [backup-simplify]: Simplify (- 0) into 0 12.404 * [backup-simplify]: Simplify (+ 0 0) into 0 12.405 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.406 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 12.417 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 12.421 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 12.428 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 12.428 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 12.428 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 12.428 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 12.428 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 12.428 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 12.428 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 12.428 * [taylor]: Taking taylor expansion of 0.5 in k 12.428 * [backup-simplify]: Simplify 0.5 into 0.5 12.428 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.429 * [taylor]: Taking taylor expansion of 1.0 in k 12.429 * [backup-simplify]: Simplify 1.0 into 1.0 12.429 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.429 * [taylor]: Taking taylor expansion of k in k 12.429 * [backup-simplify]: Simplify 0 into 0 12.429 * [backup-simplify]: Simplify 1 into 1 12.429 * [backup-simplify]: Simplify (/ 1 1) into 1 12.429 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 12.429 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 12.429 * [taylor]: Taking taylor expansion of 2.0 in k 12.429 * [backup-simplify]: Simplify 2.0 into 2.0 12.429 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.429 * [taylor]: Taking taylor expansion of PI in k 12.429 * [backup-simplify]: Simplify PI into PI 12.429 * [taylor]: Taking taylor expansion of n in k 12.429 * [backup-simplify]: Simplify n into n 12.429 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.429 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 12.429 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 12.429 * [backup-simplify]: Simplify (- 1) into -1 12.430 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.430 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 12.430 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 12.430 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 12.430 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 12.430 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.430 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.430 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 12.430 * [taylor]: Taking taylor expansion of 0.5 in n 12.430 * [backup-simplify]: Simplify 0.5 into 0.5 12.430 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.430 * [taylor]: Taking taylor expansion of 1.0 in n 12.430 * [backup-simplify]: Simplify 1.0 into 1.0 12.430 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.430 * [taylor]: Taking taylor expansion of k in n 12.430 * [backup-simplify]: Simplify k into k 12.430 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.430 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.431 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.431 * [taylor]: Taking taylor expansion of 2.0 in n 12.431 * [backup-simplify]: Simplify 2.0 into 2.0 12.431 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.431 * [taylor]: Taking taylor expansion of PI in n 12.431 * [backup-simplify]: Simplify PI into PI 12.431 * [taylor]: Taking taylor expansion of n in n 12.431 * [backup-simplify]: Simplify 0 into 0 12.431 * [backup-simplify]: Simplify 1 into 1 12.431 * [backup-simplify]: Simplify (/ PI 1) into PI 12.431 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.432 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.432 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.432 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.432 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 12.433 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.434 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 12.434 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.435 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 12.435 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.435 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.435 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 12.435 * [taylor]: Taking taylor expansion of 0.5 in n 12.435 * [backup-simplify]: Simplify 0.5 into 0.5 12.435 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.435 * [taylor]: Taking taylor expansion of 1.0 in n 12.435 * [backup-simplify]: Simplify 1.0 into 1.0 12.435 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.435 * [taylor]: Taking taylor expansion of k in n 12.435 * [backup-simplify]: Simplify k into k 12.435 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.435 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.435 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.435 * [taylor]: Taking taylor expansion of 2.0 in n 12.435 * [backup-simplify]: Simplify 2.0 into 2.0 12.435 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.435 * [taylor]: Taking taylor expansion of PI in n 12.435 * [backup-simplify]: Simplify PI into PI 12.435 * [taylor]: Taking taylor expansion of n in n 12.435 * [backup-simplify]: Simplify 0 into 0 12.435 * [backup-simplify]: Simplify 1 into 1 12.435 * [backup-simplify]: Simplify (/ PI 1) into PI 12.436 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.436 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.437 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.437 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.437 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 12.438 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.438 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 12.439 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.439 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 12.439 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 12.439 * [taylor]: Taking taylor expansion of 0.5 in k 12.439 * [backup-simplify]: Simplify 0.5 into 0.5 12.439 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 12.439 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 12.439 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.439 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.439 * [taylor]: Taking taylor expansion of 2.0 in k 12.439 * [backup-simplify]: Simplify 2.0 into 2.0 12.439 * [taylor]: Taking taylor expansion of PI in k 12.439 * [backup-simplify]: Simplify PI into PI 12.440 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.440 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.440 * [taylor]: Taking taylor expansion of (log n) in k 12.440 * [taylor]: Taking taylor expansion of n in k 12.440 * [backup-simplify]: Simplify n into n 12.440 * [backup-simplify]: Simplify (log n) into (log n) 12.441 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.441 * [taylor]: Taking taylor expansion of 1.0 in k 12.441 * [backup-simplify]: Simplify 1.0 into 1.0 12.441 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.441 * [taylor]: Taking taylor expansion of k in k 12.441 * [backup-simplify]: Simplify 0 into 0 12.441 * [backup-simplify]: Simplify 1 into 1 12.441 * [backup-simplify]: Simplify (/ 1 1) into 1 12.441 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.442 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 12.442 * [backup-simplify]: Simplify (- 1) into -1 12.442 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.443 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 12.443 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 12.445 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.446 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.447 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.448 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.450 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.450 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.450 * [backup-simplify]: Simplify (- 0) into 0 12.451 * [backup-simplify]: Simplify (+ 0 0) into 0 12.451 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 12.453 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.454 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 12.456 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.456 * [taylor]: Taking taylor expansion of 0 in k 12.456 * [backup-simplify]: Simplify 0 into 0 12.456 * [backup-simplify]: Simplify 0 into 0 12.456 * [backup-simplify]: Simplify 0 into 