45.187 * [progress]: [Phase 1 of 3] Setting up. 0.002 * * * [progress]: [1/2] Preparing points 0.144 * * * [progress]: [2/2] Setting up program. 0.149 * [progress]: [Phase 2 of 3] Improving. 0.150 * [simplify]: Simplifying: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 0.150 * * [simplify]: Extracting # 0 : cost 0 0.150 * * [simplify]: Extracting # 1 : cost 0 0.150 * * [simplify]: Extracting # 2 : cost 0 0.150 * * [simplify]: Extracting # 3 : cost 0 0.150 * * [simplify]: Extracting # 4 : cost 0 0.150 * * [simplify]: Extracting # 5 : cost 0 0.150 * * [simplify]: Extracting # 6 : cost 0 0.150 * * [simplify]: Extracting # 7 : cost 0 0.150 * * [simplify]: iteration 0 : 13 enodes (cost 16 ) 0.157 * * [simplify]: Extracting # 0 : cost 0 0.157 * * [simplify]: Extracting # 1 : cost 0 0.157 * * [simplify]: Extracting # 2 : cost 0 0.157 * * [simplify]: Extracting # 3 : cost 0 0.157 * * [simplify]: Extracting # 4 : cost 0 0.157 * * [simplify]: Extracting # 5 : cost 0 0.157 * * [simplify]: iteration 1 : 29 enodes (cost 16 ) 0.169 * * [simplify]: Extracting # 0 : cost 0 0.170 * * [simplify]: Extracting # 1 : cost 0 0.170 * * [simplify]: Extracting # 2 : cost 0 0.170 * * [simplify]: Extracting # 3 : cost 0 0.170 * * [simplify]: Extracting # 4 : cost 0 0.170 * * [simplify]: iteration 2 : 59 enodes (cost 16 ) 0.182 * * [simplify]: Extracting # 0 : cost 0 0.182 * * [simplify]: Extracting # 1 : cost 0 0.182 * * [simplify]: Extracting # 2 : cost 0 0.182 * * [simplify]: Extracting # 3 : cost 0 0.182 * * [simplify]: Extracting # 4 : cost 0 0.182 * * [simplify]: iteration 3 : 120 enodes (cost 16 ) 0.239 * * [simplify]: Extracting # 0 : cost 0 0.239 * * [simplify]: Extracting # 1 : cost 0 0.240 * * [simplify]: Extracting # 2 : cost 0 0.240 * * [simplify]: Extracting # 3 : cost 0 0.240 * * [simplify]: Extracting # 4 : cost 0 0.240 * * [simplify]: iteration 4 : 330 enodes (cost 16 ) 0.476 * * [simplify]: Extracting # 0 : cost 0 0.478 * * [simplify]: Extracting # 1 : cost 0 0.480 * * [simplify]: Extracting # 2 : cost 0 0.481 * * [simplify]: Extracting # 3 : cost 0 0.482 * * [simplify]: Extracting # 4 : cost 0 0.483 * * [simplify]: Extracting # 5 : cost 0 0.485 * * [simplify]: iteration 5 : 1555 enodes (cost 16 ) 1.274 * * [simplify]: Extracting # 0 : cost 0 1.322 * * [simplify]: Extracting # 1 : cost 0 1.329 * * [simplify]: Extracting # 2 : cost 0 1.335 * * [simplify]: Extracting # 3 : cost 0 1.349 * * [simplify]: Extracting # 4 : cost 0 1.360 * * [simplify]: iteration done: 5001 enodes (cost 16 ) 1.360 * [simplify]: Simplified to: (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1.361 * * [progress]: iteration 1 / 4 1.361 * * * [progress]: picking best candidate 1.366 * * * * [pick]: Picked # 1.366 * * * [progress]: localizing error 1.398 * * * [progress]: generating rewritten candidates 1.399 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2) 1.443 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1) 1.489 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1) 1.502 * * * * [progress]: [ 4 / 4 ] rewriting at (2) 1.582 * * * [progress]: generating series expansions 1.582 * * * * [progress]: [ 1 / 4 ] generating series at (2 2) 1.583 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 1.583 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 1.583 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.583 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.583 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.583 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.583 * [taylor]: Taking taylor expansion of 0.5 in k 1.583 * [backup-simplify]: Simplify 0.5 into 0.5 1.583 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.583 * [taylor]: Taking taylor expansion of 1.0 in k 1.583 * [backup-simplify]: Simplify 1.0 into 1.0 1.583 * [taylor]: Taking taylor expansion of k in k 1.583 * [backup-simplify]: Simplify 0 into 0 1.583 * [backup-simplify]: Simplify 1 into 1 1.583 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.583 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.583 * [taylor]: Taking taylor expansion of 2.0 in k 1.583 * [backup-simplify]: Simplify 2.0 into 2.0 1.583 * [taylor]: Taking taylor expansion of (* n PI) in k 1.583 * [taylor]: Taking taylor expansion of n in k 1.583 * [backup-simplify]: Simplify n into n 1.583 * [taylor]: Taking taylor expansion of PI in k 1.583 * [backup-simplify]: Simplify PI into PI 1.583 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.583 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.583 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.584 * [backup-simplify]: Simplify (- 0) into 0 1.584 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.584 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.584 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.584 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.584 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.584 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.584 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.584 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.584 * [taylor]: Taking taylor expansion of 0.5 in n 1.584 * [backup-simplify]: Simplify 0.5 into 0.5 1.584 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.585 * [taylor]: Taking taylor expansion of 1.0 in n 1.585 * [backup-simplify]: Simplify 1.0 into 1.0 1.585 * [taylor]: Taking taylor expansion of k in n 1.585 * [backup-simplify]: Simplify k into k 1.585 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.585 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.585 * [taylor]: Taking taylor expansion of 2.0 in n 1.585 * [backup-simplify]: Simplify 2.0 into 2.0 1.585 * [taylor]: Taking taylor expansion of (* n PI) in n 1.585 * [taylor]: Taking taylor expansion of n in n 1.585 * [backup-simplify]: Simplify 0 into 0 1.585 * [backup-simplify]: Simplify 1 into 1 1.585 * [taylor]: Taking taylor expansion of PI in n 1.585 * [backup-simplify]: Simplify PI into PI 1.585 * [backup-simplify]: Simplify (* 0 PI) into 0 1.585 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.586 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.587 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.588 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.588 * [backup-simplify]: Simplify (- k) into (- k) 1.588 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.588 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.589 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.590 * [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)))) 1.591 * [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))))) 1.591 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.591 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.591 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.591 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.591 * [taylor]: Taking taylor expansion of 0.5 in n 1.591 * [backup-simplify]: Simplify 0.5 into 0.5 1.591 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.591 * [taylor]: Taking taylor expansion of 1.0 in n 1.591 * [backup-simplify]: Simplify 1.0 into 1.0 1.591 * [taylor]: Taking taylor expansion of k in n 1.591 * [backup-simplify]: Simplify k into k 1.591 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.591 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.591 * [taylor]: Taking taylor expansion of 2.0 in n 1.591 * [backup-simplify]: Simplify 2.0 into 2.0 1.591 * [taylor]: Taking taylor expansion of (* n PI) in n 1.591 * [taylor]: Taking taylor expansion of n in n 1.591 * [backup-simplify]: Simplify 0 into 0 1.591 * [backup-simplify]: Simplify 1 into 1 1.591 * [taylor]: Taking taylor expansion of PI in n 1.591 * [backup-simplify]: Simplify PI into PI 1.591 * [backup-simplify]: Simplify (* 0 PI) into 0 1.591 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.592 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.593 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.594 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.594 * [backup-simplify]: Simplify (- k) into (- k) 1.594 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.594 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.599 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.600 * [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)))) 1.601 * [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))))) 1.601 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 1.601 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 1.601 * [taylor]: Taking taylor expansion of 0.5 in k 1.601 * [backup-simplify]: Simplify 0.5 into 0.5 1.601 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 1.601 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.601 * [taylor]: Taking taylor expansion of 1.0 in k 1.601 * [backup-simplify]: Simplify 1.0 into 1.0 1.601 * [taylor]: Taking taylor expansion of k in k 1.601 * [backup-simplify]: Simplify 0 into 0 1.601 * [backup-simplify]: Simplify 1 into 1 1.601 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 1.601 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.601 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.601 * [taylor]: Taking taylor expansion of 2.0 in k 1.601 * [backup-simplify]: Simplify 2.0 into 2.0 1.601 * [taylor]: Taking taylor expansion of PI in k 1.601 * [backup-simplify]: Simplify PI into PI 1.602 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.602 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.602 * [taylor]: Taking taylor expansion of (log n) in k 1.602 * [taylor]: Taking taylor expansion of n in k 1.602 * [backup-simplify]: Simplify n into n 1.602 * [backup-simplify]: Simplify (log n) into (log n) 1.603 * [backup-simplify]: Simplify (- 0) into 0 1.603 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.604 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 1.604 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 1.605 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 1.606 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.607 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 1.607 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.608 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.609 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.609 * [backup-simplify]: Simplify (- 0) into 0 1.609 * [backup-simplify]: Simplify (+ 0 0) into 0 1.610 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 1.611 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.611 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 1.613 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.613 * [taylor]: Taking taylor expansion of 0 in k 1.613 * [backup-simplify]: Simplify 0 into 0 1.613 * [backup-simplify]: Simplify 0 into 0 1.613 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.614 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.615 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 1.615 * [backup-simplify]: Simplify (+ 0 0) into 0 1.615 * [backup-simplify]: Simplify (- 1) into -1 1.615 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.616 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 1.618 * [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)))))) 1.622 * [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)))))) 1.623 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.623 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.625 * [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 1.626 * [backup-simplify]: Simplify (- 0) into 0 1.626 * [backup-simplify]: Simplify (+ 0 0) into 0 1.627 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 1.628 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.629 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.630 * [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 1.630 * [taylor]: Taking taylor expansion of 0 in k 1.630 * [backup-simplify]: Simplify 0 into 0 1.630 * [backup-simplify]: Simplify 0 into 0 1.630 * [backup-simplify]: Simplify 0 into 0 1.631 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.633 * [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 1.634 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 1.634 * [backup-simplify]: Simplify (+ 0 0) into 0 1.634 * [backup-simplify]: Simplify (- 0) into 0 1.635 * [backup-simplify]: Simplify (+ 0 0) into 0 1.636 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 1.638 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 1.640 * [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)))))) 1.643 * [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)))))) 1.650 * [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)))))) 1.650 * [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)))) 1.650 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 1.650 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 1.650 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 1.650 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 1.650 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 1.650 * [taylor]: Taking taylor expansion of 0.5 in k 1.650 * [backup-simplify]: Simplify 0.5 into 0.5 1.650 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.650 * [taylor]: Taking taylor expansion of 1.0 in k 1.650 * [backup-simplify]: Simplify 1.0 into 1.0 1.650 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.650 * [taylor]: Taking taylor expansion of k in k 1.651 * [backup-simplify]: Simplify 0 into 0 1.651 * [backup-simplify]: Simplify 1 into 1 1.651 * [backup-simplify]: Simplify (/ 1 1) into 1 1.651 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 1.651 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 1.651 * [taylor]: Taking taylor expansion of 2.0 in k 1.651 * [backup-simplify]: Simplify 2.0 into 2.0 1.651 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.651 * [taylor]: Taking taylor expansion of PI in k 1.651 * [backup-simplify]: Simplify PI into PI 1.651 * [taylor]: Taking taylor expansion of n in k 1.651 * [backup-simplify]: Simplify n into n 1.651 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.651 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 1.651 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 1.651 * [backup-simplify]: Simplify (- 1) into -1 1.652 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.652 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 1.652 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 1.652 * [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))))) 1.652 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.652 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.652 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.652 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.652 * [taylor]: Taking taylor expansion of 0.5 in n 1.652 * [backup-simplify]: Simplify 0.5 into 0.5 1.652 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.652 * [taylor]: Taking taylor expansion of 1.0 in n 1.652 * [backup-simplify]: Simplify 1.0 into 1.0 1.652 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.652 * [taylor]: Taking taylor expansion of k in n 1.652 * [backup-simplify]: Simplify k into k 1.653 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.653 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.653 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.653 * [taylor]: Taking taylor expansion of 2.0 in n 1.653 * [backup-simplify]: Simplify 2.0 into 2.0 1.653 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.653 * [taylor]: Taking taylor expansion of PI in n 1.653 * [backup-simplify]: Simplify PI into PI 1.653 * [taylor]: Taking taylor expansion of n in n 1.653 * [backup-simplify]: Simplify 0 into 0 1.653 * [backup-simplify]: Simplify 1 into 1 1.653 * [backup-simplify]: Simplify (/ PI 1) into PI 1.653 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.654 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.654 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.654 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.654 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.655 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.656 * [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)))) 1.657 * [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))))) 1.657 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 1.657 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 1.657 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 1.657 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 1.657 * [taylor]: Taking taylor expansion of 0.5 in n 1.657 * [backup-simplify]: Simplify 0.5 into 0.5 1.657 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 1.657 * [taylor]: Taking taylor expansion of 1.0 in n 1.657 * [backup-simplify]: Simplify 1.0 into 1.0 1.657 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.657 * [taylor]: Taking taylor expansion of k in n 1.657 * [backup-simplify]: Simplify k into k 1.657 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.657 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 1.657 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.657 * [taylor]: Taking taylor expansion of 2.0 in n 1.657 * [backup-simplify]: Simplify 2.0 into 2.0 1.657 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.657 * [taylor]: Taking taylor expansion of PI in n 1.657 * [backup-simplify]: Simplify PI into PI 1.657 * [taylor]: Taking taylor expansion of n in n 1.657 * [backup-simplify]: Simplify 0 into 0 1.657 * [backup-simplify]: Simplify 1 into 1 1.657 * [backup-simplify]: Simplify (/ PI 1) into PI 1.658 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.659 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.659 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 1.659 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 1.659 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 1.661 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.662 * [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)))) 1.663 * [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))))) 1.664 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 1.664 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 1.664 * [taylor]: Taking taylor expansion of 0.5 in k 1.664 * [backup-simplify]: Simplify 0.5 into 0.5 1.664 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 1.664 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 1.664 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 1.664 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 1.664 * [taylor]: Taking taylor expansion of 2.0 in k 1.664 * [backup-simplify]: Simplify 2.0 into 2.0 1.664 * [taylor]: Taking taylor expansion of PI in k 1.664 * [backup-simplify]: Simplify PI into PI 1.664 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.665 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.665 * [taylor]: Taking taylor expansion of (log n) in k 1.666 * [taylor]: Taking taylor expansion of n in k 1.666 * [backup-simplify]: Simplify n into n 1.666 * [backup-simplify]: Simplify (log n) into (log n) 1.666 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 1.666 * [taylor]: Taking taylor expansion of 1.0 in k 1.666 * [backup-simplify]: Simplify 1.0 into 1.0 1.666 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.666 * [taylor]: Taking taylor expansion of k in k 1.666 * [backup-simplify]: Simplify 0 into 0 1.666 * [backup-simplify]: Simplify 1 into 1 1.666 * [backup-simplify]: Simplify (/ 1 1) into 1 1.666 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.667 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 1.668 * [backup-simplify]: Simplify (- 1) into -1 1.668 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.669 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 1.671 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 1.672 * [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))))) 1.673 * [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))))) 1.674 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.675 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.677 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 1.678 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.678 * [backup-simplify]: Simplify (- 0) into 0 1.678 * [backup-simplify]: Simplify (+ 0 0) into 0 1.679 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 1.681 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.682 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 1.684 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.684 * [taylor]: Taking taylor expansion of 0 in k 1.684 * [backup-simplify]: Simplify 0 into 0 1.684 * [backup-simplify]: Simplify 0 into 0 1.684 * [backup-simplify]: Simplify 0 into 0 1.686 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.687 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.690 * [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 1.691 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.691 * [backup-simplify]: Simplify (- 0) into 0 1.691 * [backup-simplify]: Simplify (+ 0 0) into 0 1.692 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 1.694 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 1.696 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 1.698 * [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 1.698 * [taylor]: Taking taylor expansion of 0 in k 1.698 * [backup-simplify]: Simplify 0 into 0 1.698 * [backup-simplify]: Simplify 0 into 0 1.698 * [backup-simplify]: Simplify 0 into 0 1.698 * [backup-simplify]: Simplify 0 into 0 1.700 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.701 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.707 * [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 1.708 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.708 * [backup-simplify]: Simplify (- 0) into 0 1.709 * [backup-simplify]: Simplify (+ 0 0) into 0 1.710 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 1.712 * [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 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 1.725 * [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 1.725 * [taylor]: Taking taylor expansion of 0 in k 1.725 * [backup-simplify]: Simplify 0 into 0 1.725 * [backup-simplify]: Simplify 0 into 0 1.726 * [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)))) 1.727 * [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))) 1.727 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 1.727 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 1.727 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 1.728 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 1.728 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 1.728 * [taylor]: Taking taylor expansion of 0.5 in k 1.728 * [backup-simplify]: Simplify 0.5 into 0.5 1.728 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 1.728 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.728 * [taylor]: Taking taylor expansion of k in k 1.728 * [backup-simplify]: Simplify 0 into 0 1.728 * [backup-simplify]: Simplify 1 into 1 1.728 * [backup-simplify]: Simplify (/ 1 1) into 1 1.728 * [taylor]: Taking taylor expansion of 1.0 in k 1.728 * [backup-simplify]: Simplify 1.0 into 1.0 1.728 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 1.728 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 1.728 * [taylor]: Taking taylor expansion of -2.0 in k 1.728 * [backup-simplify]: Simplify -2.0 into -2.0 1.728 * [taylor]: Taking taylor expansion of (/ PI n) in k 1.728 * [taylor]: Taking taylor expansion of PI in k 1.728 * [backup-simplify]: Simplify PI into PI 1.729 * [taylor]: Taking taylor expansion of n in k 1.729 * [backup-simplify]: Simplify n into n 1.729 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 1.729 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 1.729 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 1.729 * [backup-simplify]: Simplify (+ 1 0) into 1 1.730 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 1.730 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 1.730 * [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)))))) 1.730 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.730 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.730 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.730 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.730 * [taylor]: Taking taylor expansion of 0.5 in n 1.730 * [backup-simplify]: Simplify 0.5 into 0.5 1.730 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.731 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.731 * [taylor]: Taking taylor expansion of k in n 1.731 * [backup-simplify]: Simplify k into k 1.731 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.731 * [taylor]: Taking taylor expansion of 1.0 in n 1.731 * [backup-simplify]: Simplify 1.0 into 1.0 1.731 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.731 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.731 * [taylor]: Taking taylor expansion of -2.0 in n 1.731 * [backup-simplify]: Simplify -2.0 into -2.0 1.731 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.731 * [taylor]: Taking taylor expansion of PI in n 1.731 * [backup-simplify]: Simplify PI into PI 1.731 * [taylor]: Taking taylor expansion of n in n 1.731 * [backup-simplify]: Simplify 0 into 0 1.731 * [backup-simplify]: Simplify 1 into 1 1.732 * [backup-simplify]: Simplify (/ PI 1) into PI 1.732 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.733 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.733 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.733 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.735 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.736 * [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)))) 1.738 * [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))))) 1.738 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 1.738 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 1.738 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 1.738 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 1.738 * [taylor]: Taking taylor expansion of 0.5 in n 1.738 * [backup-simplify]: Simplify 0.5 into 0.5 1.738 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 1.738 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.738 * [taylor]: Taking taylor expansion of k in n 1.738 * [backup-simplify]: Simplify k into k 1.738 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.738 * [taylor]: Taking taylor expansion of 1.0 in n 1.738 * [backup-simplify]: Simplify 1.0 into 1.0 1.738 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 1.738 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.738 * [taylor]: Taking taylor expansion of -2.0 in n 1.738 * [backup-simplify]: Simplify -2.0 into -2.0 1.738 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.738 * [taylor]: Taking taylor expansion of PI in n 1.738 * [backup-simplify]: Simplify PI into PI 1.738 * [taylor]: Taking taylor expansion of n in n 1.738 * [backup-simplify]: Simplify 0 into 0 1.738 * [backup-simplify]: Simplify 1 into 1 1.739 * [backup-simplify]: Simplify (/ PI 1) into PI 1.739 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.741 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.741 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 1.741 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 1.742 * [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 1.746 * [backup-simplify]: Simplify 1 into 1 1.746 * [backup-simplify]: Simplify (/ 1 1) into 1 1.746 * [taylor]: Taking taylor expansion of 1.0 in k 1.746 * [backup-simplify]: Simplify 1.0 into 1.0 1.746 * [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 1.747 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.748 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 1.748 * [taylor]: Taking taylor expansion of (log n) in k 1.748 * [taylor]: Taking taylor expansion of n in k 1.748 * [backup-simplify]: Simplify n into n 1.748 * [backup-simplify]: Simplify (log n) into (log n) 1.749 * [backup-simplify]: Simplify (+ 1 0) into 1 1.749 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 1.750 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 1.751 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 1.752 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 1.754 * [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))))) 1.755 * [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))))) 1.756 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.757 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.759 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 1.759 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.759 * [backup-simplify]: Simplify (+ 0 0) into 0 1.760 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 1.761 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.763 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 1.765 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 1.765 * [taylor]: Taking taylor expansion of 0 in k 1.765 * [backup-simplify]: Simplify 0 into 0 1.765 * [backup-simplify]: Simplify 0 into 0 1.765 * [backup-simplify]: Simplify 0 into 0 1.766 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.767 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.771 * [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 1.771 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.772 * [backup-simplify]: Simplify (+ 0 0) into 0 1.773 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 1.774 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.776 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 1.779 * [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 1.779 * [taylor]: Taking taylor expansion of 0 in k 1.779 * [backup-simplify]: Simplify 0 into 0 1.779 * [backup-simplify]: Simplify 0 into 0 1.779 * [backup-simplify]: Simplify 0 into 0 1.779 * [backup-simplify]: Simplify 0 into 0 1.780 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.782 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.788 * [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 1.788 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 1.789 * [backup-simplify]: Simplify (+ 0 0) into 0 1.790 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 1.792 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 1.794 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 1.797 * [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 1.797 * [taylor]: Taking taylor expansion of 0 in k 1.797 * [backup-simplify]: Simplify 0 into 0 1.797 * [backup-simplify]: Simplify 0 into 0 1.798 * [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)))))) 1.799 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1) 1.799 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.799 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 1.799 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.799 * [taylor]: Taking taylor expansion of 2.0 in n 1.799 * [backup-simplify]: Simplify 2.0 into 2.0 1.799 * [taylor]: Taking taylor expansion of (* n PI) in n 1.799 * [taylor]: Taking taylor expansion of n in n 1.799 * [backup-simplify]: Simplify 0 into 0 1.799 * [backup-simplify]: Simplify 1 into 1 1.799 * [taylor]: Taking taylor expansion of PI in n 1.799 * [backup-simplify]: Simplify PI into PI 1.799 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.799 * [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 (* n PI) in n 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 * [taylor]: Taking taylor expansion of PI in n 1.800 * [backup-simplify]: Simplify PI into PI 1.800 * [backup-simplify]: Simplify (* 0 PI) into 0 1.801 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.801 * [backup-simplify]: Simplify 0 into 0 1.802 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.804 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.805 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.806 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 1.807 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 1.807 * [backup-simplify]: Simplify 0 into 0 1.808 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 1.810 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 1.810 * [backup-simplify]: Simplify 0 into 0 1.811 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.813 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 1.813 * [backup-simplify]: Simplify 0 into 0 1.814 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.816 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 1.816 * [backup-simplify]: Simplify 0 into 0 1.818 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.820 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 1.820 * [backup-simplify]: Simplify 0 into 0 1.822 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 1.824 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 1.824 * [backup-simplify]: Simplify 0 into 0 1.824 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 1.825 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 1.825 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 1.825 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.825 * [taylor]: Taking taylor expansion of 2.0 in n 1.825 * [backup-simplify]: Simplify 2.0 into 2.0 1.825 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.825 * [taylor]: Taking taylor expansion of PI in n 1.825 * [backup-simplify]: Simplify PI into PI 1.825 * [taylor]: Taking taylor expansion of n in n 1.825 * [backup-simplify]: Simplify 0 into 0 1.825 * [backup-simplify]: Simplify 1 into 1 1.826 * [backup-simplify]: Simplify (/ PI 1) into PI 1.826 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 1.826 * [taylor]: Taking taylor expansion of 2.0 in n 1.826 * [backup-simplify]: Simplify 2.0 into 2.0 1.826 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.826 * [taylor]: Taking taylor expansion of PI in n 1.826 * [backup-simplify]: Simplify PI into PI 1.826 * [taylor]: Taking taylor expansion of n in n 1.826 * [backup-simplify]: Simplify 0 into 0 1.826 * [backup-simplify]: Simplify 1 into 1 1.826 * [backup-simplify]: Simplify (/ PI 1) into PI 1.827 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.827 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 1.828 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.828 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 1.828 * [backup-simplify]: Simplify 0 into 0 1.829 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.830 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.830 * [backup-simplify]: Simplify 0 into 0 1.830 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.831 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.831 * [backup-simplify]: Simplify 0 into 0 1.832 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.832 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.832 * [backup-simplify]: Simplify 0 into 0 1.833 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.834 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.834 * [backup-simplify]: Simplify 0 into 0 1.835 * [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 1.835 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.836 * [backup-simplify]: Simplify 0 into 0 1.836 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 1.836 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 1.836 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 