0 12.457 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.458 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.462 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.462 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.463 * [backup-simplify]: Simplify (- 0) into 0 12.463 * [backup-simplify]: Simplify (+ 0 0) into 0 12.464 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 12.466 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.467 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 12.470 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.470 * [taylor]: Taking taylor expansion of 0 in k 12.470 * [backup-simplify]: Simplify 0 into 0 12.470 * [backup-simplify]: Simplify 0 into 0 12.470 * [backup-simplify]: Simplify 0 into 0 12.470 * [backup-simplify]: Simplify 0 into 0 12.471 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.473 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.479 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 12.479 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.480 * [backup-simplify]: Simplify (- 0) into 0 12.480 * [backup-simplify]: Simplify (+ 0 0) into 0 12.481 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 12.483 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.485 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 12.488 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.489 * [taylor]: Taking taylor expansion of 0 in k 12.489 * [backup-simplify]: Simplify 0 into 0 12.489 * [backup-simplify]: Simplify 0 into 0 12.490 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 12.491 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 12.491 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 12.491 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 12.491 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 12.491 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 12.491 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 12.491 * [taylor]: Taking taylor expansion of 0.5 in k 12.491 * [backup-simplify]: Simplify 0.5 into 0.5 12.491 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.491 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.491 * [taylor]: Taking taylor expansion of k in k 12.491 * [backup-simplify]: Simplify 0 into 0 12.491 * [backup-simplify]: Simplify 1 into 1 12.492 * [backup-simplify]: Simplify (/ 1 1) into 1 12.492 * [taylor]: Taking taylor expansion of 1.0 in k 12.492 * [backup-simplify]: Simplify 1.0 into 1.0 12.492 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 12.492 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 12.492 * [taylor]: Taking taylor expansion of -2.0 in k 12.492 * [backup-simplify]: Simplify -2.0 into -2.0 12.492 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.492 * [taylor]: Taking taylor expansion of PI in k 12.492 * [backup-simplify]: Simplify PI into PI 12.492 * [taylor]: Taking taylor expansion of n in k 12.492 * [backup-simplify]: Simplify n into n 12.492 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.492 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 12.492 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 12.493 * [backup-simplify]: Simplify (+ 1 0) into 1 12.493 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 12.494 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 12.494 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 12.494 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.494 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.494 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.494 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.494 * [taylor]: Taking taylor expansion of 0.5 in n 12.494 * [backup-simplify]: Simplify 0.5 into 0.5 12.494 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.494 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.494 * [taylor]: Taking taylor expansion of k in n 12.494 * [backup-simplify]: Simplify k into k 12.494 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.494 * [taylor]: Taking taylor expansion of 1.0 in n 12.494 * [backup-simplify]: Simplify 1.0 into 1.0 12.494 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.494 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.494 * [taylor]: Taking taylor expansion of -2.0 in n 12.494 * [backup-simplify]: Simplify -2.0 into -2.0 12.494 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.494 * [taylor]: Taking taylor expansion of PI in n 12.494 * [backup-simplify]: Simplify PI into PI 12.495 * [taylor]: Taking taylor expansion of n in n 12.495 * [backup-simplify]: Simplify 0 into 0 12.495 * [backup-simplify]: Simplify 1 into 1 12.495 * [backup-simplify]: Simplify (/ PI 1) into PI 12.496 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.497 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.497 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.497 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.498 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.500 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 12.501 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.501 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.501 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.501 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.501 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.501 * [taylor]: Taking taylor expansion of 0.5 in n 12.501 * [backup-simplify]: Simplify 0.5 into 0.5 12.501 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.501 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.501 * [taylor]: Taking taylor expansion of k in n 12.501 * [backup-simplify]: Simplify k into k 12.502 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.502 * [taylor]: Taking taylor expansion of 1.0 in n 12.502 * [backup-simplify]: Simplify 1.0 into 1.0 12.502 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.502 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.502 * [taylor]: Taking taylor expansion of -2.0 in n 12.502 * [backup-simplify]: Simplify -2.0 into -2.0 12.502 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.502 * [taylor]: Taking taylor expansion of PI in n 12.502 * [backup-simplify]: Simplify PI into PI 12.502 * [taylor]: Taking taylor expansion of n in n 12.502 * [backup-simplify]: Simplify 0 into 0 12.502 * [backup-simplify]: Simplify 1 into 1 12.502 * [backup-simplify]: Simplify (/ PI 1) into PI 12.503 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.504 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.504 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.504 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.506 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.507 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 12.508 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.508 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 12.509 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 12.509 * [taylor]: Taking taylor expansion of 0.5 in k 12.509 * [backup-simplify]: Simplify 0.5 into 0.5 12.509 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 12.509 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.509 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.509 * [taylor]: Taking taylor expansion of k in k 12.509 * [backup-simplify]: Simplify 0 into 0 12.509 * [backup-simplify]: Simplify 1 into 1 12.509 * [backup-simplify]: Simplify (/ 1 1) into 1 12.509 * [taylor]: Taking taylor expansion of 1.0 in k 12.509 * [backup-simplify]: Simplify 1.0 into 1.0 12.509 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 12.509 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 12.509 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 12.509 * [taylor]: Taking taylor expansion of -2.0 in k 12.509 * [backup-simplify]: Simplify -2.0 into -2.0 12.509 * [taylor]: Taking taylor expansion of PI in k 12.510 * [backup-simplify]: Simplify PI into PI 12.510 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.511 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.511 * [taylor]: Taking taylor expansion of (log n) in k 12.511 * [taylor]: Taking taylor expansion of n in k 12.511 * [backup-simplify]: Simplify n into n 12.511 * [backup-simplify]: Simplify (log n) into (log n) 12.512 * [backup-simplify]: Simplify (+ 1 0) into 1 12.512 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.513 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 12.514 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 12.515 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 12.517 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.518 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.519 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.520 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 12.522 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 12.522 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.522 * [backup-simplify]: Simplify (+ 0 0) into 0 12.523 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 12.524 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.526 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 12.528 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.528 * [taylor]: Taking taylor expansion of 0 in k 12.528 * [backup-simplify]: Simplify 0 into 0 12.528 * [backup-simplify]: Simplify 0 into 0 12.528 * [backup-simplify]: Simplify 0 into 0 12.529 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.530 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.533 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 12.533 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.533 * [backup-simplify]: Simplify (+ 0 0) into 0 12.534 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 12.536 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.537 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 12.540 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.540 * [taylor]: Taking taylor expansion of 0 in k 12.540 * [backup-simplify]: Simplify 0 into 0 12.540 * [backup-simplify]: Simplify 0 into 0 12.540 * [backup-simplify]: Simplify 0 into 0 12.540 * [backup-simplify]: Simplify 0 into 0 12.540 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.541 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.545 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 12.545 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.545 * [backup-simplify]: Simplify (+ 0 0) into 0 12.546 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 12.548 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.559 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 12.562 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.562 * [taylor]: Taking taylor expansion of 0 in k 12.562 * [backup-simplify]: Simplify 0 into 0 12.562 * [backup-simplify]: Simplify 0 into 0 12.563 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 12.563 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1 2) 12.563 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 12.563 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 12.563 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 12.563 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 12.563 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 12.564 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 12.564 * [taylor]: Taking taylor expansion of 0.5 in k 12.564 * [backup-simplify]: Simplify 0.5 into 0.5 12.564 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.564 * [taylor]: Taking taylor expansion of 1.0 in k 12.564 * [backup-simplify]: Simplify 1.0 into 1.0 12.564 * [taylor]: Taking taylor expansion of k in k 12.564 * [backup-simplify]: Simplify 0 into 0 12.564 * [backup-simplify]: Simplify 1 into 1 12.564 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 12.564 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 12.564 * [taylor]: Taking taylor expansion of 2.0 in k 12.564 * [backup-simplify]: Simplify 2.0 into 2.0 12.564 * [taylor]: Taking taylor expansion of (* n PI) in k 12.564 * [taylor]: Taking taylor expansion of n in k 12.564 * [backup-simplify]: Simplify n into n 12.564 * [taylor]: Taking taylor expansion of PI in k 12.564 * [backup-simplify]: Simplify PI into PI 12.564 * [backup-simplify]: Simplify (* n PI) into (* n PI) 12.564 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 12.564 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 12.564 * [backup-simplify]: Simplify (- 0) into 0 12.565 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.565 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 12.565 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 12.565 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 12.565 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 12.565 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.565 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.565 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.565 * [taylor]: Taking taylor expansion of 0.5 in n 12.565 * [backup-simplify]: Simplify 0.5 into 0.5 12.565 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.565 * [taylor]: Taking taylor expansion of 1.0 in n 12.565 * [backup-simplify]: Simplify 1.0 into 1.0 12.565 * [taylor]: Taking taylor expansion of k in n 12.565 * [backup-simplify]: Simplify k into k 12.565 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.565 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.565 * [taylor]: Taking taylor expansion of 2.0 in n 12.565 * [backup-simplify]: Simplify 2.0 into 2.0 12.565 * [taylor]: Taking taylor expansion of (* n PI) in n 12.565 * [taylor]: Taking taylor expansion of n in n 12.565 * [backup-simplify]: Simplify 0 into 0 12.565 * [backup-simplify]: Simplify 1 into 1 12.565 * [taylor]: Taking taylor expansion of PI in n 12.565 * [backup-simplify]: Simplify PI into PI 12.566 * [backup-simplify]: Simplify (* 0 PI) into 0 12.566 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.567 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.568 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.569 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.569 * [backup-simplify]: Simplify (- k) into (- k) 12.569 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.569 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.570 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.571 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.572 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.572 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 12.572 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 12.572 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 12.572 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 12.572 * [taylor]: Taking taylor expansion of 0.5 in n 12.572 * [backup-simplify]: Simplify 0.5 into 0.5 12.572 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 12.572 * [taylor]: Taking taylor expansion of 1.0 in n 12.572 * [backup-simplify]: Simplify 1.0 into 1.0 12.572 * [taylor]: Taking taylor expansion of k in n 12.572 * [backup-simplify]: Simplify k into k 12.572 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 12.572 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.572 * [taylor]: Taking taylor expansion of 2.0 in n 12.572 * [backup-simplify]: Simplify 2.0 into 2.0 12.572 * [taylor]: Taking taylor expansion of (* n PI) in n 12.572 * [taylor]: Taking taylor expansion of n in n 12.572 * [backup-simplify]: Simplify 0 into 0 12.572 * [backup-simplify]: Simplify 1 into 1 12.572 * [taylor]: Taking taylor expansion of PI in n 12.572 * [backup-simplify]: Simplify PI into PI 12.572 * [backup-simplify]: Simplify (* 0 PI) into 0 12.573 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.573 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.574 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.575 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.575 * [backup-simplify]: Simplify (- k) into (- k) 12.575 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 12.575 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 12.576 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.577 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) 12.577 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 12.578 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 12.578 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 12.578 * [taylor]: Taking taylor expansion of 0.5 in k 12.578 * [backup-simplify]: Simplify 0.5 into 0.5 12.578 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 12.578 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 12.578 * [taylor]: Taking taylor expansion of 1.0 in k 12.578 * [backup-simplify]: Simplify 1.0 into 1.0 12.578 * [taylor]: Taking taylor expansion of k in k 12.578 * [backup-simplify]: Simplify 0 into 0 12.578 * [backup-simplify]: Simplify 1 into 1 12.578 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 