1.836 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.836 * [taylor]: Taking taylor expansion of -2.0 in n 1.836 * [backup-simplify]: Simplify -2.0 into -2.0 1.836 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.836 * [taylor]: Taking taylor expansion of PI in n 1.836 * [backup-simplify]: Simplify PI into PI 1.836 * [taylor]: Taking taylor expansion of n in n 1.836 * [backup-simplify]: Simplify 0 into 0 1.837 * [backup-simplify]: Simplify 1 into 1 1.837 * [backup-simplify]: Simplify (/ PI 1) into PI 1.837 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 1.837 * [taylor]: Taking taylor expansion of -2.0 in n 1.837 * [backup-simplify]: Simplify -2.0 into -2.0 1.837 * [taylor]: Taking taylor expansion of (/ PI n) in n 1.837 * [taylor]: Taking taylor expansion of PI in n 1.837 * [backup-simplify]: Simplify PI into PI 1.837 * [taylor]: Taking taylor expansion of n in n 1.837 * [backup-simplify]: Simplify 0 into 0 1.837 * [backup-simplify]: Simplify 1 into 1 1.837 * [backup-simplify]: Simplify (/ PI 1) into PI 1.838 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.838 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 1.839 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 1.839 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 1.839 * [backup-simplify]: Simplify 0 into 0 1.840 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.840 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 1.840 * [backup-simplify]: Simplify 0 into 0 1.841 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.842 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 1.842 * [backup-simplify]: Simplify 0 into 0 1.842 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.843 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 1.843 * [backup-simplify]: Simplify 0 into 0 1.844 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.845 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 1.845 * [backup-simplify]: Simplify 0 into 0 1.845 * [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 1.846 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 1.846 * [backup-simplify]: Simplify 0 into 0 1.847 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 1.847 * * * * [progress]: [ 3 / 4 ] generating series at (2 1) 1.847 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k))) 1.847 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0 1.847 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 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 (/ 1 k)) in k 1.847 * [taylor]: Taking taylor expansion of (/ 1 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 (/ 1 1) into 1 1.848 * [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 (/ 1 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 (/ 1 k)) in k 1.849 * [taylor]: Taking taylor expansion of (/ 1 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 (/ 1 1) into 1 1.849 * [backup-simplify]: Simplify (sqrt 0) into 0 1.850 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.850 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.850 * [backup-simplify]: Simplify 0 into 0 1.851 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 1.851 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.852 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1.854 * [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) 1.856 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.857 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.869 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.871 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 1.872 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.873 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0))))) 1.874 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k)) 1.874 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0 1.874 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.874 * [taylor]: Taking taylor expansion of 1.0 in k 1.874 * [backup-simplify]: Simplify 1.0 into 1.0 1.874 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.874 * [taylor]: Taking taylor expansion of k in k 1.874 * [backup-simplify]: Simplify 0 into 0 1.874 * [backup-simplify]: Simplify 1 into 1 1.874 * [backup-simplify]: Simplify (sqrt 0) into 0 1.875 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.875 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k 1.875 * [taylor]: Taking taylor expansion of 1.0 in k 1.875 * [backup-simplify]: Simplify 1.0 into 1.0 1.875 * [taylor]: Taking taylor expansion of (sqrt k) in k 1.875 * [taylor]: Taking taylor expansion of k in k 1.875 * [backup-simplify]: Simplify 0 into 0 1.875 * [backup-simplify]: Simplify 1 into 1 1.875 * [backup-simplify]: Simplify (sqrt 0) into 0 1.876 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.876 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.876 * [backup-simplify]: Simplify 0 into 0 1.877 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0) 1.878 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.880 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.881 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0) 1.881 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.884 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.885 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0) 1.885 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.886 * [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)))))))) 1.886 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k))) 1.886 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0 1.886 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k 1.886 * [taylor]: Taking taylor expansion of 1.0 in k 1.886 * [backup-simplify]: Simplify 1.0 into 1.0 1.887 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 1.887 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.887 * [taylor]: Taking taylor expansion of -1 in k 1.887 * [backup-simplify]: Simplify -1 into -1 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 * [backup-simplify]: Simplify (/ -1 1) into -1 1.887 * [backup-simplify]: Simplify (sqrt 0) into 0 1.888 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 1.888 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 1.888 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 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)) in k 1.888 * [taylor]: Taking taylor expansion of (/ -1 k) in k 1.888 * [taylor]: Taking taylor expansion of -1 in k 1.888 * [backup-simplify]: Simplify -1 into -1 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 1.889 * [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 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0 1.890 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.891 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 1.893 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.894 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0) 1.895 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.895 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 1.897 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 1.900 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0) 1.900 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0) 1.901 * [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))))) 1.901 * * * * [progress]: [ 4 / 4 ] generating series at (2) 1.902 * [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))))) 1.902 * [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 1.902 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n 1.902 * [taylor]: Taking taylor expansion of 1.0 in n 1.902 * [backup-simplify]: Simplify 1.0 into 1.0 1.902 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n 1.902 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 1.902 * [taylor]: Taking taylor expansion of (/ 1 k) in n 1.902 * [taylor]: Taking taylor expansion of k in n 1.902 * [backup-simplify]: Simplify k into k 1.902 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 1.902 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 1.902 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 1.902 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 1.902 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 1.902 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 1.902 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 1.902 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 1.902 * [taylor]: Taking taylor expansion of 0.5 in n 1.902 * [backup-simplify]: Simplify 0.5 into 0.5 1.902 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 1.902 * [taylor]: Taking taylor expansion of 1.0 in n 1.902 * [backup-simplify]: Simplify 1.0 into 1.0 1.902 * [taylor]: Taking taylor expansion of k in n 1.902 * [backup-simplify]: Simplify k into k 1.902 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.902 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.902 * [taylor]: Taking taylor expansion of 2.0 in n 1.902 * [backup-simplify]: Simplify 2.0 into 2.0 1.902 * [taylor]: Taking taylor expansion of (* n PI) in n 1.902 * [taylor]: Taking taylor expansion of n in n 1.902 * [backup-simplify]: Simplify 0 into 0 1.902 * [backup-simplify]: Simplify 1 into 1 1.902 * [taylor]: Taking taylor expansion of PI in n 1.902 * [backup-simplify]: Simplify PI into PI 1.903 * [backup-simplify]: Simplify (* 0 PI) into 0 1.903 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.904 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.905 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.906 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 1.906 * [backup-simplify]: Simplify (- k) into (- k) 1.906 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 1.906 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 1.907 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 1.907 * [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)))) 1.908 * [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))))) 1.908 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 1.908 * [taylor]: Taking taylor expansion of 1.0 in k 1.908 * [backup-simplify]: Simplify 1.0 into 1.0 1.908 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 1.908 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.908 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.908 * [taylor]: Taking taylor expansion of k in k 1.908 * [backup-simplify]: Simplify 0 into 0 1.908 * [backup-simplify]: Simplify 1 into 1 1.909 * [backup-simplify]: Simplify (/ 1 1) into 1 1.909 * [backup-simplify]: Simplify (sqrt 0) into 0 1.910 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.910 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.910 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.910 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.910 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.910 * [taylor]: Taking taylor expansion of 0.5 in k 1.910 * [backup-simplify]: Simplify 0.5 into 0.5 1.910 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.910 * [taylor]: Taking taylor expansion of 1.0 in k 1.910 * [backup-simplify]: Simplify 1.0 into 1.0 1.910 * [taylor]: Taking taylor expansion of k in k 1.910 * [backup-simplify]: Simplify 0 into 0 1.910 * [backup-simplify]: Simplify 1 into 1 1.910 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.910 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.910 * [taylor]: Taking taylor expansion of 2.0 in k 1.910 * [backup-simplify]: Simplify 2.0 into 2.0 1.910 * [taylor]: Taking taylor expansion of (* n PI) in k 1.910 * [taylor]: Taking taylor expansion of n in k 1.910 * [backup-simplify]: Simplify n into n 1.910 * [taylor]: Taking taylor expansion of PI in k 1.910 * [backup-simplify]: Simplify PI into PI 1.911 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.911 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.911 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.911 * [backup-simplify]: Simplify (- 0) into 0 1.912 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.912 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.912 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.912 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.912 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k 1.912 * [taylor]: Taking taylor expansion of 1.0 in k 1.912 * [backup-simplify]: Simplify 1.0 into 1.0 1.912 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k 1.913 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 1.913 * [taylor]: Taking taylor expansion of (/ 1 k) in k 1.913 * [taylor]: Taking taylor expansion of k in k 1.913 * [backup-simplify]: Simplify 0 into 0 1.913 * [backup-simplify]: Simplify 1 into 1 1.913 * [backup-simplify]: Simplify (/ 1 1) into 1 1.913 * [backup-simplify]: Simplify (sqrt 0) into 0 1.915 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 1.915 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 1.915 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 1.915 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 1.915 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 1.915 * [taylor]: Taking taylor expansion of 0.5 in k 1.915 * [backup-simplify]: Simplify 0.5 into 0.5 1.915 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 1.915 * [taylor]: Taking taylor expansion of 1.0 in k 1.915 * [backup-simplify]: Simplify 1.0 into 1.0 1.915 * [taylor]: Taking taylor expansion of k in k 1.915 * [backup-simplify]: Simplify 0 into 0 1.915 * [backup-simplify]: Simplify 1 into 1 1.915 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 1.915 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 1.915 * [taylor]: Taking taylor expansion of 2.0 in k 1.915 * [backup-simplify]: Simplify 2.0 into 2.0 1.915 * [taylor]: Taking taylor expansion of (* n PI) in k 1.915 * [taylor]: Taking taylor expansion of n in k 1.915 * [backup-simplify]: Simplify n into n 1.915 * [taylor]: Taking taylor expansion of PI in k 1.915 * [backup-simplify]: Simplify PI into PI 1.915 * [backup-simplify]: Simplify (* n PI) into (* n PI) 1.916 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 1.916 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 1.916 * [backup-simplify]: Simplify (- 0) into 0 1.917 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 1.917 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 1.917 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 1.917 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 1.918 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0 1.918 * [backup-simplify]: Simplify (* 1.0 0) into 0 1.918 * [taylor]: Taking taylor expansion of 0 in n 1.918 * [backup-simplify]: Simplify 0 into 0 1.918 * [backup-simplify]: Simplify 0 into 0 1.919 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0 1.919 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0 1.920 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0 1.921 * [backup-simplify]: Simplify (- 1) into -1 1.921 * [backup-simplify]: Simplify (+ 0 -1) into -1 1.923 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5) 1.924 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI))))) 1.924 * [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))) 1.926 * [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))) 1.928 * [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))) 1.928 * [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 1.928 * [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 1.928 * [taylor]: Taking taylor expansion of +nan.0 in n 1.928 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.928 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 1.928 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 1.928 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 1.928 * [taylor]: Taking taylor expansion of 0.5 in n 1.929 * [backup-simplify]: Simplify 0.5 into 0.5 1.929 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 1.929 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 1.929 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 1.929 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 1.929 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 1.929 * [taylor]: Taking taylor expansion of 1.0 in n 1.929 * [backup-simplify]: Simplify 1.0 into 1.0 1.929 * [taylor]: Taking taylor expansion of (log PI) in n 1.929 * [taylor]: Taking taylor expansion of PI in n 1.929 * [backup-simplify]: Simplify PI into PI 1.929 * [backup-simplify]: Simplify (log PI) into (log PI) 1.930 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 1.932 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 1.932 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 1.932 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 1.932 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 1.932 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 1.932 * [taylor]: Taking taylor expansion of 1.0 in n 1.932 * [backup-simplify]: Simplify 1.0 into 1.0 1.932 * [taylor]: Taking taylor expansion of (log n) in n 1.932 * [taylor]: Taking taylor expansion of n in n 1.932 * [backup-simplify]: Simplify 0 into 0 1.932 * [backup-simplify]: Simplify 1 into 1 1.933 * [backup-simplify]: Simplify (log 1) into 0 1.933 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1.933 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 1.933 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 1.933 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 1.933 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 1.933 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 1.934 * [taylor]: Taking taylor expansion of 1.0 in n 1.934 * [backup-simplify]: Simplify 1.0 into 1.0 1.934 * [taylor]: Taking taylor expansion of (log 2.0) in n 1.934 * [taylor]: Taking taylor expansion of 2.0 in n 1.934 * [backup-simplify]: Simplify 2.0 into 2.0 1.934 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 1.935 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 1.936 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 1.937 * [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) 1.938 * [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) 1.940 * [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)) 1.941 * [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))) 1.943 * [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) 1.944 * [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)) 1.946 * [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))) 1.947 * [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))) 1.947 * [backup-simplify]: Simplify 0 into 0 1.948 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0 1.949 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0 1.951 * [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 1.951 * [backup-simplify]: Simplify (- 0) into 0 1.952 * [backup-simplify]: Simplify (+ 0 0) into 0 1.953 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0 1.954 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0 1.955 * [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))) 1.956 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 1.959 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 1.963 * [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)))))))) 1.969 * [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)))))))) 1.969 * [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 1.969 * [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 1.969 * [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 1.969 * [taylor]: Taking taylor expansion of +nan.0 in n 1.969 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.969 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n 1.969 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n 1.969 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n 1.969 * [taylor]: Taking taylor expansion of 0.5 in n 1.969 * [backup-simplify]: Simplify 0.5 into 0.5 1.969 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n 1.969 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n 1.969 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 1.969 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 1.969 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 1.969 * [taylor]: Taking taylor expansion of 1.0 in n 1.969 * [backup-simplify]: Simplify 1.0 into 1.0 1.969 * [taylor]: Taking taylor expansion of (log PI) in n 1.969 * [taylor]: Taking taylor expansion of PI in n 1.969 * [backup-simplify]: Simplify PI into PI 1.970 * [backup-simplify]: Simplify (log PI) into (log PI) 1.971 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 1.973 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 1.973 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n 1.973 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 1.973 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 1.973 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 1.973 * [taylor]: Taking taylor expansion of 1.0 in n 1.973 * [backup-simplify]: Simplify 1.0 into 1.0 1.973 * [taylor]: Taking taylor expansion of (log n) in n 1.973 * [taylor]: Taking taylor expansion of n in n 1.973 * [backup-simplify]: Simplify 0 into 0 1.973 * [backup-simplify]: Simplify 1 into 1 1.973 * [backup-simplify]: Simplify (log 1) into 0 1.974 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1.974 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 1.974 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 1.974 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 1.974 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 1.974 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 1.974 * [taylor]: Taking taylor expansion of 1.0 in n 1.974 * [backup-simplify]: Simplify 1.0 into 1.0 1.974 * [taylor]: Taking taylor expansion of (log 2.0) in n 1.974 * [taylor]: Taking taylor expansion of 2.0 in n 1.974 * [backup-simplify]: Simplify 2.0 into 2.0 1.975 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 1.976 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 1.977 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 1.978 * [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) 1.979 * [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) 1.979 * [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)) 1.980 * [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))) 1.981 * [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) 1.981 * [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 1.981 * [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 1.981 * [taylor]: Taking taylor expansion of +nan.0 in n 1.981 * [backup-simplify]: Simplify +nan.0 into +nan.0 1.981 * [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 1.981 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 1.981 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 1.981 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 1.981 * [taylor]: Taking taylor expansion of 0.5 in n 1.981 * [backup-simplify]: Simplify 0.5 into 0.5 1.981 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 1.981 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 1.981 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 1.982 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 1.982 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 1.982 * [taylor]: Taking taylor expansion of 1.0 in n 1.982 * [backup-simplify]: Simplify 1.0 into 1.0 1.982 * [taylor]: Taking taylor expansion of (log 2.0) in n 1.982 * [taylor]: Taking taylor expansion of 2.0 in n 1.982 * [backup-simplify]: Simplify 2.0 into 2.0 1.982 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 1.982 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 1.983 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 1.983 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 1.983 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 1.983 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 1.983 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 1.983 * [taylor]: Taking taylor expansion of 1.0 in n 1.983 * [backup-simplify]: Simplify 1.0 into 1.0 1.983 * [taylor]: Taking taylor expansion of (log PI) in n 1.983 * [taylor]: Taking taylor expansion of PI in n 1.983 * [backup-simplify]: Simplify PI into PI 1.984 * [backup-simplify]: Simplify (log PI) into (log PI) 1.984 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 1.985 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 1.985 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 1.985 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 1.985 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 1.985 * [taylor]: Taking taylor expansion of 1.0 in n 1.985 * [backup-simplify]: Simplify 1.0 into 1.0 1.985 * [taylor]: Taking taylor expansion of (log n) in n 1.985 * [taylor]: Taking taylor expansion of n in n 1.985 * [backup-simplify]: Simplify 0 into 0 1.985 * [backup-simplify]: Simplify 1 into 1 1.986 * [backup-simplify]: Simplify (log 1) into 0 1.986 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 1.986 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 1.986 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 1.987 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 1.987 * [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) 1.988 * [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)) 1.989 * [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))) 1.990 * [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) 1.990 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 1.990 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 1.990 * [taylor]: Taking taylor expansion of 2.0 in n 1.990 * [backup-simplify]: Simplify 2.0 into 2.0 1.990 * [taylor]: Taking taylor expansion of (* n PI) in n 1.990 * [taylor]: Taking taylor expansion of n in n 1.990 * [backup-simplify]: Simplify 0 into 0 1.990 * [backup-simplify]: Simplify 1 into 1 1.990 * [taylor]: Taking taylor expansion of PI in n 1.990 * [backup-simplify]: Simplify PI into PI 1.990 * [backup-simplify]: Simplify (* 0 PI) into 0 1.991 * [backup-simplify]: Simplify (* 2.0 0) into 0 1.997 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 1.998 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 1.999 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.000 * [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)) 2.001 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.003 * [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)) 2.004 * [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))) 2.006 * [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)))))) 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 (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)))))))) 2.018 * [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)))))))) 2.022 * [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)))))))) 2.023 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0 2.023 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0 2.024 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0 2.025 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 2.025 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.025 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0 2.026 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 2.026 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0 2.027 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0 2.028 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0 2.029 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0 2.030 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0 2.031 * [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 2.032 * [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 2.034 * [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 2.038 * [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 2.039 * [backup-simplify]: Simplify (- 0) into 0 2.039 * [backup-simplify]: Simplify (+ 0 0) into 0 2.040 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0 2.041 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0 2.042 * [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))) 2.043 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.045 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.048 * [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)))))))) 2.059 * [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)))))))) 2.060 * [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 2.060 * [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 2.060 * [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 2.060 * [taylor]: Taking taylor expansion of +nan.0 in n 2.060 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.060 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n 2.060 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n 2.060 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n 2.060 * [taylor]: Taking taylor expansion of 0.5 in n 2.060 * [backup-simplify]: Simplify 0.5 into 0.5 2.060 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n 2.060 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n 2.060 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.060 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.060 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.060 * [taylor]: Taking taylor expansion of 1.0 in n 2.060 * [backup-simplify]: Simplify 1.0 into 1.0 2.060 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.060 * [taylor]: Taking taylor expansion of 2.0 in n 2.060 * [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 2.064 * [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 2.070 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n 2.070 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n 2.070 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n 2.070 * [taylor]: Taking taylor expansion of 0.5 in n 2.070 * [backup-simplify]: Simplify 0.5 into 0.5 2.070 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n 2.070 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n 2.070 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n 2.070 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n 2.070 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n 2.070 * [taylor]: Taking taylor expansion of 1.0 in n 2.070 * [backup-simplify]: Simplify 1.0 into 1.0 2.070 * [taylor]: Taking taylor expansion of (log 2.0) in n 2.070 * [taylor]: Taking taylor expansion of 2.0 in n 2.070 * [backup-simplify]: Simplify 2.0 into 2.0 2.070 * [backup-simplify]: Simplify (log 2.0) into (log 2.0) 2.071 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.072 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.072 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.072 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.072 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.072 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.072 * [taylor]: Taking taylor expansion of 1.0 in n 2.072 * [backup-simplify]: Simplify 1.0 into 1.0 2.072 * [taylor]: Taking taylor expansion of (log PI) in n 2.072 * [taylor]: Taking taylor expansion of PI in n 2.072 * [backup-simplify]: Simplify PI into PI 2.072 * [backup-simplify]: Simplify (log PI) into (log PI) 2.073 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.074 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.074 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.074 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.074 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.074 * [taylor]: Taking taylor expansion of 1.0 in n 2.074 * [backup-simplify]: Simplify 1.0 into 1.0 2.074 * [taylor]: Taking taylor expansion of (log n) in n 2.074 * [taylor]: Taking taylor expansion of n in n 2.074 * [backup-simplify]: Simplify 0 into 0 2.074 * [backup-simplify]: Simplify 1 into 1 2.074 * [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) 2.075 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.076 * [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) 2.077 * [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)) 2.078 * [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) 2.079 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.079 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.079 * [taylor]: Taking taylor expansion of 2.0 in n 2.079 * [backup-simplify]: Simplify 2.0 into 2.0 2.079 * [taylor]: Taking taylor expansion of (* n PI) in n 2.079 * [taylor]: Taking taylor expansion of n in n 2.079 * [backup-simplify]: Simplify 0 into 0 2.079 * [backup-simplify]: Simplify 1 into 1 2.079 * [taylor]: Taking taylor expansion of PI in n 2.079 * [backup-simplify]: Simplify PI into PI 2.079 * [backup-simplify]: Simplify (* 0 PI) into 0 2.079 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.080 * [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) 2.083 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0)) 2.084 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0) 2.084 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n 2.084 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n 2.084 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n 2.084 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n 2.084 * [taylor]: Taking taylor expansion of 1.0 in n 2.084 * [backup-simplify]: Simplify 1.0 into 1.0 2.084 * [taylor]: Taking taylor expansion of (log PI) in n 2.084 * [taylor]: Taking taylor expansion of PI in n 2.084 * [backup-simplify]: Simplify PI into PI 2.085 * [backup-simplify]: Simplify (log PI) into (log PI) 2.085 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI)) 2.086 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0) 2.086 * [taylor]: Taking taylor expansion of (pow n 1.0) in n 2.086 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n 2.086 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n 2.086 * [taylor]: Taking taylor expansion of 1.0 in n 2.086 * [backup-simplify]: Simplify 1.0 into 1.0 2.086 * [taylor]: Taking taylor expansion of (log n) in n 2.086 * [taylor]: Taking taylor expansion of n in n 2.086 * [backup-simplify]: Simplify 0 into 0 2.086 * [backup-simplify]: Simplify 1 into 1 2.087 * [backup-simplify]: Simplify (log 1) into 0 2.087 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 2.087 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n)) 2.087 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0) 2.088 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0) 2.088 * [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) 2.089 * [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)) 2.090 * [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))) 2.091 * [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) 2.091 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n 2.091 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 2.091 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 2.091 * [taylor]: Taking taylor expansion of 2.0 in n 2.091 * [backup-simplify]: Simplify 2.0 into 2.0 2.091 * [taylor]: Taking taylor expansion of (* n PI) in n 2.091 * [taylor]: Taking taylor expansion of n in n 2.091 * [backup-simplify]: Simplify 0 into 0 2.091 * [backup-simplify]: Simplify 1 into 1 2.091 * [taylor]: Taking taylor expansion of PI in n 2.091 * [backup-simplify]: Simplify PI into PI 2.091 * [backup-simplify]: Simplify (* 0 PI) into 0 2.092 * [backup-simplify]: Simplify (* 2.0 0) into 0 2.093 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 2.094 