12.578 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.578 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.578 * [taylor]: Taking taylor expansion of 2.0 in k 12.578 * [backup-simplify]: Simplify 2.0 into 2.0 12.578 * [taylor]: Taking taylor expansion of PI in k 12.578 * [backup-simplify]: Simplify PI into PI 12.578 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.579 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.579 * [taylor]: Taking taylor expansion of (log n) in k 12.579 * [taylor]: Taking taylor expansion of n in k 12.579 * [backup-simplify]: Simplify n into n 12.579 * [backup-simplify]: Simplify (log n) into (log n) 12.579 * [backup-simplify]: Simplify (- 0) into 0 12.579 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 12.580 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 12.581 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 12.581 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 12.582 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 12.583 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 12.583 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.584 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.585 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.585 * [backup-simplify]: Simplify (- 0) into 0 12.585 * [backup-simplify]: Simplify (+ 0 0) into 0 12.586 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 12.587 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.588 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 12.589 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.589 * [taylor]: Taking taylor expansion of 0 in k 12.589 * [backup-simplify]: Simplify 0 into 0 12.589 * [backup-simplify]: Simplify 0 into 0 12.589 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.590 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.591 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 12.591 * [backup-simplify]: Simplify (+ 0 0) into 0 12.591 * [backup-simplify]: Simplify (- 1) into -1 12.592 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.592 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 12.594 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 12.596 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 12.598 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 12.598 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.599 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.601 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.601 * [backup-simplify]: Simplify (- 0) into 0 12.601 * [backup-simplify]: Simplify (+ 0 0) into 0 12.602 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 12.603 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 12.604 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.605 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.605 * [taylor]: Taking taylor expansion of 0 in k 12.605 * [backup-simplify]: Simplify 0 into 0 12.605 * [backup-simplify]: Simplify 0 into 0 12.605 * [backup-simplify]: Simplify 0 into 0 12.606 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.608 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.609 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 12.609 * [backup-simplify]: Simplify (+ 0 0) into 0 12.609 * [backup-simplify]: Simplify (- 0) into 0 12.610 * [backup-simplify]: Simplify (+ 0 0) into 0 12.611 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 12.613 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 12.616 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 12.619 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 12.625 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 12.626 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 12.626 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 12.626 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 12.626 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 12.626 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 12.626 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 12.626 * [taylor]: Taking taylor expansion of 0.5 in k 12.626 * [backup-simplify]: Simplify 0.5 into 0.5 12.626 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.626 * [taylor]: Taking taylor expansion of 1.0 in k 12.626 * [backup-simplify]: Simplify 1.0 into 1.0 12.626 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.626 * [taylor]: Taking taylor expansion of k in k 12.626 * [backup-simplify]: Simplify 0 into 0 12.626 * [backup-simplify]: Simplify 1 into 1 12.626 * [backup-simplify]: Simplify (/ 1 1) into 1 12.626 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 12.626 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 12.626 * [taylor]: Taking taylor expansion of 2.0 in k 12.626 * [backup-simplify]: Simplify 2.0 into 2.0 12.626 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.626 * [taylor]: Taking taylor expansion of PI in k 12.626 * [backup-simplify]: Simplify PI into PI 12.626 * [taylor]: Taking taylor expansion of n in k 12.626 * [backup-simplify]: Simplify n into n 12.626 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.626 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 12.626 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 12.627 * [backup-simplify]: Simplify (- 1) into -1 12.627 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.627 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 12.627 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 12.628 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) 12.628 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 12.628 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.628 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.628 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 12.628 * [taylor]: Taking taylor expansion of 0.5 in n 12.628 * [backup-simplify]: Simplify 0.5 into 0.5 12.628 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.628 * [taylor]: Taking taylor expansion of 1.0 in n 12.628 * [backup-simplify]: Simplify 1.0 into 1.0 12.628 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.628 * [taylor]: Taking taylor expansion of k in n 12.628 * [backup-simplify]: Simplify k into k 12.628 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.628 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.628 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.628 * [taylor]: Taking taylor expansion of 2.0 in n 12.628 * [backup-simplify]: Simplify 2.0 into 2.0 12.628 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.628 * [taylor]: Taking taylor expansion of PI in n 12.628 * [backup-simplify]: Simplify PI into PI 12.628 * [taylor]: Taking taylor expansion of n in n 12.628 * [backup-simplify]: Simplify 0 into 0 12.628 * [backup-simplify]: Simplify 1 into 1 12.628 * [backup-simplify]: Simplify (/ PI 1) into PI 12.629 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.629 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.629 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.629 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.630 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 12.630 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.631 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 12.632 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.632 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 12.632 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 12.632 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 12.632 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 12.632 * [taylor]: Taking taylor expansion of 0.5 in n 12.632 * [backup-simplify]: Simplify 0.5 into 0.5 12.632 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 12.632 * [taylor]: Taking taylor expansion of 1.0 in n 12.632 * [backup-simplify]: Simplify 1.0 into 1.0 12.632 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.632 * [taylor]: Taking taylor expansion of k in n 12.632 * [backup-simplify]: Simplify k into k 12.632 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.632 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 12.632 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.632 * [taylor]: Taking taylor expansion of 2.0 in n 12.632 * [backup-simplify]: Simplify 2.0 into 2.0 12.632 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.632 * [taylor]: Taking taylor expansion of PI in n 12.632 * [backup-simplify]: Simplify PI into PI 12.632 * [taylor]: Taking taylor expansion of n