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 2.094 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.095 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.096 * [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)) 2.097 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.099 * [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)) 2.105 * [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))) 2.106 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.107 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 2.109 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2) 2.111 * [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)) 2.114 * [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))) 2.117 * [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)))))))))))) 2.145 * [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)))))))))))) 2.159 * [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)))))))))))))) 2.169 * [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)))))))))))))) 2.179 * [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)))))))))))))) 2.202 * [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)))))))))))))))))))))) 2.203 * [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)))))) 2.203 * [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 2.203 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 2.203 * [taylor]: Taking taylor expansion of 1.0 in n 2.203 * [backup-simplify]: Simplify 1.0 into 1.0 2.203 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 2.203 * [taylor]: Taking taylor expansion of (sqrt k) in n 2.203 * [taylor]: Taking taylor expansion of k in n 2.203 * [backup-simplify]: Simplify k into k 2.203 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 2.203 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 2.204 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 2.204 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 2.204 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 2.204 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 2.204 * [taylor]: Taking taylor expansion of 0.5 in n 2.204 * [backup-simplify]: Simplify 0.5 into 0.5 2.204 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.204 * [taylor]: Taking taylor expansion of 1.0 in n 2.204 * [backup-simplify]: Simplify 1.0 into 1.0 2.204 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.204 * [taylor]: Taking taylor expansion of k in n 2.204 * [backup-simplify]: Simplify k into k 2.204 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.204 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.204 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.204 * [taylor]: Taking taylor expansion of 2.0 in n 2.204 * [backup-simplify]: Simplify 2.0 into 2.0 2.204 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.204 * [taylor]: Taking taylor expansion of PI in n 2.204 * [backup-simplify]: Simplify PI into PI 2.204 * [taylor]: Taking taylor expansion of n in n 2.204 * [backup-simplify]: Simplify 0 into 0 2.204 * [backup-simplify]: Simplify 1 into 1 2.205 * [backup-simplify]: Simplify (/ PI 1) into PI 2.205 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.206 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.206 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.206 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.207 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 2.208 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.209 * [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)))) 2.210 * [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))))) 2.210 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 2.210 * [taylor]: Taking taylor expansion of 1.0 in k 2.210 * [backup-simplify]: Simplify 1.0 into 1.0 2.210 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 2.210 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.211 * [taylor]: Taking taylor expansion of k in k 2.211 * [backup-simplify]: Simplify 0 into 0 2.211 * [backup-simplify]: Simplify 1 into 1 2.211 * [backup-simplify]: Simplify (sqrt 0) into 0 2.212 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.212 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.212 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.212 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.212 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.212 * [taylor]: Taking taylor expansion of 0.5 in k 2.212 * [backup-simplify]: Simplify 0.5 into 0.5 2.212 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.212 * [taylor]: Taking taylor expansion of 1.0 in k 2.213 * [backup-simplify]: Simplify 1.0 into 1.0 2.213 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.213 * [taylor]: Taking taylor expansion of k in k 2.213 * [backup-simplify]: Simplify 0 into 0 2.213 * [backup-simplify]: Simplify 1 into 1 2.213 * [backup-simplify]: Simplify (/ 1 1) into 1 2.213 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.213 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.213 * [taylor]: Taking taylor expansion of 2.0 in k 2.213 * [backup-simplify]: Simplify 2.0 into 2.0 2.213 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.213 * [taylor]: Taking taylor expansion of PI in k 2.213 * [backup-simplify]: Simplify PI into PI 2.213 * [taylor]: Taking taylor expansion of n in k 2.213 * [backup-simplify]: Simplify n into n 2.213 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.213 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.214 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.214 * [backup-simplify]: Simplify (- 1) into -1 2.214 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.215 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.215 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.215 * [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))))) 2.215 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 2.215 * [taylor]: Taking taylor expansion of 1.0 in k 2.215 * [backup-simplify]: Simplify 1.0 into 1.0 2.215 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 2.215 * [taylor]: Taking taylor expansion of (sqrt k) in k 2.215 * [taylor]: Taking taylor expansion of k in k 2.215 * [backup-simplify]: Simplify 0 into 0 2.215 * [backup-simplify]: Simplify 1 into 1 2.216 * [backup-simplify]: Simplify (sqrt 0) into 0 2.217 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 2.217 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 2.217 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 2.217 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 2.217 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 2.217 * [taylor]: Taking taylor expansion of 0.5 in k 2.217 * [backup-simplify]: Simplify 0.5 into 0.5 2.217 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 2.217 * [taylor]: Taking taylor expansion of 1.0 in k 2.217 * [backup-simplify]: Simplify 1.0 into 1.0 2.217 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.217 * [taylor]: Taking taylor expansion of k in k 2.217 * [backup-simplify]: Simplify 0 into 0 2.218 * [backup-simplify]: Simplify 1 into 1 2.218 * [backup-simplify]: Simplify (/ 1 1) into 1 2.218 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 2.218 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 2.218 * [taylor]: Taking taylor expansion of 2.0 in k 2.218 * [backup-simplify]: Simplify 2.0 into 2.0 2.218 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.218 * [taylor]: Taking taylor expansion of PI in k 2.218 * [backup-simplify]: Simplify PI into PI 2.218 * [taylor]: Taking taylor expansion of n in k 2.218 * [backup-simplify]: Simplify n into n 2.218 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.218 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 2.218 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 2.219 * [backup-simplify]: Simplify (- 1) into -1 2.219 * [backup-simplify]: Simplify (+ 0 -1) into -1 2.220 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 2.220 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 2.220 * [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))))) 2.221 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0 2.221 * [backup-simplify]: Simplify (* 1.0 0) into 0 2.221 * [taylor]: Taking taylor expansion of 0 in n 2.221 * [backup-simplify]: Simplify 0 into 0 2.221 * [backup-simplify]: Simplify 0 into 0 2.222 * [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))))))) 2.223 * [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))))))) 2.223 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.223 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.223 * [taylor]: Taking taylor expansion of +nan.0 in n 2.223 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.223 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.223 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.223 * [taylor]: Taking taylor expansion of 0.5 in n 2.223 * [backup-simplify]: Simplify 0.5 into 0.5 2.223 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.223 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.223 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.223 * [taylor]: Taking taylor expansion of 2.0 in n 2.223 * [backup-simplify]: Simplify 2.0 into 2.0 2.223 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.223 * [taylor]: Taking taylor expansion of PI in n 2.223 * [backup-simplify]: Simplify PI into PI 2.223 * [taylor]: Taking taylor expansion of n in n 2.223 * [backup-simplify]: Simplify 0 into 0 2.223 * [backup-simplify]: Simplify 1 into 1 2.224 * [backup-simplify]: Simplify (/ PI 1) into PI 2.224 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.226 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.226 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.226 * [taylor]: Taking taylor expansion of 1.0 in n 2.226 * [backup-simplify]: Simplify 1.0 into 1.0 2.226 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.226 * [taylor]: Taking taylor expansion of k in n 2.226 * [backup-simplify]: Simplify k into k 2.226 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.227 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.228 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.228 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.229 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.231 * [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)))) 2.232 * [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))))) 2.239 * [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)))))) 2.240 * [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))))))) 2.241 * [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))))))) 2.241 * [backup-simplify]: Simplify 0 into 0 2.243 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.243 * [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))))))) 2.244 * [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))))))) 2.244 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.244 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.244 * [taylor]: Taking taylor expansion of +nan.0 in n 2.244 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.244 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.244 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.244 * [taylor]: Taking taylor expansion of 0.5 in n 2.244 * [backup-simplify]: Simplify 0.5 into 0.5 2.244 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.244 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.244 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.244 * [taylor]: Taking taylor expansion of 2.0 in n 2.244 * [backup-simplify]: Simplify 2.0 into 2.0 2.244 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.244 * [taylor]: Taking taylor expansion of PI in n 2.244 * [backup-simplify]: Simplify PI into PI 2.244 * [taylor]: Taking taylor expansion of n in n 2.244 * [backup-simplify]: Simplify 0 into 0 2.244 * [backup-simplify]: Simplify 1 into 1 2.245 * [backup-simplify]: Simplify (/ PI 1) into PI 2.245 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.246 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.246 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.246 * [taylor]: Taking taylor expansion of 1.0 in n 2.246 * [backup-simplify]: Simplify 1.0 into 1.0 2.246 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.246 * [taylor]: Taking taylor expansion of k in n 2.246 * [backup-simplify]: Simplify k into k 2.246 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.247 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.247 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.247 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.248 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.248 * [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)))) 2.249 * [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))))) 2.250 * [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)))))) 2.251 * [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))))))) 2.251 * [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))))))) 2.252 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.253 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.253 * [backup-simplify]: Simplify (- 0) into 0 2.253 * [backup-simplify]: Simplify (+ 0 0) into 0 2.254 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.254 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 2.255 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 2.256 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0 2.257 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0 2.258 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.259 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 2.259 * [backup-simplify]: Simplify (- 0) into 0 2.259 * [backup-simplify]: Simplify 0 into 0 2.259 * [backup-simplify]: Simplify 0 into 0 2.261 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.262 * [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))))))) 2.263 * [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))))))) 2.263 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n 2.263 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n 2.263 * [taylor]: Taking taylor expansion of +nan.0 in n 2.263 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.263 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n 2.263 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n 2.263 * [taylor]: Taking taylor expansion of 0.5 in n 2.263 * [backup-simplify]: Simplify 0.5 into 0.5 2.263 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n 2.263 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 2.263 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 2.263 * [taylor]: Taking taylor expansion of 2.0 in n 2.263 * [backup-simplify]: Simplify 2.0 into 2.0 2.263 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.264 * [taylor]: Taking taylor expansion of PI in n 2.264 * [backup-simplify]: Simplify PI into PI 2.264 * [taylor]: Taking taylor expansion of n in n 2.264 * [backup-simplify]: Simplify 0 into 0 2.264 * [backup-simplify]: Simplify 1 into 1 2.264 * [backup-simplify]: Simplify (/ PI 1) into PI 2.264 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 2.265 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 2.265 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 2.265 * [taylor]: Taking taylor expansion of 1.0 in n 2.265 * [backup-simplify]: Simplify 1.0 into 1.0 2.265 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.265 * [taylor]: Taking taylor expansion of k in n 2.265 * [backup-simplify]: Simplify k into k 2.265 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.266 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 2.266 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 2.266 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 2.267 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) 2.267 * [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)))) 2.268 * [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))))) 2.269 * [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)))))) 2.270 * [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))))))) 2.272 * [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))))))) 2.277 * [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)))))))) 2.278 * [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)))) 2.278 * [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 2.278 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 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 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 2.278 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 2.278 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 2.278 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 2.278 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 2.278 * [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) 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 2.279 * [taylor]: Taking taylor expansion of -2.0 in n 2.279 * [backup-simplify]: Simplify -2.0 into -2.0 2.279 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.279 * [taylor]: Taking taylor expansion of PI in n 2.279 * [backup-simplify]: Simplify PI into PI 2.279 * [taylor]: Taking taylor expansion of n in n 2.279 * [backup-simplify]: Simplify 0 into 0 2.279 * [backup-simplify]: Simplify 1 into 1 2.279 * [backup-simplify]: Simplify (/ PI 1) into PI 2.280 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.281 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.281 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.281 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 2.283 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.284 * [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)))) 2.285 * [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))))) 2.285 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 2.285 * [taylor]: Taking taylor expansion of (/ -1 k) in n 2.285 * [taylor]: Taking taylor expansion of -1 in n 2.285 * [backup-simplify]: Simplify -1 into -1 2.285 * [taylor]: Taking taylor expansion of k in n 2.285 * [backup-simplify]: Simplify k into k 2.285 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 2.286 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 2.286 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 2.286 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 2.287 * [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))) 2.287 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.287 * [taylor]: Taking taylor expansion of 1.0 in k 2.287 * [backup-simplify]: Simplify 1.0 into 1.0 2.287 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.287 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.287 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.287 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.288 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.288 * [taylor]: Taking taylor expansion of 0.5 in k 2.288 * [backup-simplify]: Simplify 0.5 into 0.5 2.288 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.288 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.288 * [taylor]: Taking taylor expansion of k in k 2.288 * [backup-simplify]: Simplify 0 into 0 2.288 * [backup-simplify]: Simplify 1 into 1 2.288 * [backup-simplify]: Simplify (/ 1 1) into 1 2.288 * [taylor]: Taking taylor expansion of 1.0 in k 2.288 * [backup-simplify]: Simplify 1.0 into 1.0 2.288 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.288 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.288 * [taylor]: Taking taylor expansion of -2.0 in k 2.288 * [backup-simplify]: Simplify -2.0 into -2.0 2.288 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.288 * [taylor]: Taking taylor expansion of PI in k 2.288 * [backup-simplify]: Simplify PI into PI 2.288 * [taylor]: Taking taylor expansion of n in k 2.289 * [backup-simplify]: Simplify n into n 2.289 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.289 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.289 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.289 * [backup-simplify]: Simplify (+ 1 0) into 1 2.290 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.290 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.290 * [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)))))) 2.291 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.291 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.291 * [taylor]: Taking taylor expansion of -1 in k 2.291 * [backup-simplify]: Simplify -1 into -1 2.291 * [taylor]: Taking taylor expansion of k in k 2.291 * [backup-simplify]: Simplify 0 into 0 2.291 * [backup-simplify]: Simplify 1 into 1 2.291 * [backup-simplify]: Simplify (/ -1 1) into -1 2.292 * [backup-simplify]: Simplify (sqrt 0) into 0 2.293 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.293 * [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))))))) 2.293 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 2.294 * [taylor]: Taking taylor expansion of 1.0 in k 2.294 * [backup-simplify]: Simplify 1.0 into 1.0 2.294 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 2.294 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 2.294 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 2.294 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 2.294 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 2.294 * [taylor]: Taking taylor expansion of 0.5 in k 2.294 * [backup-simplify]: Simplify 0.5 into 0.5 2.294 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 2.294 * [taylor]: Taking taylor expansion of (/ 1 k) in k 2.294 * [taylor]: Taking taylor expansion of k in k 2.294 * [backup-simplify]: Simplify 0 into 0 2.294 * [backup-simplify]: Simplify 1 into 1 2.294 * [backup-simplify]: Simplify (/ 1 1) into 1 2.294 * [taylor]: Taking taylor expansion of 1.0 in k 2.294 * [backup-simplify]: Simplify 1.0 into 1.0 2.295 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 2.295 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 2.295 * [taylor]: Taking taylor expansion of -2.0 in k 2.295 * [backup-simplify]: Simplify -2.0 into -2.0 2.295 * [taylor]: Taking taylor expansion of (/ PI n) in k 2.295 * [taylor]: Taking taylor expansion of PI in k 2.295 * [backup-simplify]: Simplify PI into PI 2.295 * [taylor]: Taking taylor expansion of n in k 2.295 * [backup-simplify]: Simplify n into n 2.295 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 2.295 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 2.295 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 2.296 * [backup-simplify]: Simplify (+ 1 0) into 1 2.296 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 2.296 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 2.297 * [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)))))) 2.297 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 2.297 * [taylor]: Taking taylor expansion of (/ -1 k) in k 2.297 * [taylor]: Taking taylor expansion of -1 in k 2.297 * [backup-simplify]: Simplify -1 into -1 2.297 * [taylor]: Taking taylor expansion of k in k 2.297 * [backup-simplify]: Simplify 0 into 0 2.297 * [backup-simplify]: Simplify 1 into 1 2.297 * [backup-simplify]: Simplify (/ -1 1) into -1 2.298 * [backup-simplify]: Simplify (sqrt 0) into 0 2.299 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 2.300 * [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))))))) 2.300 * [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))))))) 2.300 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.300 * [taylor]: Taking taylor expansion of +nan.0 in n 2.300 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.300 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.300 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.300 * [taylor]: Taking taylor expansion of 0.5 in n 2.300 * [backup-simplify]: Simplify 0.5 into 0.5 2.300 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.300 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.300 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.300 * [taylor]: Taking taylor expansion of k in n 2.300 * [backup-simplify]: Simplify k into k 2.300 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.301 * [taylor]: Taking taylor expansion of 1.0 in n 2.301 * [backup-simplify]: Simplify 1.0 into 1.0 2.301 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.301 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.301 * [taylor]: Taking taylor expansion of -2.0 in n 2.301 * [backup-simplify]: Simplify -2.0 into -2.0 2.301 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.301 * [taylor]: Taking taylor expansion of PI in n 2.301 * [backup-simplify]: Simplify PI into PI 2.301 * [taylor]: Taking taylor expansion of n in n 2.301 * [backup-simplify]: Simplify 0 into 0 2.301 * [backup-simplify]: Simplify 1 into 1 2.301 * [backup-simplify]: Simplify (/ PI 1) into PI 2.302 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.303 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.303 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.305 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.306 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.307 * [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)))) 2.307 * [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))))) 2.308 * [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)))))) 2.309 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 2.311 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 2.312 * [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)))))))) 2.312 * [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)))))))) 2.312 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 2.312 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.312 * [taylor]: Taking taylor expansion of +nan.0 in n 2.312 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.313 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.313 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.313 * [taylor]: Taking taylor expansion of 0.5 in n 2.313 * [backup-simplify]: Simplify 0.5 into 0.5 2.313 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.313 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.313 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.313 * [taylor]: Taking taylor expansion of k in n 2.313 * [backup-simplify]: Simplify k into k 2.313 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.313 * [taylor]: Taking taylor expansion of 1.0 in n 2.313 * [backup-simplify]: Simplify 1.0 into 1.0 2.313 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.313 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.313 * [taylor]: Taking taylor expansion of -2.0 in n 2.313 * [backup-simplify]: Simplify -2.0 into -2.0 2.313 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.313 * [taylor]: Taking taylor expansion of PI in n 2.313 * [backup-simplify]: Simplify PI into PI 2.313 * [taylor]: Taking taylor expansion of n in n 2.313 * [backup-simplify]: Simplify 0 into 0 2.313 * [backup-simplify]: Simplify 1 into 1 2.313 * [backup-simplify]: Simplify (/ PI 1) into PI 2.314 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.314 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.314 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 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) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.317 * [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)))) 2.317 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2.318 * [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)))))) 2.319 * [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))))))) 2.320 * [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))))))) 2.320 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 2.321 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 2.322 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 2.322 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 2.322 * [backup-simplify]: Simplify (+ 0 0) into 0 2.323 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.324 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 2.325 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0 2.326 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 2.327 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0 2.327 * [backup-simplify]: Simplify 0 into 0 2.328 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 2.330 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 2.331 * [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)))))))) 2.332 * [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)))))))) 2.332 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n 2.332 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n 2.332 * [taylor]: Taking taylor expansion of +nan.0 in n 2.332 * [backup-simplify]: Simplify +nan.0 into +nan.0 2.332 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n 2.332 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n 2.332 * [taylor]: Taking taylor expansion of 0.5 in n 2.332 * [backup-simplify]: Simplify 0.5 into 0.5 2.332 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n 2.332 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 2.332 * [taylor]: Taking taylor expansion of (/ 1 k) in n 2.332 * [taylor]: Taking taylor expansion of k in n 2.332 * [backup-simplify]: Simplify k into k 2.332 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 2.332 * [taylor]: Taking taylor expansion of 1.0 in n 2.332 * [backup-simplify]: Simplify 1.0 into 1.0 2.332 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 2.332 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 2.332 * [taylor]: Taking taylor expansion of -2.0 in n 2.332 * [backup-simplify]: Simplify -2.0 into -2.0 2.332 * [taylor]: Taking taylor expansion of (/ PI n) in n 2.332 * [taylor]: Taking taylor expansion of PI in n 2.332 * [backup-simplify]: Simplify PI into PI 2.332 * [taylor]: Taking taylor expansion of n in n 2.332 * [backup-simplify]: Simplify 0 into 0 2.332 * [backup-simplify]: Simplify 1 into 1 2.333 * [backup-simplify]: Simplify (/ PI 1) into PI 2.333 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 2.334 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 2.334 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 2.335 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 2.337 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) 2.338 * [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)))) 2.339 * [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))))) 2.340 * [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)))))) 2.341 * [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))))))) 2.343 * [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))))))) 2.348 * [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)))))))))))) 2.348 * * * [progress]: simplifying candidates 2.360 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (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)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 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) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (- (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) (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (+ (- (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) 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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)))))))))))) 2.366 * * [simplify]: Extracting # 0 : cost 0 2.366 * * [simplify]: Extracting # 1 : cost 0 2.366 * * [simplify]: Extracting # 2 : cost 0 2.367 * * [simplify]: Extracting # 3 : cost 0 2.367 * * [simplify]: Extracting # 4 : cost 0 2.367 * * [simplify]: Extracting # 5 : cost 0 2.368 * * [simplify]: Extracting # 6 : cost 0 2.368 * * [simplify]: Extracting # 7 : cost 0 2.369 * * [simplify]: Extracting # 8 : cost 0 2.369 * * [simplify]: Extracting # 9 : cost 0 2.370 * * [simplify]: Extracting # 10 : cost 0 2.370 * * [simplify]: Extracting # 11 : cost 0 2.371 * * [simplify]: Extracting # 12 : cost 0 2.371 * * [simplify]: Extracting # 13 : cost 0 2.372 * * [simplify]: Extracting # 14 : cost 0 2.372 * * [simplify]: Extracting # 15 : cost 0 2.373 * * [simplify]: Extracting # 16 : cost 0 2.373 * * [simplify]: Extracting # 17 : cost 0 2.374 * * [simplify]: Extracting # 18 : cost 0 2.375 * * [simplify]: Extracting # 19 : cost 0 2.375 * * [simplify]: Extracting # 20 : cost 0 2.376 * * [simplify]: Extracting # 21 : cost 0 2.376 * * [simplify]: Extracting # 22 : cost 0 2.377 * * [simplify]: Extracting # 23 : cost 0 2.377 * * [simplify]: Extracting # 24 : cost 0 2.378 * * [simplify]: Extracting # 25 : cost 0 2.378 * * [simplify]: Extracting # 26 : cost 0 2.379 * * [simplify]: Extracting # 27 : cost 0 2.379 * * [simplify]: Extracting # 28 : cost 0 2.380 * * [simplify]: Extracting # 29 : cost 0 2.380 * * [simplify]: Extracting # 30 : cost 0 2.381 * * [simplify]: Extracting # 31 : cost 0 2.381 * * [simplify]: Extracting # 32 : cost 0 2.382 * * [simplify]: iteration 0 : 369 enodes (cost 2880 ) 2.577 * * [simplify]: Extracting # 0 : cost 0 2.579 * * [simplify]: Extracting # 1 : cost 0 2.582 * * [simplify]: Extracting # 2 : cost 0 2.585 * * [simplify]: Extracting # 3 : cost 0 2.588 * * [simplify]: Extracting # 4 : cost 0 2.591 * * [simplify]: Extracting # 5 : cost 0 2.600 * * [simplify]: Extracting # 6 : cost 0 2.603 * * [simplify]: iteration 1 : 1037 enodes (cost 2720 ) 3.390 * * [simplify]: Extracting # 0 : cost 0 3.401 * * [simplify]: Extracting # 1 : cost 0 3.414 * * [simplify]: Extracting # 2 : cost 0 3.426 * * [simplify]: Extracting # 3 : cost 0 3.438 * * [simplify]: Extracting # 4 : cost 0 3.456 * * [simplify]: Extracting # 5 : cost 0 3.469 * * [simplify]: iteration 2 : 4907 enodes (cost 2552 ) 5.435 * * [simplify]: Extracting # 0 : cost 0 5.447 * * [simplify]: Extracting # 1 : cost 0 5.460 * * [simplify]: Extracting # 2 : cost 0 5.472 * * [simplify]: Extracting # 3 : cost 0 5.485 * * [simplify]: Extracting # 4 : cost 0 5.497 * * [simplify]: iteration done: 5000 enodes (cost 2549 ) 5.500 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (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))) (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))) (* (* 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)) (expm1 (* (* 2.0 PI) n)) (log1p (* (* 2.0 PI) n)) (* (* 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) (* PI n) (expm1 (/ 1.0 (sqrt k))) (log1p (/ 1.0 (sqrt k))) (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) (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log1p (* (/ 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)))) (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))) (fma (* 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))) (- (fma 0.25 (* (* (pow k 2) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log n))) (pow (* (* 2.0 PI) n) 0.5)) (* (* k (+ (* (pow (* (* 2.0 PI) n) 0.5) (log (* 2.0 PI))) (* (pow (* (* 2.0 PI) n) 0.5) (log 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)))))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (- (fma +nan.0 k (- (fma +nan.0 (pow k 2) (- +nan.0))))) (- (+ (- (/ +nan.0 (pow k 2)) (/ +nan.0 k)) (/ +nan.0 (pow k 3)))) (- (- (/ +nan.0 (pow k 2)) (- (/ +nan.0 k) +nan.0))) (+ (- (* +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))) (fma (* (* (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 (fma (* +nan.0 (* (pow k 2) (log n))) (- (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (fma +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)))) (fma (* +nan.0 (* k (log n))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (fma (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (- +nan.0) (* +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))))))))))) (- (* +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))))) (+ (* (/ (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)))))) (pow k 2)) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)))) 5.502 * * * [progress]: adding candidates to table 6.232 * * [progress]: iteration 2 / 4 6.232 * * * [progress]: picking best candidate 6.282 * * * * [pick]: Picked # 6.282 * * * [progress]: localizing error 6.303 * * * [progress]: generating rewritten candidates 6.303 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1 2) 6.326 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 2 1) 6.358 * * * * [progress]: [ 3 / 3 ] rewriting at (2) 6.389 * * * [progress]: generating series expansions 6.389 * * * * [progress]: [ 1 / 3 ] generating series at (2 1 2) 6.390 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) 6.390 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0 6.390 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 6.390 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.390 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.390 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 6.390 * [taylor]: Taking taylor expansion of 0.5 in k 6.390 * [backup-simplify]: Simplify 0.5 into 0.5 6.390 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.390 * [taylor]: Taking taylor expansion of 1.0 in k 6.390 * [backup-simplify]: Simplify 1.0 into 1.0 6.390 * [taylor]: Taking taylor expansion of k in k 6.390 * [backup-simplify]: Simplify 0 into 0 6.390 * [backup-simplify]: Simplify 1 into 1 6.391 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.391 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.391 * [taylor]: Taking taylor expansion of 2.0 in k 6.391 * [backup-simplify]: Simplify 2.0 into 2.0 6.391 * [taylor]: Taking taylor expansion of (* n PI) in k 6.391 * [taylor]: Taking taylor expansion of n in k 6.391 * [backup-simplify]: Simplify n into n 6.391 * [taylor]: Taking taylor expansion of PI in k 6.391 * [backup-simplify]: Simplify PI into PI 6.391 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.391 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.391 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.391 * [backup-simplify]: Simplify (- 0) into 0 6.391 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.392 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 6.392 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 6.392 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 6.392 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 6.392 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.392 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.392 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 6.392 * [taylor]: Taking taylor expansion of 0.5 in n 6.392 * [backup-simplify]: Simplify 0.5 into 0.5 6.392 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.392 * [taylor]: Taking taylor expansion of 1.0 in n 6.392 * [backup-simplify]: Simplify 1.0 into 1.0 6.392 * [taylor]: Taking taylor expansion of k in n 6.392 * [backup-simplify]: Simplify k into k 6.392 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.392 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.392 * [taylor]: Taking taylor expansion of 2.0 in n 6.392 * [backup-simplify]: Simplify 2.0 into 2.0 6.392 * [taylor]: Taking taylor expansion of (* n PI) in n 6.392 * [taylor]: Taking taylor expansion of n in n 6.392 * [backup-simplify]: Simplify 0 into 0 6.392 * [backup-simplify]: Simplify 1 into 1 6.392 * [taylor]: Taking taylor expansion of PI in n 6.392 * [backup-simplify]: Simplify PI into PI 6.393 * [backup-simplify]: Simplify (* 0 PI) into 0 6.393 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.394 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.395 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.396 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.396 * [backup-simplify]: Simplify (- k) into (- k) 6.396 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.396 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 6.397 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.398 * [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)))) 6.398 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 6.398 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 6.398 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.398 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.398 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 6.398 * [taylor]: Taking taylor expansion of 0.5 in n 6.398 * [backup-simplify]: Simplify 0.5 into 0.5 6.398 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.398 * [taylor]: Taking taylor expansion of 1.0 in n 6.398 * [backup-simplify]: Simplify 1.0 into 1.0 6.398 * [taylor]: Taking taylor expansion of k in n 6.398 * [backup-simplify]: Simplify k into k 6.399 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.399 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.399 * [taylor]: Taking taylor expansion of 2.0 in n 6.399 * [backup-simplify]: Simplify 2.0 into 2.0 6.399 * [taylor]: Taking taylor expansion of (* n PI) in n 6.399 * [taylor]: Taking taylor expansion of n in n 6.399 * [backup-simplify]: Simplify 0 into 0 6.399 * [backup-simplify]: Simplify 1 into 1 6.399 * [taylor]: Taking taylor expansion of PI in n 6.399 * [backup-simplify]: Simplify PI into PI 6.399 * [backup-simplify]: Simplify (* 0 PI) into 0 6.399 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.400 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.401 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.402 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.402 * [backup-simplify]: Simplify (- k) into (- k) 6.402 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.402 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 6.403 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.403 * [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)))) 6.404 * [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))))) 6.404 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 6.404 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 6.404 * [taylor]: Taking taylor expansion of 0.5 in k 6.404 * [backup-simplify]: Simplify 0.5 into 0.5 6.404 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 6.404 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.404 * [taylor]: Taking taylor expansion of 1.0 in k 6.404 * [backup-simplify]: Simplify 1.0 into 1.0 6.404 * [taylor]: Taking taylor expansion of k in k 6.404 * [backup-simplify]: Simplify 0 into 0 6.404 * [backup-simplify]: Simplify 1 into 1 6.404 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 6.404 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.404 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.405 * [taylor]: Taking taylor expansion of 2.0 in k 6.405 * [backup-simplify]: Simplify 2.0 into 2.0 6.405 * [taylor]: Taking taylor expansion of PI in k 6.405 * [backup-simplify]: Simplify PI into PI 6.405 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.406 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.406 * [taylor]: Taking taylor expansion of (log n) in k 6.406 * [taylor]: Taking taylor expansion of n in k 6.406 * [backup-simplify]: Simplify n into n 6.406 * [backup-simplify]: Simplify (log n) into (log n) 6.406 * [backup-simplify]: Simplify (- 0) into 0 6.407 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.408 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 6.409 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 6.410 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 6.411 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 6.413 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 6.414 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.415 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.417 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.418 * [backup-simplify]: Simplify (- 0) into 0 6.418 * [backup-simplify]: Simplify (+ 0 0) into 0 6.419 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 6.420 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.421 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 6.423 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.423 * [taylor]: Taking taylor expansion of 0 in k 6.423 * [backup-simplify]: Simplify 0 into 0 6.424 * [backup-simplify]: Simplify 0 into 0 6.424 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.426 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.427 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.428 * [backup-simplify]: Simplify (+ 0 0) into 0 6.428 * [backup-simplify]: Simplify (- 1) into -1 6.428 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.430 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 6.432 * [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)))) 6.435 * [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)))))) 6.438 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 6.440 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.441 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.445 * [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 6.445 * [backup-simplify]: Simplify (- 0) into 0 6.446 * [backup-simplify]: Simplify (+ 0 0) into 0 6.447 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 6.448 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.450 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.452 * [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 6.452 * [taylor]: Taking taylor expansion of 0 in k 6.452 * [backup-simplify]: Simplify 0 into 0 6.452 * [backup-simplify]: Simplify 0 into 0 6.453 * [backup-simplify]: Simplify 0 into 0 6.454 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.457 * [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 6.459 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.459 * [backup-simplify]: Simplify (+ 0 0) into 0 6.460 * [backup-simplify]: Simplify (- 0) into 0 6.460 * [backup-simplify]: Simplify (+ 0 0) into 0 6.462 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.464 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.468 * [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)))))) 6.474 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 6.483 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) 6.484 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) 6.484 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0 6.484 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 6.484 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.484 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.484 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 6.484 * [taylor]: Taking taylor expansion of 0.5 in k 6.484 * [backup-simplify]: Simplify 0.5 into 0.5 6.484 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.484 * [taylor]: Taking taylor expansion of 1.0 in k 6.484 * [backup-simplify]: Simplify 1.0 into 1.0 6.484 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.484 * [taylor]: Taking taylor expansion of k in k 6.484 * [backup-simplify]: Simplify 0 into 0 6.484 * [backup-simplify]: Simplify 1 into 1 6.484 * [backup-simplify]: Simplify (/ 1 1) into 1 6.484 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.484 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.485 * [taylor]: Taking taylor expansion of 2.0 in k 6.485 * [backup-simplify]: Simplify 2.0 into 2.0 6.485 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.485 * [taylor]: Taking taylor expansion of PI in k 6.485 * [backup-simplify]: Simplify PI into PI 6.485 * [taylor]: Taking taylor expansion of n in k 6.485 * [backup-simplify]: Simplify n into n 6.485 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.485 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.485 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.485 * [backup-simplify]: Simplify (- 1) into -1 6.485 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.486 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 6.486 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 6.486 * [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))))) 6.486 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 6.486 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.486 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.486 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 6.486 * [taylor]: Taking taylor expansion of 0.5 in n 6.486 * [backup-simplify]: Simplify 0.5 into 0.5 6.486 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.486 * [taylor]: Taking taylor expansion of 1.0 in n 6.486 * [backup-simplify]: Simplify 1.0 into 1.0 6.486 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.486 * [taylor]: Taking taylor expansion of k in n 6.486 * [backup-simplify]: Simplify k into k 6.486 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.486 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.486 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.486 * [taylor]: Taking taylor expansion of 2.0 in n 6.486 * [backup-simplify]: Simplify 2.0 into 2.0 6.486 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.486 * [taylor]: Taking taylor expansion of PI in n 6.486 * [backup-simplify]: Simplify PI into PI 6.486 * [taylor]: Taking taylor expansion of n in n 6.486 * [backup-simplify]: Simplify 0 into 0 6.486 * [backup-simplify]: Simplify 1 into 1 6.487 * [backup-simplify]: Simplify (/ PI 1) into PI 6.487 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.488 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.488 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.488 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.488 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.489 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.489 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) 6.490 * [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))))) 6.490 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 6.490 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.490 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.490 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 6.490 * [taylor]: Taking taylor expansion of 0.5 in n 6.490 * [backup-simplify]: Simplify 0.5 into 0.5 6.490 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.490 * [taylor]: Taking taylor expansion of 1.0 in n 6.490 * [backup-simplify]: Simplify 1.0 into 1.0 6.490 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.490 * [taylor]: Taking taylor expansion of k in n 6.490 * [backup-simplify]: Simplify k into k 6.490 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.491 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.491 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.491 * [taylor]: Taking taylor expansion of 2.0 in n 6.491 * [backup-simplify]: Simplify 2.0 into 2.0 6.491 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.491 * [taylor]: Taking taylor expansion of PI in n 6.491 * [backup-simplify]: Simplify PI into PI 6.491 * [taylor]: Taking taylor expansion of n in n 6.491 * [backup-simplify]: Simplify 0 into 0 6.491 * [backup-simplify]: Simplify 1 into 1 6.491 * [backup-simplify]: Simplify (/ PI 1) into PI 6.491 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.492 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.492 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.492 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.492 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.493 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.494 * [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)))) 6.495 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.495 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 6.495 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 6.495 * [taylor]: Taking taylor expansion of 0.5 in k 6.495 * [backup-simplify]: Simplify 0.5 into 0.5 6.495 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 6.495 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.495 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.495 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.495 * [taylor]: Taking taylor expansion of 2.0 in k 6.495 * [backup-simplify]: Simplify 2.0 into 2.0 6.495 * [taylor]: Taking taylor expansion of PI in k 6.495 * [backup-simplify]: Simplify PI into PI 6.499 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.500 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.500 * [taylor]: Taking taylor expansion of (log n) in k 6.500 * [taylor]: Taking taylor expansion of n in k 6.500 * [backup-simplify]: Simplify n into n 6.500 * [backup-simplify]: Simplify (log n) into (log n) 6.500 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.500 * [taylor]: Taking taylor expansion of 1.0 in k 6.500 * [backup-simplify]: Simplify 1.0 into 1.0 6.500 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.500 * [taylor]: Taking taylor expansion of k in k 6.500 * [backup-simplify]: Simplify 0 into 0 6.500 * [backup-simplify]: Simplify 1 into 1 6.500 * [backup-simplify]: Simplify (/ 1 1) into 1 6.500 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.501 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.501 * [backup-simplify]: Simplify (- 1) into -1 6.501 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.502 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.503 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 6.504 * [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))))) 6.504 * [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))))) 6.505 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.505 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.506 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.506 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.507 * [backup-simplify]: Simplify (- 0) into 0 6.507 * [backup-simplify]: Simplify (+ 0 0) into 0 6.507 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.508 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.509 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.510 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.510 * [taylor]: Taking taylor expansion of 0 in k 6.510 * [backup-simplify]: Simplify 0 into 0 6.510 * [backup-simplify]: Simplify 0 into 0 6.510 * [backup-simplify]: Simplify 0 into 0 6.511 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.511 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.513 * [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 6.513 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.514 * [backup-simplify]: Simplify (- 0) into 0 6.514 * [backup-simplify]: Simplify (+ 0 0) into 0 6.515 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.516 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.518 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.520 * [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 6.520 * [taylor]: Taking taylor expansion of 0 in k 6.520 * [backup-simplify]: Simplify 0 into 0 6.520 * [backup-simplify]: Simplify 0 into 0 6.520 * [backup-simplify]: Simplify 0 into 0 6.520 * [backup-simplify]: Simplify 0 into 0 6.522 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.523 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.529 * [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 6.530 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.530 * [backup-simplify]: Simplify (- 0) into 0 6.531 * [backup-simplify]: Simplify (+ 0 0) into 0 6.532 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 6.534 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.536 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 6.539 * [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 6.539 * [taylor]: Taking taylor expansion of 0 in k 6.539 * [backup-simplify]: Simplify 0 into 0 6.539 * [backup-simplify]: Simplify 0 into 0 6.540 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) 6.541 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) 6.541 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0 6.541 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 6.541 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 6.541 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 6.541 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 6.541 * [taylor]: Taking taylor expansion of 0.5 in k 6.542 * [backup-simplify]: Simplify 0.5 into 0.5 6.542 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.542 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.542 * [taylor]: Taking taylor expansion of k in k 6.542 * [backup-simplify]: Simplify 0 into 0 6.542 * [backup-simplify]: Simplify 1 into 1 6.542 * [backup-simplify]: Simplify (/ 1 1) into 1 6.542 * [taylor]: Taking taylor expansion of 1.0 in k 6.542 * [backup-simplify]: Simplify 1.0 into 1.0 6.542 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 6.542 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 6.542 * [taylor]: Taking taylor expansion of -2.0 in k 6.542 * [backup-simplify]: Simplify -2.0 into -2.0 6.542 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.542 * [taylor]: Taking taylor expansion of PI in k 6.542 * [backup-simplify]: Simplify PI into PI 6.542 * [taylor]: Taking taylor expansion of n in k 6.542 * [backup-simplify]: Simplify n into n 6.542 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.543 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 6.543 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 6.543 * [backup-simplify]: Simplify (+ 1 0) into 1 6.544 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 6.544 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 6.544 * [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)))))) 6.544 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 6.544 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.544 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.544 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 6.544 * [taylor]: Taking taylor expansion of 0.5 in n 6.544 * [backup-simplify]: Simplify 0.5 into 0.5 6.544 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.544 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.544 * [taylor]: Taking taylor expansion of k in n 6.544 * [backup-simplify]: Simplify k into k 6.545 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.545 * [taylor]: Taking taylor expansion of 1.0 in n 6.545 * [backup-simplify]: Simplify 1.0 into 1.0 6.545 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.545 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.545 * [taylor]: Taking taylor expansion of -2.0 in n 6.545 * [backup-simplify]: Simplify -2.0 into -2.0 6.545 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.545 * [taylor]: Taking taylor expansion of PI in n 6.545 * [backup-simplify]: Simplify PI into PI 6.545 * [taylor]: Taking taylor expansion of n in n 6.545 * [backup-simplify]: Simplify 0 into 0 6.545 * [backup-simplify]: Simplify 1 into 1 6.545 * [backup-simplify]: Simplify (/ PI 1) into PI 6.546 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.547 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.547 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.547 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 6.549 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.550 * [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)))) 6.551 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 6.551 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 6.551 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 6.552 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 6.552 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 6.552 * [taylor]: Taking taylor expansion of 0.5 in n 6.552 * [backup-simplify]: Simplify 0.5 into 0.5 6.552 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 6.552 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.552 * [taylor]: Taking taylor expansion of k in n 6.552 * [backup-simplify]: Simplify k into k 6.552 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.552 * [taylor]: Taking taylor expansion of 1.0 in n 6.552 * [backup-simplify]: Simplify 1.0 into 1.0 6.552 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 6.552 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.552 * [taylor]: Taking taylor expansion of -2.0 in n 6.552 * [backup-simplify]: Simplify -2.0 into -2.0 6.552 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.552 * [taylor]: Taking taylor expansion of PI in n 6.552 * [backup-simplify]: Simplify PI into PI 6.552 * [taylor]: Taking taylor expansion of n in n 6.552 * [backup-simplify]: Simplify 0 into 0 6.552 * [backup-simplify]: Simplify 1 into 1 6.553 * [backup-simplify]: Simplify (/ PI 1) into PI 6.553 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.554 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.554 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 6.555 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 6.556 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.558 * [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)))) 6.559 * [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))))) 6.559 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 6.559 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 6.559 * [taylor]: Taking taylor expansion of 0.5 in k 6.559 * [backup-simplify]: Simplify 0.5 into 0.5 6.559 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 6.559 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 6.559 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.559 * [taylor]: Taking taylor expansion of k in k 6.559 * [backup-simplify]: Simplify 0 into 0 6.560 * [backup-simplify]: Simplify 1 into 1 6.560 * [backup-simplify]: Simplify (/ 1 1) into 1 6.560 * [taylor]: Taking taylor expansion of 1.0 in k 6.560 * [backup-simplify]: Simplify 1.0 into 1.0 6.560 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 6.560 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 6.560 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 6.560 * [taylor]: Taking taylor expansion of -2.0 in k 6.560 * [backup-simplify]: Simplify -2.0 into -2.0 6.560 * [taylor]: Taking taylor expansion of PI in k 6.560 * [backup-simplify]: Simplify PI into PI 6.561 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.563 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 6.563 * [taylor]: Taking taylor expansion of (log n) in k 6.563 * [taylor]: Taking taylor expansion of n in k 6.563 * [backup-simplify]: Simplify n into n 6.563 * [backup-simplify]: Simplify (log n) into (log n) 6.564 * [backup-simplify]: Simplify (+ 1 0) into 1 6.564 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.565 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 6.566 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 6.568 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 6.569 * [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))))) 6.570 * [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))))) 6.571 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.572 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.575 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 6.575 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.575 * [backup-simplify]: Simplify (+ 0 0) into 0 6.576 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 6.578 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.579 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 6.581 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.581 * [taylor]: Taking taylor expansion of 0 in k 6.581 * [backup-simplify]: Simplify 0 into 0 6.581 * [backup-simplify]: Simplify 0 into 0 6.581 * [backup-simplify]: Simplify 0 into 0 6.582 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.583 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.584 * [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 6.585 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.585 * [backup-simplify]: Simplify (+ 0 0) into 0 6.585 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 6.586 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.587 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 6.589 * [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 6.589 * [taylor]: Taking taylor expansion of 0 in k 6.589 * [backup-simplify]: Simplify 0 into 0 6.589 * [backup-simplify]: Simplify 0 into 0 6.589 * [backup-simplify]: Simplify 0 into 0 6.589 * [backup-simplify]: Simplify 0 into 0 6.590 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.590 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.593 * [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 6.594 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.594 * [backup-simplify]: Simplify (+ 0 0) into 0 6.595 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 6.596 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 6.597 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 6.598 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 6.598 * [taylor]: Taking taylor expansion of 0 in k 6.598 * [backup-simplify]: Simplify 0 into 0 6.598 * [backup-simplify]: Simplify 0 into 0 6.599 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 6.599 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 2 1) 6.600 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 6.600 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 6.600 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.600 * [taylor]: Taking taylor expansion of 2.0 in n 6.600 * [backup-simplify]: Simplify 2.0 into 2.0 6.600 * [taylor]: Taking taylor expansion of (* n PI) in n 6.600 * [taylor]: Taking taylor expansion of n in n 6.600 * [backup-simplify]: Simplify 0 into 0 6.600 * [backup-simplify]: Simplify 1 into 1 6.600 * [taylor]: Taking taylor expansion of PI in n 6.600 * [backup-simplify]: Simplify PI into PI 6.600 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.600 * [taylor]: Taking taylor expansion of 2.0 in n 6.600 * [backup-simplify]: Simplify 2.0 into 2.0 6.600 * [taylor]: Taking taylor expansion of (* n PI) in n 6.600 * [taylor]: Taking taylor expansion of n in n 6.600 * [backup-simplify]: Simplify 0 into 0 6.600 * [backup-simplify]: Simplify 1 into 1 6.600 * [taylor]: Taking taylor expansion of PI in n 6.600 * [backup-simplify]: Simplify PI into PI 6.600 * [backup-simplify]: Simplify (* 0 PI) into 0 6.601 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.601 * [backup-simplify]: Simplify 0 into 0 6.602 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.603 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.603 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.603 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.604 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.604 * [backup-simplify]: Simplify 0 into 0 6.605 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.606 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.606 * [backup-simplify]: Simplify 0 into 0 6.606 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.607 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 6.607 * [backup-simplify]: Simplify 0 into 0 6.608 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.609 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 6.609 * [backup-simplify]: Simplify 0 into 0 6.610 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.611 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 6.611 * [backup-simplify]: Simplify 0 into 0 6.612 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 6.613 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 6.613 * [backup-simplify]: Simplify 0 into 0 6.613 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 6.614 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 6.614 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 6.614 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.614 * [taylor]: Taking taylor expansion of 2.0 in n 6.614 * [backup-simplify]: Simplify 2.0 into 2.0 6.614 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.614 * [taylor]: Taking taylor expansion of PI in n 6.614 * [backup-simplify]: Simplify PI into PI 6.614 * [taylor]: Taking taylor expansion of n in n 6.614 * [backup-simplify]: Simplify 0 into 0 6.614 * [backup-simplify]: Simplify 1 into 1 6.614 * [backup-simplify]: Simplify (/ PI 1) into PI 6.614 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.614 * [taylor]: Taking taylor expansion of 2.0 in n 6.614 * [backup-simplify]: Simplify 2.0 into 2.0 6.614 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.614 * [taylor]: Taking taylor expansion of PI in n 6.614 * [backup-simplify]: Simplify PI into PI 6.614 * [taylor]: Taking taylor expansion of n in n 6.614 * [backup-simplify]: Simplify 0 into 0 6.614 * [backup-simplify]: Simplify 1 into 1 6.615 * [backup-simplify]: Simplify (/ PI 1) into PI 6.615 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.615 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.616 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.616 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.616 * [backup-simplify]: Simplify 0 into 0 6.617 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.617 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.618 * [backup-simplify]: Simplify 0 into 0 6.619 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.624 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.624 * [backup-simplify]: Simplify 0 into 0 6.626 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.627 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.627 * [backup-simplify]: Simplify 0 into 0 6.628 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.630 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.630 * [backup-simplify]: Simplify 0 into 0 6.631 * [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 6.633 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.633 * [backup-simplify]: Simplify 0 into 0 6.634 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 6.634 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 6.634 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 6.634 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.634 * [taylor]: Taking taylor expansion of -2.0 in n 6.634 * [backup-simplify]: Simplify -2.0 into -2.0 6.634 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.634 * [taylor]: Taking taylor expansion of PI in n 6.634 * [backup-simplify]: Simplify PI into PI 6.634 * [taylor]: Taking taylor expansion of n in n 6.634 * [backup-simplify]: Simplify 0 into 0 6.635 * [backup-simplify]: Simplify 1 into 1 6.635 * [backup-simplify]: Simplify (/ PI 1) into PI 6.635 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 6.635 * [taylor]: Taking taylor expansion of -2.0 in n 6.635 * [backup-simplify]: Simplify -2.0 into -2.0 6.635 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.635 * [taylor]: Taking taylor expansion of PI in n 6.636 * [backup-simplify]: Simplify PI into PI 6.636 * [taylor]: Taking taylor expansion of n in n 6.636 * [backup-simplify]: Simplify 0 into 0 6.636 * [backup-simplify]: Simplify 1 into 1 6.636 * [backup-simplify]: Simplify (/ PI 1) into PI 6.637 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.637 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 6.638 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.639 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 6.639 * [backup-simplify]: Simplify 0 into 0 6.640 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.641 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.641 * [backup-simplify]: Simplify 0 into 0 6.642 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.643 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.643 * [backup-simplify]: Simplify 0 into 0 6.644 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.646 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.646 * [backup-simplify]: Simplify 0 into 0 6.647 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.649 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 6.649 * [backup-simplify]: Simplify 0 into 0 6.650 * [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 6.651 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 6.651 * [backup-simplify]: Simplify 0 into 0 6.652 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 6.652 * * * * [progress]: [ 3 / 3 ] generating series at (2) 6.653 * [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)))) 6.653 * [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 6.653 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k 6.653 * [taylor]: Taking taylor expansion of 1.0 in k 6.653 * [backup-simplify]: Simplify 1.0 into 1.0 6.653 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k 6.653 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k 6.653 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 6.653 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 6.653 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k 6.653 * [taylor]: Taking taylor expansion of 0.5 in k 6.654 * [backup-simplify]: Simplify 0.5 into 0.5 6.654 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.654 * [taylor]: Taking taylor expansion of 1.0 in k 6.654 * [backup-simplify]: Simplify 1.0 into 1.0 6.654 * [taylor]: Taking taylor expansion of k in k 6.654 * [backup-simplify]: Simplify 0 into 0 6.654 * [backup-simplify]: Simplify 1 into 1 6.654 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 6.654 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 6.654 * [taylor]: Taking taylor expansion of 2.0 in k 6.654 * [backup-simplify]: Simplify 2.0 into 2.0 6.654 * [taylor]: Taking taylor expansion of (* n PI) in k 6.654 * [taylor]: Taking taylor expansion of n in k 6.654 * [backup-simplify]: Simplify n into n 6.654 * [taylor]: Taking taylor expansion of PI in k 6.654 * [backup-simplify]: Simplify PI into PI 6.654 * [backup-simplify]: Simplify (* n PI) into (* n PI) 6.654 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 6.654 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 6.655 * [backup-simplify]: Simplify (- 0) into 0 6.655 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.655 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5 6.656 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI)))) 6.656 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5) 6.656 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.656 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.656 * [taylor]: Taking taylor expansion of k in k 6.656 * [backup-simplify]: Simplify 0 into 0 6.656 * [backup-simplify]: Simplify 1 into 1 6.656 * [backup-simplify]: Simplify (/ 1 1) into 1 6.657 * [backup-simplify]: Simplify (sqrt 0) into 0 6.658 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.658 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 6.658 * [taylor]: Taking taylor expansion of 1.0 in n 6.658 * [backup-simplify]: Simplify 1.0 into 1.0 6.658 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 6.658 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 6.658 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.658 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.658 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 6.658 * [taylor]: Taking taylor expansion of 0.5 in n 6.659 * [backup-simplify]: Simplify 0.5 into 0.5 6.659 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.659 * [taylor]: Taking taylor expansion of 1.0 in n 6.659 * [backup-simplify]: Simplify 1.0 into 1.0 6.659 * [taylor]: Taking taylor expansion of k in n 6.659 * [backup-simplify]: Simplify k into k 6.659 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.659 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.659 * [taylor]: Taking taylor expansion of 2.0 in n 6.659 * [backup-simplify]: Simplify 2.0 into 2.0 6.659 * [taylor]: Taking taylor expansion of (* n PI) in n 6.659 * [taylor]: Taking taylor expansion of n in n 6.659 * [backup-simplify]: Simplify 0 into 0 6.659 * [backup-simplify]: Simplify 1 into 1 6.659 * [taylor]: Taking taylor expansion of PI in n 6.659 * [backup-simplify]: Simplify PI into PI 6.659 * [backup-simplify]: Simplify (* 0 PI) into 0 6.660 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.661 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.663 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.664 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.664 * [backup-simplify]: Simplify (- k) into (- k) 6.664 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.664 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 6.666 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.667 * [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)))) 6.668 * [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))))) 6.668 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 6.668 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.668 * [taylor]: Taking taylor expansion of k in n 6.669 * [backup-simplify]: Simplify k into k 6.669 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.669 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 6.669 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.669 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 6.669 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n 6.669 * [taylor]: Taking taylor expansion of 1.0 in n 6.669 * [backup-simplify]: Simplify 1.0 into 1.0 6.669 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n 6.669 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n 6.669 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 6.669 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 6.669 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n 6.669 * [taylor]: Taking taylor expansion of 0.5 in n 6.669 * [backup-simplify]: Simplify 0.5 into 0.5 6.669 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 6.669 * [taylor]: Taking taylor expansion of 1.0 in n 6.669 * [backup-simplify]: Simplify 1.0 into 1.0 6.669 * [taylor]: Taking taylor expansion of k in n 6.670 * [backup-simplify]: Simplify k into k 6.670 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 6.670 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 6.670 * [taylor]: Taking taylor expansion of 2.0 in n 6.670 * [backup-simplify]: Simplify 2.0 into 2.0 6.670 * [taylor]: Taking taylor expansion of (* n PI) in n 6.670 * [taylor]: Taking taylor expansion of n in n 6.670 * [backup-simplify]: Simplify 0 into 0 6.670 * [backup-simplify]: Simplify 1 into 1 6.670 * [taylor]: Taking taylor expansion of PI in n 6.670 * [backup-simplify]: Simplify PI into PI 6.670 * [backup-simplify]: Simplify (* 0 PI) into 0 6.671 * [backup-simplify]: Simplify (* 2.0 0) into 0 6.672 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 6.674 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 6.675 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.675 * [backup-simplify]: Simplify (- k) into (- k) 6.675 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 6.675 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k)) 6.677 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.678 * [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)))) 6.679 * [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))))) 6.679 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n 6.679 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.679 * [taylor]: Taking taylor expansion of k in n 6.679 * [backup-simplify]: Simplify k into k 6.679 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.679 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k)) 6.680 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.680 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0 6.681 * [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)))))) 6.682 * [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))))))) 6.683 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))) in k 6.683 * [taylor]: Taking taylor expansion of 1.0 in k 6.683 * [backup-simplify]: Simplify 1.0 into 1.0 6.683 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) in k 6.683 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k 6.683 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.683 * [taylor]: Taking taylor expansion of k in k 6.683 * [backup-simplify]: Simplify 0 into 0 6.683 * [backup-simplify]: Simplify 1 into 1 6.683 * [backup-simplify]: Simplify (/ 1 1) into 1 6.684 * [backup-simplify]: Simplify (sqrt 0) into 0 6.685 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.685 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 6.685 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 6.685 * [taylor]: Taking taylor expansion of 0.5 in k 6.685 * [backup-simplify]: Simplify 0.5 into 0.5 6.685 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 6.685 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 6.685 * [taylor]: Taking taylor expansion of 1.0 in k 6.685 * [backup-simplify]: Simplify 1.0 into 1.0 6.685 * [taylor]: Taking taylor expansion of k in k 6.685 * [backup-simplify]: Simplify 0 into 0 6.685 * [backup-simplify]: Simplify 1 into 1 6.685 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 6.685 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.686 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.686 * [taylor]: Taking taylor expansion of 2.0 in k 6.686 * [backup-simplify]: Simplify 2.0 into 2.0 6.686 * [taylor]: Taking taylor expansion of PI in k 6.686 * [backup-simplify]: Simplify PI into PI 6.686 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.687 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.687 * [taylor]: Taking taylor expansion of (log n) in k 6.687 * [taylor]: Taking taylor expansion of n in k 6.687 * [backup-simplify]: Simplify n into n 6.687 * [backup-simplify]: Simplify (log n) into (log n) 6.688 * [backup-simplify]: Simplify (- 0) into 0 6.688 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 6.689 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 6.690 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 6.692 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n))) 6.693 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 6.694 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) into 0 6.694 * [backup-simplify]: Simplify (* 1.0 0) into 0 6.694 * [backup-simplify]: Simplify 0 into 0 6.695 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 6.696 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 6.698 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.699 * [backup-simplify]: Simplify (- 0) into 0 6.699 * [backup-simplify]: Simplify (+ 0 0) into 0 6.700 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0 6.701 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.702 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 6.704 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.705 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0 6.707 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))))) into 0 6.707 * [taylor]: Taking taylor expansion of 0 in k 6.707 * [backup-simplify]: Simplify 0 into 0 6.708 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.710 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.711 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 6.711 * [backup-simplify]: Simplify (+ 0 0) into 0 6.712 * [backup-simplify]: Simplify (- 1) into -1 6.712 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.714 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 6.716 * [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)))) 6.720 * [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)))))) 6.724 * [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)))))) 6.726 * [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)))))) 6.727 * [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)))))) 6.727 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.728 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0 6.729 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 6.730 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 6.734 * [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 6.734 * [backup-simplify]: Simplify (- 0) into 0 6.735 * [backup-simplify]: Simplify (+ 0 0) into 0 6.736 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 6.737 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.739 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.741 * [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 6.743 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0 6.745 * [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 6.745 * [taylor]: Taking taylor expansion of 0 in k 6.745 * [backup-simplify]: Simplify 0 into 0 6.745 * [backup-simplify]: Simplify 0 into 0 6.746 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.750 * [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 6.751 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 6.751 * [backup-simplify]: Simplify (+ 0 0) into 0 6.751 * [backup-simplify]: Simplify (- 0) into 0 6.752 * [backup-simplify]: Simplify (+ 0 0) into 0 6.753 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 6.754 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.757 * [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)))))) 6.757 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 6.759 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.768 * [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)))))))) 6.772 * [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)))))))) 6.775 * [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)))))))) 6.775 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.776 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0 6.777 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 6.777 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 6.781 * [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 6.781 * [backup-simplify]: Simplify (- 0) into 0 6.781 * [backup-simplify]: Simplify (+ 0 0) into 0 6.782 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0 6.784 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 6.786 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.789 * [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 6.791 * [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 6.793 * [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 6.793 * [taylor]: Taking taylor expansion of 0 in k 6.793 * [backup-simplify]: Simplify 0 into 0 6.793 * [backup-simplify]: Simplify 0 into 0 6.794 * [backup-simplify]: Simplify 0 into 0 6.795 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.801 * [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 6.804 * [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 6.805 * [backup-simplify]: Simplify (+ 0 0) into 0 6.805 * [backup-simplify]: Simplify (- 0) into 0 6.805 * [backup-simplify]: Simplify (+ 0 0) into 0 6.808 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0 6.811 * [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 6.817 * [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))))))) 6.818 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.822 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 6.840 * [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)))))))))))))))) 6.858 * [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)))))))))))))) 6.871 * [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)))))))))))))) 6.895 * [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)))))))))))))))))))))))) 6.896 * [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)))))) 6.896 * [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 6.896 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k 6.896 * [taylor]: Taking taylor expansion of 1.0 in k 6.897 * [backup-simplify]: Simplify 1.0 into 1.0 6.897 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k 6.897 * [taylor]: Taking taylor expansion of (sqrt k) in k 6.897 * [taylor]: Taking taylor expansion of k in k 6.897 * [backup-simplify]: Simplify 0 into 0 6.897 * [backup-simplify]: Simplify 1 into 1 6.901 * [backup-simplify]: Simplify (sqrt 0) into 0 6.903 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.903 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k 6.903 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 6.903 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 6.903 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k 6.903 * [taylor]: Taking taylor expansion of 0.5 in k 6.903 * [backup-simplify]: Simplify 0.5 into 0.5 6.903 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.903 * [taylor]: Taking taylor expansion of 1.0 in k 6.903 * [backup-simplify]: Simplify 1.0 into 1.0 6.903 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.903 * [taylor]: Taking taylor expansion of k in k 6.903 * [backup-simplify]: Simplify 0 into 0 6.903 * [backup-simplify]: Simplify 1 into 1 6.904 * [backup-simplify]: Simplify (/ 1 1) into 1 6.904 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 6.904 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 6.904 * [taylor]: Taking taylor expansion of 2.0 in k 6.904 * [backup-simplify]: Simplify 2.0 into 2.0 6.904 * [taylor]: Taking taylor expansion of (/ PI n) in k 6.904 * [taylor]: Taking taylor expansion of PI in k 6.904 * [backup-simplify]: Simplify PI into PI 6.904 * [taylor]: Taking taylor expansion of n in k 6.904 * [backup-simplify]: Simplify n into n 6.904 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 6.904 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 6.904 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 6.904 * [backup-simplify]: Simplify (- 1) into -1 6.905 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.905 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5 6.905 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n)))) 6.906 * [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))))) 6.906 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 6.906 * [taylor]: Taking taylor expansion of 1.0 in n 6.906 * [backup-simplify]: Simplify 1.0 into 1.0 6.906 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 6.906 * [taylor]: Taking taylor expansion of (sqrt k) in n 6.906 * [taylor]: Taking taylor expansion of k in n 6.906 * [backup-simplify]: Simplify k into k 6.906 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 6.906 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 6.906 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 6.906 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.906 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.906 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 6.906 * [taylor]: Taking taylor expansion of 0.5 in n 6.906 * [backup-simplify]: Simplify 0.5 into 0.5 6.906 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.906 * [taylor]: Taking taylor expansion of 1.0 in n 6.906 * [backup-simplify]: Simplify 1.0 into 1.0 6.906 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.906 * [taylor]: Taking taylor expansion of k in n 6.906 * [backup-simplify]: Simplify k into k 6.906 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.906 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.907 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.907 * [taylor]: Taking taylor expansion of 2.0 in n 6.907 * [backup-simplify]: Simplify 2.0 into 2.0 6.907 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.907 * [taylor]: Taking taylor expansion of PI in n 6.907 * [backup-simplify]: Simplify PI into PI 6.907 * [taylor]: Taking taylor expansion of n in n 6.907 * [backup-simplify]: Simplify 0 into 0 6.907 * [backup-simplify]: Simplify 1 into 1 6.907 * [backup-simplify]: Simplify (/ PI 1) into PI 6.908 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.909 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.909 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.909 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.909 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.911 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.912 * [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)))) 6.913 * [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))))) 6.913 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n 6.913 * [taylor]: Taking taylor expansion of 1.0 in n 6.913 * [backup-simplify]: Simplify 1.0 into 1.0 6.913 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n 6.913 * [taylor]: Taking taylor expansion of (sqrt k) in n 6.913 * [taylor]: Taking taylor expansion of k in n 6.913 * [backup-simplify]: Simplify k into k 6.913 * [backup-simplify]: Simplify (sqrt k) into (sqrt k) 6.913 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0 6.913 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n 6.914 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 6.914 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 6.914 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n 6.914 * [taylor]: Taking taylor expansion of 0.5 in n 6.914 * [backup-simplify]: Simplify 0.5 into 0.5 6.914 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 6.914 * [taylor]: Taking taylor expansion of 1.0 in n 6.914 * [backup-simplify]: Simplify 1.0 into 1.0 6.914 * [taylor]: Taking taylor expansion of (/ 1 k) in n 6.914 * [taylor]: Taking taylor expansion of k in n 6.914 * [backup-simplify]: Simplify k into k 6.914 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 6.914 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 6.914 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 6.914 * [taylor]: Taking taylor expansion of 2.0 in n 6.914 * [backup-simplify]: Simplify 2.0 into 2.0 6.914 * [taylor]: Taking taylor expansion of (/ PI n) in n 6.914 * [taylor]: Taking taylor expansion of PI in n 6.914 * [backup-simplify]: Simplify PI into PI 6.914 * [taylor]: Taking taylor expansion of n in n 6.914 * [backup-simplify]: Simplify 0 into 0 6.914 * [backup-simplify]: Simplify 1 into 1 6.915 * [backup-simplify]: Simplify (/ PI 1) into PI 6.915 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.916 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.917 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 6.917 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 6.917 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k))) 6.918 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.919 * [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)))) 6.921 * [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))))) 6.922 * [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)))))) 6.924 * [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))))))) 6.924 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) in k 6.924 * [taylor]: Taking taylor expansion of 1.0 in k 6.924 * [backup-simplify]: Simplify 1.0 into 1.0 6.924 * [taylor]: Taking taylor expansion of (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) in k 6.924 * [taylor]: Taking taylor expansion of (sqrt k) in k 6.924 * [taylor]: Taking taylor expansion of k in k 6.924 * [backup-simplify]: Simplify 0 into 0 6.924 * [backup-simplify]: Simplify 1 into 1 6.924 * [backup-simplify]: Simplify (sqrt 0) into 0 6.925 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0 6.925 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 6.926 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 6.926 * [taylor]: Taking taylor expansion of 0.5 in k 6.926 * [backup-simplify]: Simplify 0.5 into 0.5 6.926 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 6.926 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 6.926 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 6.926 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 6.926 * [taylor]: Taking taylor expansion of 2.0 in k 6.926 * [backup-simplify]: Simplify 2.0 into 2.0 6.926 * [taylor]: Taking taylor expansion of PI in k 6.926 * [backup-simplify]: Simplify PI into PI 6.926 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 6.928 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 6.928 * [taylor]: Taking taylor expansion of (log n) in k 6.928 * [taylor]: Taking taylor expansion of n in k 6.928 * [backup-simplify]: Simplify n into n 6.928 * [backup-simplify]: Simplify (log n) into (log n) 6.928 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 6.928 * [taylor]: Taking taylor expansion of 1.0 in k 6.928 * [backup-simplify]: Simplify 1.0 into 1.0 6.928 * [taylor]: Taking taylor expansion of (/ 1 k) in k 6.928 * [taylor]: Taking taylor expansion of k in k 6.928 * [backup-simplify]: Simplify 0 into 0 6.928 * [backup-simplify]: Simplify 1 into 1 6.928 * [backup-simplify]: Simplify (/ 1 1) into 1 6.928 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 6.929 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 6.930 * [backup-simplify]: Simplify (- 1) into -1 6.930 * [backup-simplify]: Simplify (+ 0 -1) into -1 6.931 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 6.932 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n))) 6.933 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 6.935 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into 0 6.935 * [backup-simplify]: Simplify (* 1.0 0) into 0 6.935 * [backup-simplify]: Simplify 0 into 0 6.936 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 6.937 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 6.939 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 6.939 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 6.940 * [backup-simplify]: Simplify (- 0) into 0 6.940 * [backup-simplify]: Simplify (+ 0 0) into 0 6.940 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0 6.942 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.943 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 6.945 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 6.946 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0 6.948 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0 6.948 * [taylor]: Taking taylor expansion of 0 in k 6.948 * [backup-simplify]: Simplify 0 into 0 6.948 * [backup-simplify]: Simplify 0 into 0 6.950 * [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))))))) 6.952 * [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))))))) 6.953 * [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))))))) 6.954 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.955 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 6.959 * [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 6.959 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.960 * [backup-simplify]: Simplify (- 0) into 0 6.960 * [backup-simplify]: Simplify (+ 0 0) into 0 6.961 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 6.963 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.964 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 6.966 * [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 6.967 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0 6.969 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0 6.971 * [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 6.971 * [taylor]: Taking taylor expansion of 0 in k 6.971 * [backup-simplify]: Simplify 0 into 0 6.971 * [backup-simplify]: Simplify 0 into 0 6.971 * [backup-simplify]: Simplify 0 into 0 6.975 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 6.977 * [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))))))) 6.980 * [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))))))) 6.982 * [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))))))) 6.983 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 6.984 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 6.991 * [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 6.991 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 6.992 * [backup-simplify]: Simplify (- 0) into 0 6.992 * [backup-simplify]: Simplify (+ 0 0) into 0 6.993 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 6.995 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 6.997 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 7.000 * [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 7.001 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0 7.003 * [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 7.005 * [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 7.005 * [taylor]: Taking taylor expansion of 0 in k 7.005 * [backup-simplify]: Simplify 0 into 0 7.005 * [backup-simplify]: Simplify 0 into 0 7.006 * [backup-simplify]: Simplify 0 into 0 7.006 * [backup-simplify]: Simplify 0 into 0 7.009 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 7.012 * [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))))))) 7.016 * [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))))))) 7.018 * [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))))))) 7.023 * [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)))))))) 7.024 * [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)))) 7.024 * [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 7.024 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k 7.024 * [taylor]: Taking taylor expansion of 1.0 in k 7.024 * [backup-simplify]: Simplify 1.0 into 1.0 7.024 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k 7.024 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k 7.024 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 7.024 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 7.024 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k 7.024 * [taylor]: Taking taylor expansion of 0.5 in k 7.024 * [backup-simplify]: Simplify 0.5 into 0.5 7.024 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 7.024 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.024 * [taylor]: Taking taylor expansion of k in k 7.024 * [backup-simplify]: Simplify 0 into 0 7.024 * [backup-simplify]: Simplify 1 into 1 7.025 * [backup-simplify]: Simplify (/ 1 1) into 1 7.025 * [taylor]: Taking taylor expansion of 1.0 in k 7.025 * [backup-simplify]: Simplify 1.0 into 1.0 7.025 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 7.025 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 7.025 * [taylor]: Taking taylor expansion of -2.0 in k 7.025 * [backup-simplify]: Simplify -2.0 into -2.0 7.025 * [taylor]: Taking taylor expansion of (/ PI n) in k 7.025 * [taylor]: Taking taylor expansion of PI in k 7.025 * [backup-simplify]: Simplify PI into PI 7.025 * [taylor]: Taking taylor expansion of n in k 7.025 * [backup-simplify]: Simplify n into n 7.025 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 7.025 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 7.025 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 7.026 * [backup-simplify]: Simplify (+ 1 0) into 1 7.026 * [backup-simplify]: Simplify (* 0.5 1) into 0.5 7.027 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n)))) 7.027 * [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)))))) 7.027 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 7.027 * [taylor]: Taking taylor expansion of (/ -1 k) in k 7.027 * [taylor]: Taking taylor expansion of -1 in k 7.027 * [backup-simplify]: Simplify -1 into -1 7.027 * [taylor]: Taking taylor expansion of k in k 7.027 * [backup-simplify]: Simplify 0 into 0 7.027 * [backup-simplify]: Simplify 1 into 1 7.027 * [backup-simplify]: Simplify (/ -1 1) into -1 7.028 * [backup-simplify]: Simplify (sqrt 0) into 0 7.029 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 7.030 * [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))))))) 7.030 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 7.030 * [taylor]: Taking taylor expansion of 1.0 in n 7.030 * [backup-simplify]: Simplify 1.0 into 1.0 7.030 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 7.030 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 7.030 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 7.030 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 7.030 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 7.030 * [taylor]: Taking taylor expansion of 0.5 in n 7.030 * [backup-simplify]: Simplify 0.5 into 0.5 7.030 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 7.030 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.030 * [taylor]: Taking taylor expansion of k in n 7.030 * [backup-simplify]: Simplify k into k 7.030 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.030 * [taylor]: Taking taylor expansion of 1.0 in n 7.030 * [backup-simplify]: Simplify 1.0 into 1.0 7.030 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 7.030 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 7.030 * [taylor]: Taking taylor expansion of -2.0 in n 7.030 * [backup-simplify]: Simplify -2.0 into -2.0 7.030 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.030 * [taylor]: Taking taylor expansion of PI in n 7.030 * [backup-simplify]: Simplify PI into PI 7.030 * [taylor]: Taking taylor expansion of n in n 7.030 * [backup-simplify]: Simplify 0 into 0 7.030 * [backup-simplify]: Simplify 1 into 1 7.031 * [backup-simplify]: Simplify (/ PI 1) into PI 7.032 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 7.033 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 7.033 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 7.033 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 7.034 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.035 * [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)))) 7.037 * [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))))) 7.037 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 7.037 * [taylor]: Taking taylor expansion of (/ -1 k) in n 7.037 * [taylor]: Taking taylor expansion of -1 in n 7.037 * [backup-simplify]: Simplify -1 into -1 7.037 * [taylor]: Taking taylor expansion of k in n 7.037 * [backup-simplify]: Simplify k into k 7.037 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 7.037 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 7.038 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 7.038 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 7.039 * [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))) 7.039 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n 7.039 * [taylor]: Taking taylor expansion of 1.0 in n 7.039 * [backup-simplify]: Simplify 1.0 into 1.0 7.039 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n 7.039 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n 7.039 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 7.039 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 7.039 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n 