in n 12.632 * [backup-simplify]: Simplify 0 into 0 12.632 * [backup-simplify]: Simplify 1 into 1 12.633 * [backup-simplify]: Simplify (/ PI 1) into PI 12.633 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.634 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.634 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 12.634 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 12.634 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 12.635 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.636 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 12.637 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.637 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 12.637 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 12.638 * [taylor]: Taking taylor expansion of 0.5 in k 12.638 * [backup-simplify]: Simplify 0.5 into 0.5 12.638 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 12.638 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 12.638 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 12.638 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 12.638 * [taylor]: Taking taylor expansion of 2.0 in k 12.638 * [backup-simplify]: Simplify 2.0 into 2.0 12.638 * [taylor]: Taking taylor expansion of PI in k 12.638 * [backup-simplify]: Simplify PI into PI 12.639 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.640 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 12.640 * [taylor]: Taking taylor expansion of (log n) in k 12.640 * [taylor]: Taking taylor expansion of n in k 12.640 * [backup-simplify]: Simplify n into n 12.640 * [backup-simplify]: Simplify (log n) into (log n) 12.640 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 12.640 * [taylor]: Taking taylor expansion of 1.0 in k 12.640 * [backup-simplify]: Simplify 1.0 into 1.0 12.640 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.640 * [taylor]: Taking taylor expansion of k in k 12.640 * [backup-simplify]: Simplify 0 into 0 12.640 * [backup-simplify]: Simplify 1 into 1 12.640 * [backup-simplify]: Simplify (/ 1 1) into 1 12.641 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.642 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 12.642 * [backup-simplify]: Simplify (- 1) into -1 12.643 * [backup-simplify]: Simplify (+ 0 -1) into -1 12.644 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 12.645 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 12.646 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.648 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 12.649 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.650 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.651 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 12.652 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.652 * [backup-simplify]: Simplify (- 0) into 0 12.652 * [backup-simplify]: Simplify (+ 0 0) into 0 12.653 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 12.655 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.656 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 12.658 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.658 * [taylor]: Taking taylor expansion of 0 in k 12.658 * [backup-simplify]: Simplify 0 into 0 12.658 * [backup-simplify]: Simplify 0 into 0 12.658 * [backup-simplify]: Simplify 0 into 0 12.659 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.660 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.676 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 12.676 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.677 * [backup-simplify]: Simplify (- 0) into 0 12.677 * [backup-simplify]: Simplify (+ 0 0) into 0 12.678 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 12.679 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.681 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 12.684 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.684 * [taylor]: Taking taylor expansion of 0 in k 12.684 * [backup-simplify]: Simplify 0 into 0 12.684 * [backup-simplify]: Simplify 0 into 0 12.684 * [backup-simplify]: Simplify 0 into 0 12.684 * [backup-simplify]: Simplify 0 into 0 12.685 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.686 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.692 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0 12.693 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.693 * [backup-simplify]: Simplify (- 0) into 0 12.694 * [backup-simplify]: Simplify (+ 0 0) into 0 12.695 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 12.696 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 12.698 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 12.701 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.701 * [taylor]: Taking taylor expansion of 0 in k 12.701 * [backup-simplify]: Simplify 0 into 0 12.701 * [backup-simplify]: Simplify 0 into 0 12.703 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 12.704 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 12.704 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 12.704 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 12.704 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 12.704 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 12.704 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 12.704 * [taylor]: Taking taylor expansion of 0.5 in k 12.704 * [backup-simplify]: Simplify 0.5 into 0.5 12.704 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.704 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.704 * [taylor]: Taking taylor expansion of k in k 12.704 * [backup-simplify]: Simplify 0 into 0 12.704 * [backup-simplify]: Simplify 1 into 1 12.704 * [backup-simplify]: Simplify (/ 1 1) into 1 12.704 * [taylor]: Taking taylor expansion of 1.0 in k 12.705 * [backup-simplify]: Simplify 1.0 into 1.0 12.705 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 12.705 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 12.705 * [taylor]: Taking taylor expansion of -2.0 in k 12.705 * [backup-simplify]: Simplify -2.0 into -2.0 12.705 * [taylor]: Taking taylor expansion of (/ PI n) in k 12.705 * [taylor]: Taking taylor expansion of PI in k 12.705 * [backup-simplify]: Simplify PI into PI 12.705 * [taylor]: Taking taylor expansion of n in k 12.705 * [backup-simplify]: Simplify n into n 12.705 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 12.705 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 12.705 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 12.706 * [backup-simplify]: Simplify (+ 1 0) into 1 12.706 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 12.706 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 12.706 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 12.706 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.707 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.707 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.707 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.707 * [taylor]: Taking taylor expansion of 0.5 in n 12.707 * [backup-simplify]: Simplify 0.5 into 0.5 12.707 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.707 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.707 * [taylor]: Taking taylor expansion of k in n 12.707 * [backup-simplify]: Simplify k into k 12.707 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.707 * [taylor]: Taking taylor expansion of 1.0 in n 12.707 * [backup-simplify]: Simplify 1.0 into 1.0 12.707 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.707 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.707 * [taylor]: Taking taylor expansion of -2.0 in n 12.707 * [backup-simplify]: Simplify -2.0 into -2.0 12.707 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.707 * [taylor]: Taking taylor expansion of PI in n 12.707 * [backup-simplify]: Simplify PI into PI 12.707 * [taylor]: Taking taylor expansion of n in n 12.707 * [backup-simplify]: Simplify 0 into 0 12.707 * [backup-simplify]: Simplify 1 into 1 12.708 * [backup-simplify]: Simplify (/ PI 1) into PI 12.708 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.709 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.709 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.709 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.711 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.712 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 12.713 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.713 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 12.713 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 12.714 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 12.714 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 12.714 * [taylor]: Taking taylor expansion of 0.5 in n 12.714 * [backup-simplify]: Simplify 0.5 into 0.5 12.714 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 12.714 * [taylor]: Taking taylor expansion of (/ 1 k) in n 12.714 * [taylor]: Taking taylor expansion of k in n 12.714 * [backup-simplify]: Simplify k into k 12.714 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 12.714 * [taylor]: Taking taylor expansion of 1.0 in n 12.714 * [backup-simplify]: Simplify 1.0 into 1.0 12.714 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 12.714 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.714 * [taylor]: Taking taylor expansion of -2.0 in n 12.714 * [backup-simplify]: Simplify -2.0 into -2.0 12.714 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.714 * [taylor]: Taking taylor expansion of PI in n 12.714 * [backup-simplify]: Simplify PI into PI 12.714 * [taylor]: Taking taylor expansion of n in n 12.714 * [backup-simplify]: Simplify 0 into 0 12.714 * [backup-simplify]: Simplify 1 into 1 12.715 * [backup-simplify]: Simplify (/ PI 1) into PI 12.715 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.716 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.716 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 12.716 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 12.718 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.719 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) 12.720 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.720 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 12.720 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 12.721 * [taylor]: Taking taylor expansion of 0.5 in k 12.721 * [backup-simplify]: Simplify 0.5 into 0.5 12.721 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 12.721 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 12.721 * [taylor]: Taking taylor expansion of (/ 1 k) in k 12.721 * [taylor]: Taking taylor expansion of k in k 12.721 * [backup-simplify]: Simplify 0 into 0 12.721 * [backup-simplify]: Simplify 1 into 1 12.721 * [backup-simplify]: Simplify (/ 1 1) into 1 12.721 * [taylor]: Taking taylor expansion of 1.0 in k 12.721 * [backup-simplify]: Simplify 1.0 into 1.0 12.721 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 12.721 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 12.721 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 12.721 * [taylor]: Taking taylor expansion of -2.0 in k 12.721 * [backup-simplify]: Simplify -2.0 into -2.0 12.721 * [taylor]: Taking taylor expansion of PI in k 12.721 * [backup-simplify]: Simplify PI into PI 12.722 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.723 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 12.723 * [taylor]: Taking taylor expansion of (log n) in k 12.723 * [taylor]: Taking taylor expansion of n in k 12.723 * [backup-simplify]: Simplify n into n 12.723 * [backup-simplify]: Simplify (log n) into (log n) 12.724 * [backup-simplify]: Simplify (+ 1 0) into 1 12.724 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 12.725 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 12.726 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 12.727 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 12.728 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.729 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 12.730 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.731 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 12.733 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 12.733 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 12.734 * [backup-simplify]: Simplify (+ 0 0) into 0 12.734 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 12.736 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.737 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 12.739 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 12.739 * [taylor]: Taking taylor expansion of 0 in k 12.739 * [backup-simplify]: Simplify 0 into 0 12.739 * [backup-simplify]: Simplify 0 into 0 12.739 * [backup-simplify]: Simplify 0 into 0 12.740 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.741 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.745 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0 12.746 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.746 * [backup-simplify]: Simplify (+ 0 0) into 0 12.747 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 12.748 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.751 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 12.753 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 12.753 * [taylor]: Taking taylor expansion of 0 in k 12.753 * [backup-simplify]: Simplify 0 into 0 12.753 * [backup-simplify]: Simplify 0 into 0 12.753 * [backup-simplify]: Simplify 0 into 0 12.753 * [backup-simplify]: Simplify 0 into 0 12.755 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.756 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.762 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0 12.762 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 12.763 * [backup-simplify]: Simplify (+ 0 0) into 0 12.764 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 12.766 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 12.767 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 12.769 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 12.769 * [taylor]: Taking taylor expansion of 0 in k 12.769 * [backup-simplify]: Simplify 0 into 0 12.769 * [backup-simplify]: Simplify 0 into 0 12.770 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 12.770 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1 2 1) 12.770 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 12.770 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 12.771 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.771 * [taylor]: Taking taylor expansion of 2.0 in n 12.771 * [backup-simplify]: Simplify 2.0 into 2.0 12.771 * [taylor]: Taking taylor expansion of (* n PI) in n 12.771 * [taylor]: Taking taylor expansion of n in n 12.771 * [backup-simplify]: Simplify 0 into 0 12.771 * [backup-simplify]: Simplify 1 into 1 12.771 * [taylor]: Taking taylor expansion of PI in n 12.771 * [backup-simplify]: Simplify PI into PI 12.771 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.771 * [taylor]: Taking taylor expansion of 2.0 in n 12.771 * [backup-simplify]: Simplify 2.0 into 2.0 12.771 * [taylor]: Taking taylor expansion of (* n PI) in n 12.771 * [taylor]: Taking taylor expansion of n in n 12.771 * [backup-simplify]: Simplify 0 into 0 12.771 * [backup-simplify]: Simplify 1 into 1 12.771 * [taylor]: Taking taylor expansion of PI in n 12.771 * [backup-simplify]: Simplify PI into PI 12.771 * [backup-simplify]: Simplify (* 0 PI) into 0 12.771 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.771 * [backup-simplify]: Simplify 0 into 0 12.772 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.773 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.774 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.774 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.775 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.775 * [backup-simplify]: Simplify 0 into 0 12.776 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.776 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.776 * [backup-simplify]: Simplify 0 into 0 12.777 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.778 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 12.778 * [backup-simplify]: Simplify 0 into 0 12.779 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.779 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 12.780 * [backup-simplify]: Simplify 0 into 0 12.780 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.781 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 12.781 * [backup-simplify]: Simplify 0 into 0 12.782 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 12.784 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 12.784 * [backup-simplify]: Simplify 0 into 0 12.784 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 12.784 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 12.784 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 12.784 