7.040 * [taylor]: Taking taylor expansion of 0.5 in n 7.040 * [backup-simplify]: Simplify 0.5 into 0.5 7.040 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 7.040 * [taylor]: Taking taylor expansion of (/ 1 k) in n 7.040 * [taylor]: Taking taylor expansion of k in n 7.040 * [backup-simplify]: Simplify k into k 7.040 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 7.040 * [taylor]: Taking taylor expansion of 1.0 in n 7.040 * [backup-simplify]: Simplify 1.0 into 1.0 7.040 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 7.040 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 7.040 * [taylor]: Taking taylor expansion of -2.0 in n 7.040 * [backup-simplify]: Simplify -2.0 into -2.0 7.040 * [taylor]: Taking taylor expansion of (/ PI n) in n 7.040 * [taylor]: Taking taylor expansion of PI in n 7.040 * [backup-simplify]: Simplify PI into PI 7.040 * [taylor]: Taking taylor expansion of n in n 7.040 * [backup-simplify]: Simplify 0 into 0 7.040 * [backup-simplify]: Simplify 1 into 1 7.041 * [backup-simplify]: Simplify (/ PI 1) into PI 7.041 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 7.042 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 7.042 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 7.042 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0)) 7.044 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.045 * [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)))) 7.046 * [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))))) 7.046 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n 7.047 * [taylor]: Taking taylor expansion of (/ -1 k) in n 7.047 * [taylor]: Taking taylor expansion of -1 in n 7.047 * [backup-simplify]: Simplify -1 into -1 7.047 * [taylor]: Taking taylor expansion of k in n 7.047 * [backup-simplify]: Simplify k into k 7.047 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k) 7.047 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k)) 7.047 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0 7.047 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0 7.048 * [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))) 7.050 * [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)))) 7.050 * [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 7.050 * [taylor]: Taking taylor expansion of 1.0 in k 7.050 * [backup-simplify]: Simplify 1.0 into 1.0 7.050 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) in k 7.050 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 7.050 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 7.050 * [taylor]: Taking taylor expansion of 0.5 in k 7.050 * [backup-simplify]: Simplify 0.5 into 0.5 7.050 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 7.050 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 7.050 * [taylor]: Taking taylor expansion of (/ 1 k) in k 7.050 * [taylor]: Taking taylor expansion of k in k 7.050 * [backup-simplify]: Simplify 0 into 0 7.050 * [backup-simplify]: Simplify 1 into 1 7.051 * [backup-simplify]: Simplify (/ 1 1) into 1 7.051 * [taylor]: Taking taylor expansion of 1.0 in k 7.051 * [backup-simplify]: Simplify 1.0 into 1.0 7.051 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 7.051 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 7.051 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 7.051 * [taylor]: Taking taylor expansion of -2.0 in k 7.051 * [backup-simplify]: Simplify -2.0 into -2.0 7.051 * [taylor]: Taking taylor expansion of PI in k 7.051 * [backup-simplify]: Simplify PI into PI 7.052 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 7.053 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 7.053 * [taylor]: Taking taylor expansion of (log n) in k 7.053 * [taylor]: Taking taylor expansion of n in k 7.053 * [backup-simplify]: Simplify n into n 7.053 * [backup-simplify]: Simplify (log n) into (log n) 7.053 * [backup-simplify]: Simplify (+ 1 0) into 1 7.053 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 7.059 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 7.060 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 7.061 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n))) 7.063 * [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))))) 7.063 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k 7.063 * [taylor]: Taking taylor expansion of (/ -1 k) in k 7.063 * [taylor]: Taking taylor expansion of -1 in k 7.063 * [backup-simplify]: Simplify -1 into -1 7.063 * [taylor]: Taking taylor expansion of k in k 7.063 * [backup-simplify]: Simplify 0 into 0 7.063 * [backup-simplify]: Simplify 1 into 1 7.063 * [backup-simplify]: Simplify (/ -1 1) into -1 7.064 * [backup-simplify]: Simplify (sqrt 0) into 0 7.065 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0 7.067 * [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)))))) 7.068 * [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)))))) 7.069 * [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)))))) 7.070 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 7.071 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 7.073 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 7.073 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 7.074 * [backup-simplify]: Simplify (+ 0 0) into 0 7.074 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0 7.076 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.077 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 7.079 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 7.081 * [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 7.082 * [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 7.082 * [taylor]: Taking taylor expansion of 0 in k 7.083 * [backup-simplify]: Simplify 0 into 0 7.083 * [backup-simplify]: Simplify 0 into 0 7.083 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0 7.086 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0 7.089 * [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))))))) 7.091 * [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))))))) 7.093 * [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))))))) 7.094 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.095 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 7.098 * [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 7.099 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.099 * [backup-simplify]: Simplify (+ 0 0) into 0 7.100 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 7.101 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 7.103 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 7.105 * [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 7.106 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 7.106 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0 7.108 * [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 7.110 * [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 7.110 * [taylor]: Taking taylor expansion of 0 in k 7.110 * [backup-simplify]: Simplify 0 into 0 7.110 * [backup-simplify]: Simplify 0 into 0 7.111 * [backup-simplify]: Simplify 0 into 0 7.112 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 7.116 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0 7.120 * [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))))))) 7.124 * [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))))))) 7.126 * [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))))))) 7.131 * [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)))))))))))) 7.131 * * * [progress]: simplifying candidates 7.134 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (+ (+ (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 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(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)))))))))))) 7.139 * * [simplify]: Extracting # 0 : cost 0 7.139 * * [simplify]: Extracting # 1 : cost 0 7.139 * * [simplify]: Extracting # 2 : cost 0 7.139 * * [simplify]: Extracting # 3 : cost 0 7.140 * * [simplify]: Extracting # 4 : cost 0 7.140 * * [simplify]: Extracting # 5 : cost 0 7.140 * * [simplify]: Extracting # 6 : cost 0 7.141 * * [simplify]: Extracting # 7 : cost 0 7.141 * * [simplify]: Extracting # 8 : cost 0 7.141 * * [simplify]: Extracting # 9 : cost 0 7.141 * * [simplify]: Extracting # 10 : cost 0 7.142 * * [simplify]: Extracting # 11 : cost 0 7.142 * * [simplify]: Extracting # 12 : cost 0 7.142 * * [simplify]: Extracting # 13 : cost 0 7.143 * * [simplify]: Extracting # 14 : cost 0 7.143 * * [simplify]: Extracting # 15 : cost 0 7.143 * * [simplify]: Extracting # 16 : cost 0 7.144 * * [simplify]: Extracting # 17 : cost 0 7.144 * * [simplify]: Extracting # 18 : cost 0 7.144 * * [simplify]: Extracting # 19 : cost 0 7.145 * * [simplify]: Extracting # 20 : cost 0 7.145 * * [simplify]: Extracting # 21 : cost 0 7.145 * * [simplify]: Extracting # 22 : cost 0 7.146 * * [simplify]: Extracting # 23 : cost 0 7.146 * * [simplify]: Extracting # 24 : cost 0 7.146 * * [simplify]: Extracting # 25 : cost 0 7.147 * * [simplify]: Extracting # 26 : cost 0 7.147 * * [simplify]: Extracting # 27 : cost 0 7.148 * * [simplify]: Extracting # 28 : cost 0 7.148 * * [simplify]: Extracting # 29 : cost 0 7.148 * * [simplify]: Extracting # 30 : cost 0 7.149 * * [simplify]: Extracting # 31 : cost 0 7.149 * * [simplify]: Extracting # 32 : cost 0 7.149 * * [simplify]: iteration 0 : 270 enodes (cost 1898 ) 7.228 * * [simplify]: Extracting # 0 : cost 0 7.230 * * [simplify]: Extracting # 1 : cost 0 7.232 * * [simplify]: Extracting # 2 : cost 0 7.234 * * [simplify]: Extracting # 3 : cost 0 7.236 * * [simplify]: Extracting # 4 : cost 0 7.238 * * [simplify]: Extracting # 5 : cost 0 7.241 * * [simplify]: Extracting # 6 : cost 0 7.243 * * [simplify]: Extracting # 7 : cost 0 7.245 * * [simplify]: Extracting # 8 : cost 0 7.247 * * [simplify]: Extracting # 9 : cost 0 7.249 * * [simplify]: Extracting # 10 : cost 0 7.251 * * [simplify]: Extracting # 11 : cost 0 7.253 * * [simplify]: iteration 1 : 771 enodes (cost 1770 ) 7.705 * * [simplify]: Extracting # 0 : cost 0 7.710 * * [simplify]: Extracting # 1 : cost 0 7.715 * * [simplify]: Extracting # 2 : cost 0 7.720 * * [simplify]: Extracting # 3 : cost 0 7.725 * * [simplify]: Extracting # 4 : cost 0 7.734 * * [simplify]: Extracting # 5 : cost 0 7.738 * * [simplify]: Extracting # 6 : cost 0 7.743 * * [simplify]: Extracting # 7 : cost 0 7.748 * * [simplify]: iteration 2 : 3672 enodes (cost 1598 ) 9.274 * * [simplify]: Extracting # 0 : cost 0 9.286 * * [simplify]: Extracting # 1 : cost 0 9.296 * * [simplify]: Extracting # 2 : cost 0 9.303 * * [simplify]: Extracting # 3 : cost 0 9.309 * * [simplify]: Extracting # 4 : cost 0 9.315 * * [simplify]: iteration done: 5000 enodes (cost 1587 ) 9.316 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (log1p (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))) (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)))) 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(* (* 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 (/ (fabs (cbrt k)) (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))) (/ (* 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))) (fma (- 0.5) (* k (fma (log (* 2.0 PI)) (pow (* (* 2.0 PI) n) 0.5) (* (pow (* (* 2.0 PI) n) 0.5) (log n)))) (fma (* 0.125 (pow k 2)) (fma (pow (* (* 2.0 PI) n) 0.5) (pow (log (* 2.0 PI)) 2) (* (pow (* (* 2.0 PI) n) 0.5) (pow (log n) 2))) (fma (* k (* k (* (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (log (* 2.0 PI))))) 0.25 (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)))))) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (* (* 2.0 PI) n) (fma (- (* +nan.0 (pow k 2))) (pow (* (* 2.0 PI) n) 0.5) (- (fma (* (* (* (pow (* (* 2.0 PI) n) 0.5) k) k) (log n)) +nan.0 (fma (* +nan.0 (* (pow (* (* 2.0 PI) n) 0.5) (log n))) k (fma (* (* (pow (* (* 2.0 PI) n) 0.5) (pow (log (* 2.0 PI)) 2)) (pow k 2)) (- +nan.0) (fma (pow (* (* 2.0 PI) n) 0.5) (* +nan.0 k) (fma (* +nan.0 (pow k 2)) (- (* (* (pow (* (* 2.0 PI) n) 0.5) (log n)) (log (* 2.0 PI)))) (- (* (* (pow (* (* 2.0 PI) n) 0.5) (* k (log (* 2.0 PI)))) +nan.0) (* +nan.0 (- (* (* (pow (* (* 2.0 PI) n) 0.5) (pow (log n) 2)) (pow k 2)) (pow (* (* 2.0 PI) n) 0.5))))))))) (* (* (pow (* (* 2.0 PI) n) 0.5) (* +nan.0 (pow k 2))) (log (* 2.0 PI))))) (fma (- (/ (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)))) (fma (- (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) +nan.0 (* +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))))))))) 9.317 * * * [progress]: adding candidates to table 9.779 * * [progress]: iteration 3 / 4 9.779 * * * [progress]: picking best candidate 9.804 * * * * [pick]: Picked # 9.804 * * * [progress]: localizing error 9.837 * * * [progress]: generating rewritten candidates 9.837 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 2 2) 9.869 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 1) 9.932 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 2) 10.027 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 2 2 1) 10.066 * * * [progress]: generating series expansions 10.066 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 2 2) 10.067 * [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))) 10.067 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 10.067 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 10.067 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 10.067 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 10.067 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 10.067 * [taylor]: Taking taylor expansion of 0.25 in k 10.067 * [backup-simplify]: Simplify 0.25 into 0.25 10.067 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 10.067 * [taylor]: Taking taylor expansion of 1.0 in k 10.067 * [backup-simplify]: Simplify 1.0 into 1.0 10.067 * [taylor]: Taking taylor expansion of k in k 10.067 * [backup-simplify]: Simplify 0 into 0 10.067 * [backup-simplify]: Simplify 1 into 1 10.067 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 10.067 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 10.067 * [taylor]: Taking taylor expansion of 2.0 in k 10.067 * [backup-simplify]: Simplify 2.0 into 2.0 10.067 * [taylor]: Taking taylor expansion of (* n PI) in k 10.067 * [taylor]: Taking taylor expansion of n in k 10.067 * [backup-simplify]: Simplify n into n 10.067 * [taylor]: Taking taylor expansion of PI in k 10.067 * [backup-simplify]: Simplify PI into PI 10.067 * [backup-simplify]: Simplify (* n PI) into (* n PI) 10.067 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 10.067 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 10.068 * [backup-simplify]: Simplify (- 0) into 0 10.068 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 10.068 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 10.068 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 10.068 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 10.068 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 10.068 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 10.068 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 10.068 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 10.068 * [taylor]: Taking taylor expansion of 0.25 in n 10.068 * [backup-simplify]: Simplify 0.25 into 0.25 10.068 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 10.068 * [taylor]: Taking taylor expansion of 1.0 in n 10.068 * [backup-simplify]: Simplify 1.0 into 1.0 10.068 * [taylor]: Taking taylor expansion of k in n 10.068 * [backup-simplify]: Simplify k into k 10.068 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 10.069 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.069 * [taylor]: Taking taylor expansion of 2.0 in n 10.069 * [backup-simplify]: Simplify 2.0 into 2.0 10.069 * [taylor]: Taking taylor expansion of (* n PI) in n 10.069 * [taylor]: Taking taylor expansion of n in n 10.069 * [backup-simplify]: Simplify 0 into 0 10.069 * [backup-simplify]: Simplify 1 into 1 10.069 * [taylor]: Taking taylor expansion of PI in n 10.069 * [backup-simplify]: Simplify PI into PI 10.069 * [backup-simplify]: Simplify (* 0 PI) into 0 10.069 * [backup-simplify]: Simplify (* 2.0 0) into 0 10.070 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.071 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 10.072 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.072 * [backup-simplify]: Simplify (- k) into (- k) 10.072 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 10.072 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 10.073 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.074 * [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)))) 10.075 * [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))))) 10.075 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 10.075 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 10.075 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 10.075 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 10.075 * [taylor]: Taking taylor expansion of 0.25 in n 10.075 * [backup-simplify]: Simplify 0.25 into 0.25 10.075 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 10.075 * [taylor]: Taking taylor expansion of 1.0 in n 10.075 * [backup-simplify]: Simplify 1.0 into 1.0 10.075 * [taylor]: Taking taylor expansion of k in n 10.075 * [backup-simplify]: Simplify k into k 10.075 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 10.075 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.075 * [taylor]: Taking taylor expansion of 2.0 in n 10.075 * [backup-simplify]: Simplify 2.0 into 2.0 10.075 * [taylor]: Taking taylor expansion of (* n PI) in n 10.075 * [taylor]: Taking taylor expansion of n in n 10.075 * [backup-simplify]: Simplify 0 into 0 10.075 * [backup-simplify]: Simplify 1 into 1 10.075 * [taylor]: Taking taylor expansion of PI in n 10.075 * [backup-simplify]: Simplify PI into PI 10.076 * [backup-simplify]: Simplify (* 0 PI) into 0 10.076 * [backup-simplify]: Simplify (* 2.0 0) into 0 10.078 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.079 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 10.081 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.081 * [backup-simplify]: Simplify (- k) into (- k) 10.081 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 10.081 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 10.083 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.084 * [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)))) 10.085 * [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))))) 10.085 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 10.085 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 10.085 * [taylor]: Taking taylor expansion of 0.25 in k 10.085 * [backup-simplify]: Simplify 0.25 into 0.25 10.085 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 10.085 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 10.085 * [taylor]: Taking taylor expansion of 1.0 in k 10.085 * [backup-simplify]: Simplify 1.0 into 1.0 10.085 * [taylor]: Taking taylor expansion of k in k 10.086 * [backup-simplify]: Simplify 0 into 0 10.086 * [backup-simplify]: Simplify 1 into 1 10.086 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 10.086 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 10.086 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 10.086 * [taylor]: Taking taylor expansion of 2.0 in k 10.086 * [backup-simplify]: Simplify 2.0 into 2.0 10.086 * [taylor]: Taking taylor expansion of PI in k 10.086 * [backup-simplify]: Simplify PI into PI 10.086 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.087 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.087 * [taylor]: Taking taylor expansion of (log n) in k 10.087 * [taylor]: Taking taylor expansion of n in k 10.087 * [backup-simplify]: Simplify n into n 10.088 * [backup-simplify]: Simplify (log n) into (log n) 10.088 * [backup-simplify]: Simplify (- 0) into 0 10.088 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 10.090 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 10.091 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 10.092 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 10.093 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 10.094 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 10.095 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 10.097 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 10.098 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 10.099 * [backup-simplify]: Simplify (- 0) into 0 10.099 * [backup-simplify]: Simplify (+ 0 0) into 0 10.100 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 10.101 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.102 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 10.105 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.105 * [taylor]: Taking taylor expansion of 0 in k 10.105 * [backup-simplify]: Simplify 0 into 0 10.105 * [backup-simplify]: Simplify 0 into 0 10.105 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 10.107 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 10.108 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 10.109 * [backup-simplify]: Simplify (+ 0 0) into 0 10.109 * [backup-simplify]: Simplify (- 1) into -1 10.109 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.111 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 10.114 * [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)))) 10.117 * [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)))))) 10.120 * [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)))))) 10.122 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 10.123 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 10.126 * [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 10.127 * [backup-simplify]: Simplify (- 0) into 0 10.127 * [backup-simplify]: Simplify (+ 0 0) into 0 10.128 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 10.137 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.138 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 10.141 * [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 10.141 * [taylor]: Taking taylor expansion of 0 in k 10.141 * [backup-simplify]: Simplify 0 into 0 10.141 * [backup-simplify]: Simplify 0 into 0 10.141 * [backup-simplify]: Simplify 0 into 0 10.142 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.146 * [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 10.148 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 10.148 * [backup-simplify]: Simplify (+ 0 0) into 0 10.149 * [backup-simplify]: Simplify (- 0) into 0 10.149 * [backup-simplify]: Simplify (+ 0 0) into 0 10.151 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 10.154 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 10.158 * [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))))) 10.163 * [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))))) 10.174 * [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)))))) 10.175 * [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)))) 10.175 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 10.175 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 10.175 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 10.175 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 10.175 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 10.175 * [taylor]: Taking taylor expansion of 0.25 in k 10.175 * [backup-simplify]: Simplify 0.25 into 0.25 10.175 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 10.175 * [taylor]: Taking taylor expansion of 1.0 in k 10.175 * [backup-simplify]: Simplify 1.0 into 1.0 10.175 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.175 * [taylor]: Taking taylor expansion of k in k 10.175 * [backup-simplify]: Simplify 0 into 0 10.175 * [backup-simplify]: Simplify 1 into 1 10.176 * [backup-simplify]: Simplify (/ 1 1) into 1 10.176 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 10.176 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 10.176 * [taylor]: Taking taylor expansion of 2.0 in k 10.176 * [backup-simplify]: Simplify 2.0 into 2.0 10.176 * [taylor]: Taking taylor expansion of (/ PI n) in k 10.176 * [taylor]: Taking taylor expansion of PI in k 10.176 * [backup-simplify]: Simplify PI into PI 10.176 * [taylor]: Taking taylor expansion of n in k 10.176 * [backup-simplify]: Simplify n into n 10.176 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 10.176 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 10.176 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 10.177 * [backup-simplify]: Simplify (- 1) into -1 10.177 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.177 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 10.178 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 10.178 * [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))))) 10.178 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 10.178 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 10.178 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 10.178 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 10.178 * [taylor]: Taking taylor expansion of 0.25 in n 10.178 * [backup-simplify]: Simplify 0.25 into 0.25 10.178 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 10.178 * [taylor]: Taking taylor expansion of 1.0 in n 10.178 * [backup-simplify]: Simplify 1.0 into 1.0 10.178 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.178 * [taylor]: Taking taylor expansion of k in n 10.178 * [backup-simplify]: Simplify k into k 10.178 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.178 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 10.178 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 10.178 * [taylor]: Taking taylor expansion of 2.0 in n 10.178 * [backup-simplify]: Simplify 2.0 into 2.0 10.178 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.178 * [taylor]: Taking taylor expansion of PI in n 10.178 * [backup-simplify]: Simplify PI into PI 10.179 * [taylor]: Taking taylor expansion of n in n 10.179 * [backup-simplify]: Simplify 0 into 0 10.179 * [backup-simplify]: Simplify 1 into 1 10.179 * [backup-simplify]: Simplify (/ PI 1) into PI 10.180 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.181 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.181 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 10.181 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 10.181 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 10.182 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.184 * [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)))) 10.185 * [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))))) 10.185 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 10.185 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 10.185 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 10.185 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 10.185 * [taylor]: Taking taylor expansion of 0.25 in n 10.185 * [backup-simplify]: Simplify 0.25 into 0.25 10.185 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 10.185 * [taylor]: Taking taylor expansion of 1.0 in n 10.185 * [backup-simplify]: Simplify 1.0 into 1.0 10.185 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.185 * [taylor]: Taking taylor expansion of k in n 10.185 * [backup-simplify]: Simplify k into k 10.185 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.185 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 10.186 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 10.186 * [taylor]: Taking taylor expansion of 2.0 in n 10.186 * [backup-simplify]: Simplify 2.0 into 2.0 10.186 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.186 * [taylor]: Taking taylor expansion of PI in n 10.186 * [backup-simplify]: Simplify PI into PI 10.186 * [taylor]: Taking taylor expansion of n in n 10.186 * [backup-simplify]: Simplify 0 into 0 10.186 * [backup-simplify]: Simplify 1 into 1 10.186 * [backup-simplify]: Simplify (/ PI 1) into PI 10.187 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.188 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.188 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 10.188 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 10.188 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 10.190 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.191 * [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)))) 10.193 * [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))))) 10.193 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 10.193 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 10.193 * [taylor]: Taking taylor expansion of 0.25 in k 10.193 * [backup-simplify]: Simplify 0.25 into 0.25 10.193 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 10.193 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 10.193 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 10.193 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 10.193 * [taylor]: Taking taylor expansion of 2.0 in k 10.193 * [backup-simplify]: Simplify 2.0 into 2.0 10.193 * [taylor]: Taking taylor expansion of PI in k 10.193 * [backup-simplify]: Simplify PI into PI 10.194 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.195 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.195 * [taylor]: Taking taylor expansion of (log n) in k 10.195 * [taylor]: Taking taylor expansion of n in k 10.195 * [backup-simplify]: Simplify n into n 10.195 * [backup-simplify]: Simplify (log n) into (log n) 10.195 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 10.195 * [taylor]: Taking taylor expansion of 1.0 in k 10.195 * [backup-simplify]: Simplify 1.0 into 1.0 10.195 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.195 * [taylor]: Taking taylor expansion of k in k 10.195 * [backup-simplify]: Simplify 0 into 0 10.195 * [backup-simplify]: Simplify 1 into 1 10.196 * [backup-simplify]: Simplify (/ 1 1) into 1 10.196 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 10.197 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 10.197 * [backup-simplify]: Simplify (- 1) into -1 10.198 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.199 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 10.200 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 10.202 * [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))))) 10.203 * [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))))) 10.204 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.205 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 10.207 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 10.207 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 10.208 * [backup-simplify]: Simplify (- 0) into 0 10.208 * [backup-simplify]: Simplify (+ 0 0) into 0 10.208 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 10.210 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.211 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 10.213 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.213 * [taylor]: Taking taylor expansion of 0 in k 10.213 * [backup-simplify]: Simplify 0 into 0 10.213 * [backup-simplify]: Simplify 0 into 0 10.213 * [backup-simplify]: Simplify 0 into 0 10.215 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.216 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.220 * [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 10.220 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.220 * [backup-simplify]: Simplify (- 0) into 0 10.221 * [backup-simplify]: Simplify (+ 0 0) into 0 10.222 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 10.223 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.225 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 10.227 * [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 10.228 * [taylor]: Taking taylor expansion of 0 in k 10.228 * [backup-simplify]: Simplify 0 into 0 10.228 * [backup-simplify]: Simplify 0 into 0 10.228 * [backup-simplify]: Simplify 0 into 0 10.228 * [backup-simplify]: Simplify 0 into 0 10.229 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.230 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.236 * [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 10.237 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.237 * [backup-simplify]: Simplify (- 0) into 0 10.238 * [backup-simplify]: Simplify (+ 0 0) into 0 10.240 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 10.242 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.244 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 10.247 * [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 10.247 * [taylor]: Taking taylor expansion of 0 in k 10.247 * [backup-simplify]: Simplify 0 into 0 10.247 * [backup-simplify]: Simplify 0 into 0 10.248 * [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)))) 10.249 * [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))) 10.249 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 10.249 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 10.249 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 10.249 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 10.249 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 10.249 * [taylor]: Taking taylor expansion of 0.25 in k 10.249 * [backup-simplify]: Simplify 0.25 into 0.25 10.250 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 10.250 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.250 * [taylor]: Taking taylor expansion of k in k 10.250 * [backup-simplify]: Simplify 0 into 0 10.250 * [backup-simplify]: Simplify 1 into 1 10.250 * [backup-simplify]: Simplify (/ 1 1) into 1 10.250 * [taylor]: Taking taylor expansion of 1.0 in k 10.250 * [backup-simplify]: Simplify 1.0 into 1.0 10.250 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 10.250 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 10.250 * [taylor]: Taking taylor expansion of -2.0 in k 10.250 * [backup-simplify]: Simplify -2.0 into -2.0 10.250 * [taylor]: Taking taylor expansion of (/ PI n) in k 10.250 * [taylor]: Taking taylor expansion of PI in k 10.250 * [backup-simplify]: Simplify PI into PI 10.250 * [taylor]: Taking taylor expansion of n in k 10.250 * [backup-simplify]: Simplify n into n 10.250 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 10.251 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 10.251 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 10.251 * [backup-simplify]: Simplify (+ 1 0) into 1 10.252 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 10.252 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 10.252 * [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)))))) 10.252 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 10.252 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 10.252 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 10.252 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 10.253 * [taylor]: Taking taylor expansion of 0.25 in n 10.253 * [backup-simplify]: Simplify 0.25 into 0.25 10.253 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 10.253 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.253 * [taylor]: Taking taylor expansion of k in n 10.253 * [backup-simplify]: Simplify k into k 10.253 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.253 * [taylor]: Taking taylor expansion of 1.0 in n 10.253 * [backup-simplify]: Simplify 1.0 into 1.0 10.253 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 10.253 