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.784 * [taylor]: Taking taylor expansion of 2.0 in n 12.784 * [backup-simplify]: Simplify 2.0 into 2.0 12.784 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.784 * [taylor]: Taking taylor expansion of PI in n 12.784 * [backup-simplify]: Simplify PI into PI 12.784 * [taylor]: Taking taylor expansion of n in n 12.784 * [backup-simplify]: Simplify 0 into 0 12.784 * [backup-simplify]: Simplify 1 into 1 12.785 * [backup-simplify]: Simplify (/ PI 1) into PI 12.785 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.785 * [taylor]: Taking taylor expansion of 2.0 in n 12.785 * [backup-simplify]: Simplify 2.0 into 2.0 12.785 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.785 * [taylor]: Taking taylor expansion of PI in n 12.785 * [backup-simplify]: Simplify PI into PI 12.785 * [taylor]: Taking taylor expansion of n in n 12.785 * [backup-simplify]: Simplify 0 into 0 12.785 * [backup-simplify]: Simplify 1 into 1 12.785 * [backup-simplify]: Simplify (/ PI 1) into PI 12.786 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.786 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.786 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.787 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.787 * [backup-simplify]: Simplify 0 into 0 12.788 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.788 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.788 * [backup-simplify]: Simplify 0 into 0 12.789 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.789 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.790 * [backup-simplify]: Simplify 0 into 0 12.790 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.791 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.791 * [backup-simplify]: Simplify 0 into 0 12.792 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.792 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.792 * [backup-simplify]: Simplify 0 into 0 12.793 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.794 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.794 * [backup-simplify]: Simplify 0 into 0 12.794 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 12.795 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 12.795 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 12.795 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.795 * [taylor]: Taking taylor expansion of -2.0 in n 12.795 * [backup-simplify]: Simplify -2.0 into -2.0 12.795 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.795 * [taylor]: Taking taylor expansion of PI in n 12.795 * [backup-simplify]: Simplify PI into PI 12.795 * [taylor]: Taking taylor expansion of n in n 12.795 * [backup-simplify]: Simplify 0 into 0 12.795 * [backup-simplify]: Simplify 1 into 1 12.795 * [backup-simplify]: Simplify (/ PI 1) into PI 12.795 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.795 * [taylor]: Taking taylor expansion of -2.0 in n 12.795 * [backup-simplify]: Simplify -2.0 into -2.0 12.795 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.795 * [taylor]: Taking taylor expansion of PI in n 12.795 * [backup-simplify]: Simplify PI into PI 12.795 * [taylor]: Taking taylor expansion of n in n 12.795 * [backup-simplify]: Simplify 0 into 0 12.795 * [backup-simplify]: Simplify 1 into 1 12.796 * [backup-simplify]: Simplify (/ PI 1) into PI 12.797 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.797 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.798 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.799 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 12.799 * [backup-simplify]: Simplify 0 into 0 12.800 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.801 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.801 * [backup-simplify]: Simplify 0 into 0 12.803 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.804 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.804 * [backup-simplify]: Simplify 0 into 0 12.805 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.806 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.806 * [backup-simplify]: Simplify 0 into 0 12.807 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.809 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.809 * [backup-simplify]: Simplify 0 into 0 12.819 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.821 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.821 * [backup-simplify]: Simplify 0 into 0 12.822 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 12.822 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1 2 1) 12.823 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 12.823 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 12.823 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.823 * [taylor]: Taking taylor expansion of 2.0 in n 12.823 * [backup-simplify]: Simplify 2.0 into 2.0 12.823 * [taylor]: Taking taylor expansion of (* n PI) in n 12.823 * [taylor]: Taking taylor expansion of n in n 12.823 * [backup-simplify]: Simplify 0 into 0 12.823 * [backup-simplify]: Simplify 1 into 1 12.823 * [taylor]: Taking taylor expansion of PI in n 12.823 * [backup-simplify]: Simplify PI into PI 12.823 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 12.823 * [taylor]: Taking taylor expansion of 2.0 in n 12.823 * [backup-simplify]: Simplify 2.0 into 2.0 12.823 * [taylor]: Taking taylor expansion of (* n PI) in n 12.823 * [taylor]: Taking taylor expansion of n in n 12.823 * [backup-simplify]: Simplify 0 into 0 12.823 * [backup-simplify]: Simplify 1 into 1 12.823 * [taylor]: Taking taylor expansion of PI in n 12.823 * [backup-simplify]: Simplify PI into PI 12.824 * [backup-simplify]: Simplify (* 0 PI) into 0 12.824 * [backup-simplify]: Simplify (* 2.0 0) into 0 12.824 * [backup-simplify]: Simplify 0 into 0 12.826 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 12.827 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 12.828 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.829 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 12.830 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 12.830 * [backup-simplify]: Simplify 0 into 0 12.831 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 12.833 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 12.833 * [backup-simplify]: Simplify 0 into 0 12.834 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.836 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 12.836 * [backup-simplify]: Simplify 0 into 0 12.837 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.839 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 12.839 * [backup-simplify]: Simplify 0 into 0 12.840 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.842 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 12.842 * [backup-simplify]: Simplify 0 into 0 12.844 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 12.846 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 12.846 * [backup-simplify]: Simplify 0 into 0 12.846 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 12.847 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 12.847 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 12.847 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.847 * [taylor]: Taking taylor expansion of 2.0 in n 12.847 * [backup-simplify]: Simplify 2.0 into 2.0 12.847 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.847 * [taylor]: Taking taylor expansion of PI in n 12.847 * [backup-simplify]: Simplify PI into PI 12.847 * [taylor]: Taking taylor expansion of n in n 12.847 * [backup-simplify]: Simplify 0 into 0 12.847 * [backup-simplify]: Simplify 1 into 1 12.848 * [backup-simplify]: Simplify (/ PI 1) into PI 12.848 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 12.848 * [taylor]: Taking taylor expansion of 2.0 in n 12.848 * [backup-simplify]: Simplify 2.0 into 2.0 12.848 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.848 * [taylor]: Taking taylor expansion of PI in n 12.848 * [backup-simplify]: Simplify PI into PI 12.848 * [taylor]: Taking taylor expansion of n in n 12.848 * [backup-simplify]: Simplify 0 into 0 12.848 * [backup-simplify]: Simplify 1 into 1 12.849 * [backup-simplify]: Simplify (/ PI 1) into PI 12.849 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.850 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 12.851 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.852 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 12.852 * [backup-simplify]: Simplify 0 into 0 12.853 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.854 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.854 * [backup-simplify]: Simplify 0 into 0 12.855 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.857 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.857 * [backup-simplify]: Simplify 0 into 0 12.858 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.859 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.859 * [backup-simplify]: Simplify 0 into 0 12.860 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.862 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.862 * [backup-simplify]: Simplify 0 into 0 12.863 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.865 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.865 * [backup-simplify]: Simplify 0 into 0 12.866 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 12.866 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 12.866 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 12.866 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.866 * [taylor]: Taking taylor expansion of -2.0 in n 12.867 * [backup-simplify]: Simplify -2.0 into -2.0 12.867 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.867 * [taylor]: Taking taylor expansion of PI in n 12.867 * [backup-simplify]: Simplify PI into PI 12.867 * [taylor]: Taking taylor expansion of n in n 12.867 * [backup-simplify]: Simplify 0 into 0 12.867 * [backup-simplify]: Simplify 1 into 1 12.867 * [backup-simplify]: Simplify (/ PI 1) into PI 12.867 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 12.867 * [taylor]: Taking taylor expansion of -2.0 in n 12.867 * [backup-simplify]: Simplify -2.0 into -2.0 12.867 * [taylor]: Taking taylor expansion of (/ PI n) in n 12.867 * [taylor]: Taking taylor expansion of PI in n 12.867 * [backup-simplify]: Simplify PI into PI 12.867 * [taylor]: Taking taylor expansion of n in n 12.867 * [backup-simplify]: Simplify 0 into 0 12.867 * [backup-simplify]: Simplify 1 into 1 12.868 * [backup-simplify]: Simplify (/ PI 1) into PI 12.868 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.869 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 12.870 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 12.871 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 12.871 * [backup-simplify]: Simplify 0 into 0 12.872 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.873 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 12.873 * [backup-simplify]: Simplify 0 into 0 12.874 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.876 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 12.876 * [backup-simplify]: Simplify 0 into 0 12.877 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.878 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 12.879 * [backup-simplify]: Simplify 0 into 0 12.880 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.882 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 12.882 * [backup-simplify]: Simplify 0 into 0 12.884 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 12.886 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 12.886 * [backup-simplify]: Simplify 0 into 0 12.887 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 12.887 * * * [progress]: simplifying candidates 12.890 * [simplify]: Simplifying: (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (* 1 (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1)) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1)) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (pow (* (* 2.0 PI) n) (/ 1 1)) (pow (* (* 2.0 PI) n) 1) (pow (* (* 2.0 PI) n) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (+ (+ (log 2.0) (log PI)) (log n)) (+ (log (* 2.0 PI)) (log n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n)) (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n)) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (sqrt (* (* 2.0 PI) n)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* (* 2.0 PI) 1) (* PI n) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) (* 2.0 (* n PI)) 12.895 * * [simplify]: Extracting # 0 : cost 0 12.895 * * [simplify]: Extracting # 1 : cost 0 12.896 * * [simplify]: Extracting # 2 : cost 0 12.896 * * [simplify]: Extracting # 3 : cost 0 12.896 * * [simplify]: Extracting # 4 : cost 0 12.897 * * [simplify]: Extracting # 5 : cost 0 12.897 * * [simplify]: Extracting # 6 : cost 0 12.898 * * [simplify]: Extracting # 7 : cost 0 12.898 * * [simplify]: Extracting # 8 : cost 0 12.898 * * [simplify]: Extracting # 9 : cost 0 12.899 * * [simplify]: Extracting # 10 : cost 0 12.899 * * [simplify]: Extracting # 11 : cost 0 12.899 * * [simplify]: Extracting # 12 : cost 0 12.900 * * [simplify]: Extracting # 13 : cost 0 12.901 * * [simplify]: iteration 0 : 149 enodes (cost 1624 ) 12.971 * * [simplify]: Extracting # 0 : cost 0 12.972 * * [simplify]: Extracting # 1 : cost 0 12.973 * * [simplify]: Extracting # 2 : cost 0 12.974 * * [simplify]: Extracting # 3 : cost 0 12.983 * * [simplify]: Extracting # 4 : cost 0 12.984 * * [simplify]: Extracting # 5 : cost 0 12.985 * * [simplify]: Extracting # 6 : cost 0 12.986 * * [simplify]: iteration 1 : 428 enodes (cost 1526 ) 13.283 * * [simplify]: Extracting # 0 : cost 0 13.287 * * [simplify]: Extracting # 1 : cost 0 13.292 * * [simplify]: Extracting # 2 : cost 0 13.303 * * [simplify]: Extracting # 3 : cost 0 13.308 * * [simplify]: Extracting # 4 : cost 0 13.313 * * [simplify]: iteration 2 : 2085 enodes (cost 1402 ) 14.285 * * [simplify]: Extracting # 0 : cost 0 14.303 * * [simplify]: Extracting # 1 : cost 0 14.316 * * [simplify]: Extracting # 2 : cost 0 14.329 * * [simplify]: Extracting # 3 : cost 0 14.343 * * [simplify]: Extracting # 4 : cost 0 14.356 * * [simplify]: iteration done: 5001 enodes (cost 1394 ) 14.357 * [simplify]: Simplified to: (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* n (* 2.0 PI)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (pow (* n (* 2.0 PI)) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (/ (- 1.0 k) 2.0) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)) (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0)))) (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* n (* 2.0 PI)) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0))) (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0))) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (pow (* n (* 2.0 PI)) (- 1.0 k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 3) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (sqrt (* (* n PI) 2.0)) (sqrt (* (* n PI) 2.0)) (* (* (cbrt n) (cbrt n)) (* 2.0 PI)) (* (sqrt n) (* 2.0 PI)) (* PI 2.0) (* n PI) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (log (* (* 2.0 PI) n)) (exp (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (pow (* (* 2.0 PI) n) 3) (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* 2.0 PI) n) 3) (sqrt (* (* n PI) 2.0)) (sqrt (* (* n PI) 2.0)) (* (* (cbrt n) (cbrt n)) (* 2.0 PI)) (* (sqrt n) (* 2.0 PI)) (* PI 2.0) (* n PI) (- (+ (+ (* (* 0.125 (pow k 2)) (+ (* (pow (log (* 2.0 PI)) 2) (pow (* (* 2.0 PI) n) 0.5)) (* (pow (log n) 2) (pow (* (* 2.0 PI) n) 0.5)))) (pow (* (* 2.0 PI) n) 0.5)) (* 0.25 (* (* (pow k 2) (* (log n) (pow (* (* 2.0 PI) n) 0.5))) (log (* 2.0 PI))))) (* (* 0.5 k) (+ (* (log n) (pow (* (* 2.0 PI) n) 0.5)) (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.5))))) (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (+ (* (* 0.125 (pow k 2)) (+ (* (pow (log (* 2.0 PI)) 2) (pow (* (* 2.0 PI) n) 0.5)) (* (pow (log n) 2) (pow (* (* 2.0 PI) n) 0.5)))) (pow (* (* 2.0 PI) n) 0.5)) (* 0.25 (* (* (pow k 2) (* (log n) (pow (* (* 2.0 PI) n) 0.5))) (log (* 2.0 PI))))) (* (* 0.5 k) (+ (* (log n) (pow (* (* 2.0 PI) n) 0.5)) (* (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.5))))) (pow (pow (* (* 2.0 PI) n) 0.5) (- 1.0 k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (* n (* 2.0 PI)) (* n (* 2.0 PI)) 14.359 * * * [progress]: adding candidates to table 15.021 * [progress]: [Phase 3 of 3] Extracting. 15.021 * * [regime]: Finding splitpoints for: (# # # # # # # #) 15.026 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 15.026 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # #) 15.099 * * * * [regimes]: Trying to branch on n from (# # # # # # # #) 15.133 * * * * [regimes]: Trying to branch on k from (# # # # # # # #) 15.168 * * * [regime]: Found split indices: #