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.253 * [taylor]: Taking taylor expansion of -2.0 in n 10.253 * [backup-simplify]: Simplify -2.0 into -2.0 10.253 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.253 * [taylor]: Taking taylor expansion of PI in n 10.253 * [backup-simplify]: Simplify PI into PI 10.253 * [taylor]: Taking taylor expansion of n in n 10.253 * [backup-simplify]: Simplify 0 into 0 10.253 * [backup-simplify]: Simplify 1 into 1 10.254 * [backup-simplify]: Simplify (/ PI 1) into PI 10.254 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.256 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.256 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 10.256 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 10.258 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.259 * [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)))) 10.260 * [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))))) 10.260 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 10.260 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 10.260 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 10.260 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 10.260 * [taylor]: Taking taylor expansion of 0.25 in n 10.260 * [backup-simplify]: Simplify 0.25 into 0.25 10.260 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 10.260 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.260 * [taylor]: Taking taylor expansion of k in n 10.261 * [backup-simplify]: Simplify k into k 10.261 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.261 * [taylor]: Taking taylor expansion of 1.0 in n 10.261 * [backup-simplify]: Simplify 1.0 into 1.0 10.261 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 10.261 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.261 * [taylor]: Taking taylor expansion of -2.0 in n 10.261 * [backup-simplify]: Simplify -2.0 into -2.0 10.261 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.261 * [taylor]: Taking taylor expansion of PI in n 10.261 * [backup-simplify]: Simplify PI into PI 10.261 * [taylor]: Taking taylor expansion of n in n 10.261 * [backup-simplify]: Simplify 0 into 0 10.261 * [backup-simplify]: Simplify 1 into 1 10.261 * [backup-simplify]: Simplify (/ PI 1) into PI 10.262 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.263 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.263 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 10.263 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 10.265 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.266 * [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)))) 10.267 * [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))))) 10.267 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 10.267 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 10.268 * [taylor]: Taking taylor expansion of 0.25 in k 10.268 * [backup-simplify]: Simplify 0.25 into 0.25 10.268 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 10.268 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 10.268 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.268 * [taylor]: Taking taylor expansion of k in k 10.268 * [backup-simplify]: Simplify 0 into 0 10.268 * [backup-simplify]: Simplify 1 into 1 10.268 * [backup-simplify]: Simplify (/ 1 1) into 1 10.268 * [taylor]: Taking taylor expansion of 1.0 in k 10.268 * [backup-simplify]: Simplify 1.0 into 1.0 10.268 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 10.268 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 10.268 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 10.268 * [taylor]: Taking taylor expansion of -2.0 in k 10.268 * [backup-simplify]: Simplify -2.0 into -2.0 10.268 * [taylor]: Taking taylor expansion of PI in k 10.268 * [backup-simplify]: Simplify PI into PI 10.269 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.270 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.270 * [taylor]: Taking taylor expansion of (log n) in k 10.270 * [taylor]: Taking taylor expansion of n in k 10.270 * [backup-simplify]: Simplify n into n 10.270 * [backup-simplify]: Simplify (log n) into (log n) 10.270 * [backup-simplify]: Simplify (+ 1 0) into 1 10.270 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 10.272 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 10.273 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 10.274 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 10.275 * [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))))) 10.276 * [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))))) 10.277 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.278 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 10.280 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 10.280 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 10.280 * [backup-simplify]: Simplify (+ 0 0) into 0 10.281 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 10.282 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.284 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 10.286 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.286 * [taylor]: Taking taylor expansion of 0 in k 10.286 * [backup-simplify]: Simplify 0 into 0 10.286 * [backup-simplify]: Simplify 0 into 0 10.286 * [backup-simplify]: Simplify 0 into 0 10.287 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.288 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.295 * [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 10.296 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.296 * [backup-simplify]: Simplify (+ 0 0) into 0 10.297 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 10.299 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.300 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 10.303 * [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 10.303 * [taylor]: Taking taylor expansion of 0 in k 10.303 * [backup-simplify]: Simplify 0 into 0 10.303 * [backup-simplify]: Simplify 0 into 0 10.303 * [backup-simplify]: Simplify 0 into 0 10.303 * [backup-simplify]: Simplify 0 into 0 10.305 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.306 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.311 * [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 10.311 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.311 * [backup-simplify]: Simplify (+ 0 0) into 0 10.312 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 10.313 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.314 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 10.316 * [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 10.316 * [taylor]: Taking taylor expansion of 0 in k 10.316 * [backup-simplify]: Simplify 0 into 0 10.316 * [backup-simplify]: Simplify 0 into 0 10.317 * [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)))))) 10.317 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 1) 10.317 * [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))) 10.317 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 10.317 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 10.317 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 10.317 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 10.317 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 10.317 * [taylor]: Taking taylor expansion of 0.25 in k 10.317 * [backup-simplify]: Simplify 0.25 into 0.25 10.317 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 10.317 * [taylor]: Taking taylor expansion of 1.0 in k 10.317 * [backup-simplify]: Simplify 1.0 into 1.0 10.317 * [taylor]: Taking taylor expansion of k in k 10.317 * [backup-simplify]: Simplify 0 into 0 10.318 * [backup-simplify]: Simplify 1 into 1 10.318 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 10.318 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 10.318 * [taylor]: Taking taylor expansion of 2.0 in k 10.318 * [backup-simplify]: Simplify 2.0 into 2.0 10.318 * [taylor]: Taking taylor expansion of (* n PI) in k 10.318 * [taylor]: Taking taylor expansion of n in k 10.318 * [backup-simplify]: Simplify n into n 10.318 * [taylor]: Taking taylor expansion of PI in k 10.318 * [backup-simplify]: Simplify PI into PI 10.318 * [backup-simplify]: Simplify (* n PI) into (* n PI) 10.318 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 10.318 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 10.318 * [backup-simplify]: Simplify (- 0) into 0 10.318 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 10.319 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 10.319 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 10.319 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 10.319 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 10.319 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 10.319 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 10.319 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 10.319 * [taylor]: Taking taylor expansion of 0.25 in n 10.319 * [backup-simplify]: Simplify 0.25 into 0.25 10.319 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 10.319 * [taylor]: Taking taylor expansion of 1.0 in n 10.319 * [backup-simplify]: Simplify 1.0 into 1.0 10.319 * [taylor]: Taking taylor expansion of k in n 10.319 * [backup-simplify]: Simplify k into k 10.319 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 10.319 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.319 * [taylor]: Taking taylor expansion of 2.0 in n 10.319 * [backup-simplify]: Simplify 2.0 into 2.0 10.319 * [taylor]: Taking taylor expansion of (* n PI) in n 10.319 * [taylor]: Taking taylor expansion of n in n 10.319 * [backup-simplify]: Simplify 0 into 0 10.319 * [backup-simplify]: Simplify 1 into 1 10.319 * [taylor]: Taking taylor expansion of PI in n 10.319 * [backup-simplify]: Simplify PI into PI 10.320 * [backup-simplify]: Simplify (* 0 PI) into 0 10.320 * [backup-simplify]: Simplify (* 2.0 0) into 0 10.321 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.322 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 10.322 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.322 * [backup-simplify]: Simplify (- k) into (- k) 10.322 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 10.322 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 10.323 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.324 * [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)))) 10.325 * [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))))) 10.325 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 10.325 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 10.325 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 10.325 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 10.325 * [taylor]: Taking taylor expansion of 0.25 in n 10.325 * [backup-simplify]: Simplify 0.25 into 0.25 10.325 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 10.325 * [taylor]: Taking taylor expansion of 1.0 in n 10.325 * [backup-simplify]: Simplify 1.0 into 1.0 10.325 * [taylor]: Taking taylor expansion of k in n 10.325 * [backup-simplify]: Simplify k into k 10.325 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 10.325 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.325 * [taylor]: Taking taylor expansion of 2.0 in n 10.325 * [backup-simplify]: Simplify 2.0 into 2.0 10.325 * [taylor]: Taking taylor expansion of (* n PI) in n 10.325 * [taylor]: Taking taylor expansion of n in n 10.325 * [backup-simplify]: Simplify 0 into 0 10.325 * [backup-simplify]: Simplify 1 into 1 10.325 * [taylor]: Taking taylor expansion of PI in n 10.325 * [backup-simplify]: Simplify PI into PI 10.325 * [backup-simplify]: Simplify (* 0 PI) into 0 10.326 * [backup-simplify]: Simplify (* 2.0 0) into 0 10.327 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.328 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 10.328 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.328 * [backup-simplify]: Simplify (- k) into (- k) 10.328 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 10.328 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 10.329 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.330 * [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)))) 10.331 * [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))))) 10.331 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 10.331 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 10.331 * [taylor]: Taking taylor expansion of 0.25 in k 10.331 * [backup-simplify]: Simplify 0.25 into 0.25 10.331 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 10.331 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 10.331 * [taylor]: Taking taylor expansion of 1.0 in k 10.331 * [backup-simplify]: Simplify 1.0 into 1.0 10.331 * [taylor]: Taking taylor expansion of k in k 10.331 * [backup-simplify]: Simplify 0 into 0 10.331 * [backup-simplify]: Simplify 1 into 1 10.331 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 10.331 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 10.331 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 10.331 * [taylor]: Taking taylor expansion of 2.0 in k 10.331 * [backup-simplify]: Simplify 2.0 into 2.0 10.331 * [taylor]: Taking taylor expansion of PI in k 10.331 * [backup-simplify]: Simplify PI into PI 10.331 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.332 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.332 * [taylor]: Taking taylor expansion of (log n) in k 10.332 * [taylor]: Taking taylor expansion of n in k 10.332 * [backup-simplify]: Simplify n into n 10.332 * [backup-simplify]: Simplify (log n) into (log n) 10.332 * [backup-simplify]: Simplify (- 0) into 0 10.333 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 10.333 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 10.334 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 10.335 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 10.335 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 10.336 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 10.337 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 10.337 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 10.339 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 10.340 * [backup-simplify]: Simplify (- 0) into 0 10.340 * [backup-simplify]: Simplify (+ 0 0) into 0 10.340 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 10.342 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.343 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 10.345 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.345 * [taylor]: Taking taylor expansion of 0 in k 10.345 * [backup-simplify]: Simplify 0 into 0 10.345 * [backup-simplify]: Simplify 0 into 0 10.346 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 10.347 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 10.347 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 10.348 * [backup-simplify]: Simplify (+ 0 0) into 0 10.348 * [backup-simplify]: Simplify (- 1) into -1 10.348 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.349 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 10.350 * [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)))) 10.353 * [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)))))) 10.355 * [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)))))) 10.355 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 10.356 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 10.358 * [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 10.358 * [backup-simplify]: Simplify (- 0) into 0 10.359 * [backup-simplify]: Simplify (+ 0 0) into 0 10.359 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 10.360 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.361 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 10.362 * [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 10.362 * [taylor]: Taking taylor expansion of 0 in k 10.362 * [backup-simplify]: Simplify 0 into 0 10.362 * [backup-simplify]: Simplify 0 into 0 10.362 * [backup-simplify]: Simplify 0 into 0 10.363 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.365 * [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 10.366 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 10.366 * [backup-simplify]: Simplify (+ 0 0) into 0 10.367 * [backup-simplify]: Simplify (- 0) into 0 10.367 * [backup-simplify]: Simplify (+ 0 0) into 0 10.368 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 10.370 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 10.372 * [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))))) 10.376 * [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))))) 10.387 * [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)))))) 10.388 * [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)))) 10.388 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 10.388 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 10.388 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 10.388 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 10.388 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 10.388 * [taylor]: Taking taylor expansion of 0.25 in k 10.388 * [backup-simplify]: Simplify 0.25 into 0.25 10.388 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 10.388 * [taylor]: Taking taylor expansion of 1.0 in k 10.388 * [backup-simplify]: Simplify 1.0 into 1.0 10.388 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.388 * [taylor]: Taking taylor expansion of k in k 10.388 * [backup-simplify]: Simplify 0 into 0 10.388 * [backup-simplify]: Simplify 1 into 1 10.389 * [backup-simplify]: Simplify (/ 1 1) into 1 10.389 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 10.389 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 10.389 * [taylor]: Taking taylor expansion of 2.0 in k 10.389 * [backup-simplify]: Simplify 2.0 into 2.0 10.389 * [taylor]: Taking taylor expansion of (/ PI n) in k 10.389 * [taylor]: Taking taylor expansion of PI in k 10.389 * [backup-simplify]: Simplify PI into PI 10.389 * [taylor]: Taking taylor expansion of n in k 10.389 * [backup-simplify]: Simplify n into n 10.389 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 10.389 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 10.389 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 10.390 * [backup-simplify]: Simplify (- 1) into -1 10.390 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.391 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 10.391 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 10.391 * [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))))) 10.391 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 10.391 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 10.391 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 10.391 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 10.391 * [taylor]: Taking taylor expansion of 0.25 in n 10.391 * [backup-simplify]: Simplify 0.25 into 0.25 10.391 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 10.391 * [taylor]: Taking taylor expansion of 1.0 in n 10.391 * [backup-simplify]: Simplify 1.0 into 1.0 10.391 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.391 * [taylor]: Taking taylor expansion of k in n 10.391 * [backup-simplify]: Simplify k into k 10.391 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.391 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 10.391 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 10.391 * [taylor]: Taking taylor expansion of 2.0 in n 10.392 * [backup-simplify]: Simplify 2.0 into 2.0 10.392 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.392 * [taylor]: Taking taylor expansion of PI in n 10.392 * [backup-simplify]: Simplify PI into PI 10.392 * [taylor]: Taking taylor expansion of n in n 10.392 * [backup-simplify]: Simplify 0 into 0 10.392 * [backup-simplify]: Simplify 1 into 1 10.392 * [backup-simplify]: Simplify (/ PI 1) into PI 10.393 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.394 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.394 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 10.394 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 10.394 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 10.395 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.397 * [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)))) 10.398 * [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))))) 10.398 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 10.398 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 10.398 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 10.398 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 10.398 * [taylor]: Taking taylor expansion of 0.25 in n 10.398 * [backup-simplify]: Simplify 0.25 into 0.25 10.398 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 10.398 * [taylor]: Taking taylor expansion of 1.0 in n 10.398 * [backup-simplify]: Simplify 1.0 into 1.0 10.398 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.398 * [taylor]: Taking taylor expansion of k in n 10.398 * [backup-simplify]: Simplify k into k 10.398 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.398 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 10.398 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 10.398 * [taylor]: Taking taylor expansion of 2.0 in n 10.398 * [backup-simplify]: Simplify 2.0 into 2.0 10.398 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.398 * [taylor]: Taking taylor expansion of PI in n 10.398 * [backup-simplify]: Simplify PI into PI 10.399 * [taylor]: Taking taylor expansion of n in n 10.399 * [backup-simplify]: Simplify 0 into 0 10.399 * [backup-simplify]: Simplify 1 into 1 10.399 * [backup-simplify]: Simplify (/ PI 1) into PI 10.399 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.400 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.401 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 10.401 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 10.401 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 10.402 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.404 * [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)))) 10.405 * [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))))) 10.405 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 10.405 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 10.405 * [taylor]: Taking taylor expansion of 0.25 in k 10.405 * [backup-simplify]: Simplify 0.25 into 0.25 10.405 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 10.405 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 10.405 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 10.405 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 10.405 * [taylor]: Taking taylor expansion of 2.0 in k 10.405 * [backup-simplify]: Simplify 2.0 into 2.0 10.405 * [taylor]: Taking taylor expansion of PI in k 10.405 * [backup-simplify]: Simplify PI into PI 10.406 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.411 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.411 * [taylor]: Taking taylor expansion of (log n) in k 10.411 * [taylor]: Taking taylor expansion of n in k 10.411 * [backup-simplify]: Simplify n into n 10.412 * [backup-simplify]: Simplify (log n) into (log n) 10.412 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 10.412 * [taylor]: Taking taylor expansion of 1.0 in k 10.412 * [backup-simplify]: Simplify 1.0 into 1.0 10.412 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.412 * [taylor]: Taking taylor expansion of k in k 10.412 * [backup-simplify]: Simplify 0 into 0 10.412 * [backup-simplify]: Simplify 1 into 1 10.412 * [backup-simplify]: Simplify (/ 1 1) into 1 10.412 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 10.413 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 10.414 * [backup-simplify]: Simplify (- 1) into -1 10.414 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.415 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 10.416 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 10.418 * [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))))) 10.419 * [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))))) 10.420 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.421 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 10.423 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 10.423 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 10.423 * [backup-simplify]: Simplify (- 0) into 0 10.423 * [backup-simplify]: Simplify (+ 0 0) into 0 10.424 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 10.426 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.427 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 10.429 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.429 * [taylor]: Taking taylor expansion of 0 in k 10.429 * [backup-simplify]: Simplify 0 into 0 10.430 * [backup-simplify]: Simplify 0 into 0 10.430 * [backup-simplify]: Simplify 0 into 0 10.431 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.432 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.436 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0 10.436 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.436 * [backup-simplify]: Simplify (- 0) into 0 10.437 * [backup-simplify]: Simplify (+ 0 0) into 0 10.438 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 10.439 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.441 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 10.443 * [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 10.443 * [taylor]: Taking taylor expansion of 0 in k 10.443 * [backup-simplify]: Simplify 0 into 0 10.443 * [backup-simplify]: Simplify 0 into 0 10.443 * [backup-simplify]: Simplify 0 into 0 10.443 * [backup-simplify]: Simplify 0 into 0 10.445 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.446 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.452 * [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 10.452 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.453 * [backup-simplify]: Simplify (- 0) into 0 10.453 * [backup-simplify]: Simplify (+ 0 0) into 0 10.455 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 10.456 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.458 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 10.461 * [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 10.461 * [taylor]: Taking taylor expansion of 0 in k 10.461 * [backup-simplify]: Simplify 0 into 0 10.461 * [backup-simplify]: Simplify 0 into 0 10.462 * [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)))) 10.463 * [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))) 10.463 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 10.463 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 10.463 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 10.464 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 10.464 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 10.464 * [taylor]: Taking taylor expansion of 0.25 in k 10.464 * [backup-simplify]: Simplify 0.25 into 0.25 10.464 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 10.464 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.464 * [taylor]: Taking taylor expansion of k in k 10.464 * [backup-simplify]: Simplify 0 into 0 10.464 * [backup-simplify]: Simplify 1 into 1 10.464 * [backup-simplify]: Simplify (/ 1 1) into 1 10.464 * [taylor]: Taking taylor expansion of 1.0 in k 10.464 * [backup-simplify]: Simplify 1.0 into 1.0 10.464 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 10.464 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 10.464 * [taylor]: Taking taylor expansion of -2.0 in k 10.464 * [backup-simplify]: Simplify -2.0 into -2.0 10.464 * [taylor]: Taking taylor expansion of (/ PI n) in k 10.465 * [taylor]: Taking taylor expansion of PI in k 10.465 * [backup-simplify]: Simplify PI into PI 10.465 * [taylor]: Taking taylor expansion of n in k 10.465 * [backup-simplify]: Simplify n into n 10.465 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 10.465 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 10.465 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 10.465 * [backup-simplify]: Simplify (+ 1 0) into 1 10.466 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 10.466 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 10.466 * [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)))))) 10.466 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 10.466 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 10.466 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 10.466 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 10.466 * [taylor]: Taking taylor expansion of 0.25 in n 10.466 * [backup-simplify]: Simplify 0.25 into 0.25 10.467 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 10.467 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.467 * [taylor]: Taking taylor expansion of k in n 10.467 * [backup-simplify]: Simplify k into k 10.467 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.467 * [taylor]: Taking taylor expansion of 1.0 in n 10.467 * [backup-simplify]: Simplify 1.0 into 1.0 10.467 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 10.467 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.467 * [taylor]: Taking taylor expansion of -2.0 in n 10.467 * [backup-simplify]: Simplify -2.0 into -2.0 10.467 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.467 * [taylor]: Taking taylor expansion of PI in n 10.467 * [backup-simplify]: Simplify PI into PI 10.467 * [taylor]: Taking taylor expansion of n in n 10.467 * [backup-simplify]: Simplify 0 into 0 10.467 * [backup-simplify]: Simplify 1 into 1 10.468 * [backup-simplify]: Simplify (/ PI 1) into PI 10.468 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.469 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.469 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 10.469 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 10.471 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.472 * [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)))) 10.473 * [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))))) 10.473 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 10.473 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 10.473 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 10.473 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 10.473 * [taylor]: Taking taylor expansion of 0.25 in n 10.474 * [backup-simplify]: Simplify 0.25 into 0.25 10.474 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 10.474 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.474 * [taylor]: Taking taylor expansion of k in n 10.474 * [backup-simplify]: Simplify k into k 10.474 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.474 * [taylor]: Taking taylor expansion of 1.0 in n 10.474 * [backup-simplify]: Simplify 1.0 into 1.0 10.474 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 10.474 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.474 * [taylor]: Taking taylor expansion of -2.0 in n 10.474 * [backup-simplify]: Simplify -2.0 into -2.0 10.474 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.474 * [taylor]: Taking taylor expansion of PI in n 10.474 * [backup-simplify]: Simplify PI into PI 10.474 * [taylor]: Taking taylor expansion of n in n 10.474 * [backup-simplify]: Simplify 0 into 0 10.474 * [backup-simplify]: Simplify 1 into 1 10.475 * [backup-simplify]: Simplify (/ PI 1) into PI 10.475 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.476 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.476 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 10.476 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 10.478 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.479 * [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)))) 10.480 * [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))))) 10.481 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 10.481 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 10.481 * [taylor]: Taking taylor expansion of 0.25 in k 10.481 * [backup-simplify]: Simplify 0.25 into 0.25 10.481 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 10.481 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 10.481 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.481 * [taylor]: Taking taylor expansion of k in k 10.481 * [backup-simplify]: Simplify 0 into 0 10.481 * [backup-simplify]: Simplify 1 into 1 10.481 * [backup-simplify]: Simplify (/ 1 1) into 1 10.481 * [taylor]: Taking taylor expansion of 1.0 in k 10.481 * [backup-simplify]: Simplify 1.0 into 1.0 10.481 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 10.481 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 10.482 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 10.482 * [taylor]: Taking taylor expansion of -2.0 in k 10.482 * [backup-simplify]: Simplify -2.0 into -2.0 10.482 * [taylor]: Taking taylor expansion of PI in k 10.482 * [backup-simplify]: Simplify PI into PI 10.482 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.483 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.483 * [taylor]: Taking taylor expansion of (log n) in k 10.483 * [taylor]: Taking taylor expansion of n in k 10.483 * [backup-simplify]: Simplify n into n 10.483 * [backup-simplify]: Simplify (log n) into (log n) 10.484 * [backup-simplify]: Simplify (+ 1 0) into 1 10.484 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 10.485 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 10.486 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 10.487 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 10.489 * [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))))) 10.490 * [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))))) 10.491 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.492 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 10.494 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 10.494 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 10.494 * [backup-simplify]: Simplify (+ 0 0) into 0 10.495 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 10.497 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.498 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 10.500 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.500 * [taylor]: Taking taylor expansion of 0 in k 10.500 * [backup-simplify]: Simplify 0 into 0 10.500 * [backup-simplify]: Simplify 0 into 0 10.500 * [backup-simplify]: Simplify 0 into 0 10.501 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.502 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.506 * [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 10.507 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.507 * [backup-simplify]: Simplify (+ 0 0) into 0 10.508 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 10.510 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.512 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 10.515 * [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 10.515 * [taylor]: Taking taylor expansion of 0 in k 10.515 * [backup-simplify]: Simplify 0 into 0 10.515 * [backup-simplify]: Simplify 0 into 0 10.515 * [backup-simplify]: Simplify 0 into 0 10.515 * [backup-simplify]: Simplify 0 into 0 10.516 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.518 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.521 * [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 10.521 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.522 * [backup-simplify]: Simplify (+ 0 0) into 0 10.523 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 10.524 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.525 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 10.527 * [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 10.527 * [taylor]: Taking taylor expansion of 0 in k 10.527 * [backup-simplify]: Simplify 0 into 0 10.527 * [backup-simplify]: Simplify 0 into 0 10.528 * [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)))))) 10.528 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 2) 10.529 * [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) 10.529 * [approximate]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in (n k) around 0 10.529 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in k 10.529 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 10.529 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 10.529 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 10.529 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 10.529 * [taylor]: Taking taylor expansion of 0.25 in k 10.529 * [backup-simplify]: Simplify 0.25 into 0.25 10.529 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 10.529 * [taylor]: Taking taylor expansion of 1.0 in k 10.529 * [backup-simplify]: Simplify 1.0 into 1.0 10.529 * [taylor]: Taking taylor expansion of k in k 10.529 * [backup-simplify]: Simplify 0 into 0 10.529 * [backup-simplify]: Simplify 1 into 1 10.529 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 10.529 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 10.529 * [taylor]: Taking taylor expansion of 2.0 in k 10.529 * [backup-simplify]: Simplify 2.0 into 2.0 10.529 * [taylor]: Taking taylor expansion of (* n PI) in k 10.530 * [taylor]: Taking taylor expansion of n in k 10.530 * [backup-simplify]: Simplify n into n 10.530 * [taylor]: Taking taylor expansion of PI in k 10.530 * [backup-simplify]: Simplify PI into PI 10.530 * [backup-simplify]: Simplify (* n PI) into (* n PI) 10.530 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 10.530 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 10.530 * [backup-simplify]: Simplify (- 0) into 0 10.530 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 10.531 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 10.531 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 10.531 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 10.531 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in n 10.531 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 10.531 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 10.531 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 10.531 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 10.531 * [taylor]: Taking taylor expansion of 0.25 in n 10.531 * [backup-simplify]: Simplify 0.25 into 0.25 10.531 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 10.531 * [taylor]: Taking taylor expansion of 1.0 in n 10.531 * [backup-simplify]: Simplify 1.0 into 1.0 10.531 * [taylor]: Taking taylor expansion of k in n 10.531 * [backup-simplify]: Simplify k into k 10.531 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 10.531 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.531 * [taylor]: Taking taylor expansion of 2.0 in n 10.531 * [backup-simplify]: Simplify 2.0 into 2.0 10.531 * [taylor]: Taking taylor expansion of (* n PI) in n 10.531 * [taylor]: Taking taylor expansion of n in n 10.531 * [backup-simplify]: Simplify 0 into 0 10.531 * [backup-simplify]: Simplify 1 into 1 10.531 * [taylor]: Taking taylor expansion of PI in n 10.531 * [backup-simplify]: Simplify PI into PI 10.531 * [backup-simplify]: Simplify (* 0 PI) into 0 10.532 * [backup-simplify]: Simplify (* 2.0 0) into 0 10.533 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.534 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 10.534 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.535 * [backup-simplify]: Simplify (- k) into (- k) 10.535 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 10.535 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 10.536 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.536 * [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)))) 10.537 * [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))))) 10.537 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 2) in n 10.537 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 10.537 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 10.537 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 10.537 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 10.537 * [taylor]: Taking taylor expansion of 0.25 in n 10.537 * [backup-simplify]: Simplify 0.25 into 0.25 10.537 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 10.537 * [taylor]: Taking taylor expansion of 1.0 in n 10.537 * [backup-simplify]: Simplify 1.0 into 1.0 10.537 * [taylor]: Taking taylor expansion of k in n 10.537 * [backup-simplify]: Simplify k into k 10.537 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 10.537 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.537 * [taylor]: Taking taylor expansion of 2.0 in n 10.537 * [backup-simplify]: Simplify 2.0 into 2.0 10.538 * [taylor]: Taking taylor expansion of (* n PI) in n 10.538 * [taylor]: Taking taylor expansion of n in n 10.538 * [backup-simplify]: Simplify 0 into 0 10.538 * [backup-simplify]: Simplify 1 into 1 10.538 * [taylor]: Taking taylor expansion of PI in n 10.538 * [backup-simplify]: Simplify PI into PI 10.538 * [backup-simplify]: Simplify (* 0 PI) into 0 10.538 * [backup-simplify]: Simplify (* 2.0 0) into 0 10.539 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.540 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 10.541 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.541 * [backup-simplify]: Simplify (- k) into (- k) 10.541 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 10.541 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 10.542 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.543 * [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)))) 10.544 * [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))))) 10.546 * [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) 10.546 * [taylor]: Taking taylor expansion of (pow (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 2) in k 10.546 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 10.546 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 10.546 * [taylor]: Taking taylor expansion of 0.25 in k 10.546 * [backup-simplify]: Simplify 0.25 into 0.25 10.546 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 10.546 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 10.546 * [taylor]: Taking taylor expansion of 1.0 in k 10.546 * [backup-simplify]: Simplify 1.0 into 1.0 10.546 * [taylor]: Taking taylor expansion of k in k 10.546 * [backup-simplify]: Simplify 0 into 0 10.546 * [backup-simplify]: Simplify 1 into 1 10.546 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 10.546 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 10.546 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 10.546 * [taylor]: Taking taylor expansion of 2.0 in k 10.546 * [backup-simplify]: Simplify 2.0 into 2.0 10.546 * [taylor]: Taking taylor expansion of PI in k 10.547 * [backup-simplify]: Simplify PI into PI 10.547 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.548 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.548 * [taylor]: Taking taylor expansion of (log n) in k 10.548 * [taylor]: Taking taylor expansion of n in k 10.548 * [backup-simplify]: Simplify n into n 10.548 * [backup-simplify]: Simplify (log n) into (log n) 10.548 * [backup-simplify]: Simplify (- 0) into 0 10.548 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 10.549 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 10.555 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 10.556 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 10.558 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 10.560 * [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) 10.561 * [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) 10.563 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 10.564 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 10.566 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 10.566 * [backup-simplify]: Simplify (- 0) into 0 10.566 * [backup-simplify]: Simplify (+ 0 0) into 0 10.567 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 10.569 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.570 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 10.572 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.574 * [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 10.574 * [taylor]: Taking taylor expansion of 0 in k 10.575 * [backup-simplify]: Simplify 0 into 0 10.575 * [backup-simplify]: Simplify 0 into 0 10.575 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 10.577 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 10.578 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 10.579 * [backup-simplify]: Simplify (+ 0 0) into 0 10.579 * [backup-simplify]: Simplify (- 1) into -1 10.579 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.581 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 10.583 * [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)))) 10.587 * [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)))))) 10.595 * [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))))) 10.600 * [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))))) 10.601 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 10.602 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 10.606 * [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 10.606 * [backup-simplify]: Simplify (- 0) into 0 10.607 * [backup-simplify]: Simplify (+ 0 0) into 0 10.608 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 10.609 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 10.611 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 10.613 * [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 10.616 * [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 10.617 * [taylor]: Taking taylor expansion of 0 in k 10.617 * [backup-simplify]: Simplify 0 into 0 10.617 * [backup-simplify]: Simplify 0 into 0 10.617 * [backup-simplify]: Simplify 0 into 0 10.618 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.622 * [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 10.624 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 10.624 * [backup-simplify]: Simplify (+ 0 0) into 0 10.625 * [backup-simplify]: Simplify (- 0) into 0 10.625 * [backup-simplify]: Simplify (+ 0 0) into 0 10.628 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 10.630 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 10.635 * [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))))) 10.656 * [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))))) 10.661 * [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))))) 10.669 * [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)))))) 10.670 * [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) 10.670 * [approximate]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in (n k) around 0 10.670 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in k 10.670 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 10.670 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 10.670 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 10.670 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 10.670 * [taylor]: Taking taylor expansion of 0.25 in k 10.670 * [backup-simplify]: Simplify 0.25 into 0.25 10.671 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 10.671 * [taylor]: Taking taylor expansion of 1.0 in k 10.671 * [backup-simplify]: Simplify 1.0 into 1.0 10.671 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.671 * [taylor]: Taking taylor expansion of k in k 10.671 * [backup-simplify]: Simplify 0 into 0 10.671 * [backup-simplify]: Simplify 1 into 1 10.671 * [backup-simplify]: Simplify (/ 1 1) into 1 10.671 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 10.671 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 10.671 * [taylor]: Taking taylor expansion of 2.0 in k 10.671 * [backup-simplify]: Simplify 2.0 into 2.0 10.671 * [taylor]: Taking taylor expansion of (/ PI n) in k 10.671 * [taylor]: Taking taylor expansion of PI in k 10.671 * [backup-simplify]: Simplify PI into PI 10.671 * [taylor]: Taking taylor expansion of n in k 10.671 * [backup-simplify]: Simplify n into n 10.671 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 10.671 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 10.671 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 10.671 * [backup-simplify]: Simplify (- 1) into -1 10.672 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.672 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 10.672 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 10.672 * [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))))) 10.672 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in n 10.672 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 10.672 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 10.672 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 10.672 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 10.672 * [taylor]: Taking taylor expansion of 0.25 in n 10.672 * [backup-simplify]: Simplify 0.25 into 0.25 10.672 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 10.672 * [taylor]: Taking taylor expansion of 1.0 in n 10.672 * [backup-simplify]: Simplify 1.0 into 1.0 10.672 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.672 * [taylor]: Taking taylor expansion of k in n 10.672 * [backup-simplify]: Simplify k into k 10.673 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.673 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 10.673 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 10.673 * [taylor]: Taking taylor expansion of 2.0 in n 10.673 * [backup-simplify]: Simplify 2.0 into 2.0 10.673 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.673 * [taylor]: Taking taylor expansion of PI in n 10.673 * [backup-simplify]: Simplify PI into PI 10.673 * [taylor]: Taking taylor expansion of n in n 10.673 * [backup-simplify]: Simplify 0 into 0 10.673 * [backup-simplify]: Simplify 1 into 1 10.673 * [backup-simplify]: Simplify (/ PI 1) into PI 10.673 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.674 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.674 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 10.674 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 10.674 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 10.675 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.676 * [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)))) 10.677 * [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))))) 10.677 * [taylor]: Taking taylor expansion of (pow (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 2) in n 10.677 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 10.677 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 10.677 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 10.677 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 10.677 * [taylor]: Taking taylor expansion of 0.25 in n 10.677 * [backup-simplify]: Simplify 0.25 into 0.25 10.677 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 10.677 * [taylor]: Taking taylor expansion of 1.0 in n 10.677 * [backup-simplify]: Simplify 1.0 into 1.0 10.677 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.677 * [taylor]: Taking taylor expansion of k in n 10.677 * [backup-simplify]: Simplify k into k 10.677 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.677 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 10.677 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 10.677 * [taylor]: Taking taylor expansion of 2.0 in n 10.677 * [backup-simplify]: Simplify 2.0 into 2.0 10.677 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.677 * [taylor]: Taking taylor expansion of PI in n 10.677 * [backup-simplify]: Simplify PI into PI 10.677 * [taylor]: Taking taylor expansion of n in n 10.677 * [backup-simplify]: Simplify 0 into 0 10.677 * [backup-simplify]: Simplify 1 into 1 10.677 * [backup-simplify]: Simplify (/ PI 1) into PI 10.678 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.678 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.678 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 10.678 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 10.678 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 10.679 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.680 * [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)))) 10.681 * [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))))) 10.682 * [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) 10.682 * [taylor]: Taking taylor expansion of (pow (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) 2) in k 10.682 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 10.682 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 10.682 * [taylor]: Taking taylor expansion of 0.25 in k 10.682 * [backup-simplify]: Simplify 0.25 into 0.25 10.682 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 10.682 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 10.683 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 10.683 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 10.683 * [taylor]: Taking taylor expansion of 2.0 in k 10.683 * [backup-simplify]: Simplify 2.0 into 2.0 10.683 * [taylor]: Taking taylor expansion of PI in k 10.683 * [backup-simplify]: Simplify PI into PI 10.683 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.684 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 10.684 * [taylor]: Taking taylor expansion of (log n) in k 10.684 * [taylor]: Taking taylor expansion of n in k 10.684 * [backup-simplify]: Simplify n into n 10.684 * [backup-simplify]: Simplify (log n) into (log n) 10.684 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 10.684 * [taylor]: Taking taylor expansion of 1.0 in k 10.684 * [backup-simplify]: Simplify 1.0 into 1.0 10.684 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.684 * [taylor]: Taking taylor expansion of k in k 10.684 * [backup-simplify]: Simplify 0 into 0 10.684 * [backup-simplify]: Simplify 1 into 1 10.684 * [backup-simplify]: Simplify (/ 1 1) into 1 10.684 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 10.685 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 10.685 * [backup-simplify]: Simplify (- 1) into -1 10.685 * [backup-simplify]: Simplify (+ 0 -1) into -1 10.686 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 10.687 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 10.693 * [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))))) 10.695 * [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) 10.696 * [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) 10.698 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.698 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 10.700 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 10.700 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 10.701 * [backup-simplify]: Simplify (- 0) into 0 10.701 * [backup-simplify]: Simplify (+ 0 0) into 0 10.702 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 10.702 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.703 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 10.704 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.706 * [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 10.706 * [taylor]: Taking taylor expansion of 0 in k 10.706 * [backup-simplify]: Simplify 0 into 0 10.706 * [backup-simplify]: Simplify 0 into 0 10.707 * [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 10.707 * [backup-simplify]: Simplify 0 into 0 10.708 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.709 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.710 * [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 10.711 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.711 * [backup-simplify]: Simplify (- 0) into 0 10.711 * [backup-simplify]: Simplify (+ 0 0) into 0 10.712 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 10.712 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.713 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 10.715 * [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 10.717 * [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 10.717 * [taylor]: Taking taylor expansion of 0 in k 10.717 * [backup-simplify]: Simplify 0 into 0 10.717 * [backup-simplify]: Simplify 0 into 0 10.717 * [backup-simplify]: Simplify 0 into 0 10.719 * [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 10.719 * [backup-simplify]: Simplify 0 into 0 10.719 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.720 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.723 * [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 10.723 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.724 * [backup-simplify]: Simplify (- 0) into 0 10.724 * [backup-simplify]: Simplify (+ 0 0) into 0 10.725 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 10.726 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 10.727 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 10.728 * [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 10.730 * [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 10.730 * [taylor]: Taking taylor expansion of 0 in k 10.730 * [backup-simplify]: Simplify 0 into 0 10.730 * [backup-simplify]: Simplify 0 into 0 10.731 * [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) 10.732 * [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) 10.732 * [approximate]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in (n k) around 0 10.732 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in k 10.732 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 10.732 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 10.732 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 10.732 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 10.732 * [taylor]: Taking taylor expansion of 0.25 in k 10.732 * [backup-simplify]: Simplify 0.25 into 0.25 10.732 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 10.732 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.732 * [taylor]: Taking taylor expansion of k in k 10.732 * [backup-simplify]: Simplify 0 into 0 10.732 * [backup-simplify]: Simplify 1 into 1 10.733 * [backup-simplify]: Simplify (/ 1 1) into 1 10.733 * [taylor]: Taking taylor expansion of 1.0 in k 10.733 * [backup-simplify]: Simplify 1.0 into 1.0 10.733 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 10.733 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 10.733 * [taylor]: Taking taylor expansion of -2.0 in k 10.733 * [backup-simplify]: Simplify -2.0 into -2.0 10.733 * [taylor]: Taking taylor expansion of (/ PI n) in k 10.733 * [taylor]: Taking taylor expansion of PI in k 10.733 * [backup-simplify]: Simplify PI into PI 10.733 * [taylor]: Taking taylor expansion of n in k 10.733 * [backup-simplify]: Simplify n into n 10.733 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 10.733 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 10.733 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 10.733 * [backup-simplify]: Simplify (+ 1 0) into 1 10.734 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 10.734 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 10.734 * [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)))))) 10.734 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in n 10.734 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 10.734 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 10.734 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 10.734 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 10.734 * [taylor]: Taking taylor expansion of 0.25 in n 10.734 * [backup-simplify]: Simplify 0.25 into 0.25 10.734 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 10.734 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.734 * [taylor]: Taking taylor expansion of k in n 10.734 * [backup-simplify]: Simplify k into k 10.734 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.734 * [taylor]: Taking taylor expansion of 1.0 in n 10.734 * [backup-simplify]: Simplify 1.0 into 1.0 10.734 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 10.734 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.734 * [taylor]: Taking taylor expansion of -2.0 in n 10.734 * [backup-simplify]: Simplify -2.0 into -2.0 10.734 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.734 * [taylor]: Taking taylor expansion of PI in n 10.734 * [backup-simplify]: Simplify PI into PI 10.734 * [taylor]: Taking taylor expansion of n in n 10.734 * [backup-simplify]: Simplify 0 into 0 10.734 * [backup-simplify]: Simplify 1 into 1 10.735 * [backup-simplify]: Simplify (/ PI 1) into PI 10.735 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.736 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.736 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 10.736 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 10.737 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.737 * [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)))) 10.739 * [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))))) 10.739 * [taylor]: Taking taylor expansion of (pow (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) 2) in n 10.739 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 10.739 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 10.739 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 10.739 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 10.739 * [taylor]: Taking taylor expansion of 0.25 in n 10.739 * [backup-simplify]: Simplify 0.25 into 0.25 10.739 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 10.739 * [taylor]: Taking taylor expansion of (/ 1 k) in n 10.739 * [taylor]: Taking taylor expansion of k in n 10.739 * [backup-simplify]: Simplify k into k 10.739 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 10.739 * [taylor]: Taking taylor expansion of 1.0 in n 10.739 * [backup-simplify]: Simplify 1.0 into 1.0 10.739 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 10.739 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.739 * [taylor]: Taking taylor expansion of -2.0 in n 10.739 * [backup-simplify]: Simplify -2.0 into -2.0 10.739 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.739 * [taylor]: Taking taylor expansion of PI in n 10.739 * [backup-simplify]: Simplify PI into PI 10.739 * [taylor]: Taking taylor expansion of n in n 10.739 * [backup-simplify]: Simplify 0 into 0 10.740 * [backup-simplify]: Simplify 1 into 1 10.740 * [backup-simplify]: Simplify (/ PI 1) into PI 10.741 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.742 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.742 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 10.742 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 10.744 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.745 * [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)))) 10.746 * [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))))) 10.749 * [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) 10.749 * [taylor]: Taking taylor expansion of (pow (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 2) in k 10.749 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 10.749 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 10.749 * [taylor]: Taking taylor expansion of 0.25 in k 10.749 * [backup-simplify]: Simplify 0.25 into 0.25 10.749 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 10.749 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 10.749 * [taylor]: Taking taylor expansion of (/ 1 k) in k 10.749 * [taylor]: Taking taylor expansion of k in k 10.749 * [backup-simplify]: Simplify 0 into 0 10.749 * [backup-simplify]: Simplify 1 into 1 10.749 * [backup-simplify]: Simplify (/ 1 1) into 1 10.750 * [taylor]: Taking taylor expansion of 1.0 in k 10.750 * [backup-simplify]: Simplify 1.0 into 1.0 10.750 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 10.750 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 10.750 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 10.750 * [taylor]: Taking taylor expansion of -2.0 in k 10.750 * [backup-simplify]: Simplify -2.0 into -2.0 10.750 * [taylor]: Taking taylor expansion of PI in k 10.750 * [backup-simplify]: Simplify PI into PI 10.750 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.751 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 10.751 * [taylor]: Taking taylor expansion of (log n) in k 10.751 * [taylor]: Taking taylor expansion of n in k 10.751 * [backup-simplify]: Simplify n into n 10.752 * [backup-simplify]: Simplify (log n) into (log n) 10.752 * [backup-simplify]: Simplify (+ 1 0) into 1 10.752 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 10.753 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 10.754 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 10.755 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 10.757 * [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))))) 10.759 * [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) 10.761 * [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) 10.762 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.763 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 10.764 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 10.765 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 10.765 * [backup-simplify]: Simplify (+ 0 0) into 0 10.766 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 10.767 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.767 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 10.769 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 10.770 * [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 10.770 * [taylor]: Taking taylor expansion of 0 in k 10.770 * [backup-simplify]: Simplify 0 into 0 10.770 * [backup-simplify]: Simplify 0 into 0 10.772 * [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 10.772 * [backup-simplify]: Simplify 0 into 0 10.773 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.773 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.775 * [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 10.775 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.776 * [backup-simplify]: Simplify (+ 0 0) into 0 10.776 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 10.777 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.778 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 10.779 * [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 10.781 * [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 10.781 * [taylor]: Taking taylor expansion of 0 in k 10.781 * [backup-simplify]: Simplify 0 into 0 10.781 * [backup-simplify]: Simplify 0 into 0 10.781 * [backup-simplify]: Simplify 0 into 0 10.783 * [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 10.783 * [backup-simplify]: Simplify 0 into 0 10.784 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.785 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.788 * [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 10.788 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 10.789 * [backup-simplify]: Simplify (+ 0 0) into 0 10.789 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 10.790 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 10.791 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 10.793 * [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 10.796 * [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 10.796 * [taylor]: Taking taylor expansion of 0 in k 10.796 * [backup-simplify]: Simplify 0 into 0 10.796 * [backup-simplify]: Simplify 0 into 0 10.802 * [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) 10.802 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 2 2 1) 10.803 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 10.803 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0 10.803 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.803 * [taylor]: Taking taylor expansion of 2.0 in n 10.803 * [backup-simplify]: Simplify 2.0 into 2.0 10.803 * [taylor]: Taking taylor expansion of (* n PI) in n 10.803 * [taylor]: Taking taylor expansion of n in n 10.803 * [backup-simplify]: Simplify 0 into 0 10.803 * [backup-simplify]: Simplify 1 into 1 10.803 * [taylor]: Taking taylor expansion of PI in n 10.803 * [backup-simplify]: Simplify PI into PI 10.803 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 10.803 * [taylor]: Taking taylor expansion of 2.0 in n 10.803 * [backup-simplify]: Simplify 2.0 into 2.0 10.803 * [taylor]: Taking taylor expansion of (* n PI) in n 10.803 * [taylor]: Taking taylor expansion of n in n 10.803 * [backup-simplify]: Simplify 0 into 0 10.803 * [backup-simplify]: Simplify 1 into 1 10.803 * [taylor]: Taking taylor expansion of PI in n 10.803 * [backup-simplify]: Simplify PI into PI 10.804 * [backup-simplify]: Simplify (* 0 PI) into 0 10.804 * [backup-simplify]: Simplify (* 2.0 0) into 0 10.804 * [backup-simplify]: Simplify 0 into 0 10.806 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 10.808 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 10.808 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.809 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 10.810 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 10.810 * [backup-simplify]: Simplify 0 into 0 10.812 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 10.813 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 10.813 * [backup-simplify]: Simplify 0 into 0 10.814 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 10.816 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0 10.816 * [backup-simplify]: Simplify 0 into 0 10.818 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 10.819 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0 10.819 * [backup-simplify]: Simplify 0 into 0 10.821 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 10.823 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0 10.823 * [backup-simplify]: Simplify 0 into 0 10.825 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0 10.827 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0 10.827 * [backup-simplify]: Simplify 0 into 0 10.828 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI)) 10.829 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n)) 10.829 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0 10.829 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 10.829 * [taylor]: Taking taylor expansion of 2.0 in n 10.829 * [backup-simplify]: Simplify 2.0 into 2.0 10.829 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.829 * [taylor]: Taking taylor expansion of PI in n 10.829 * [backup-simplify]: Simplify PI into PI 10.829 * [taylor]: Taking taylor expansion of n in n 10.829 * [backup-simplify]: Simplify 0 into 0 10.829 * [backup-simplify]: Simplify 1 into 1 10.830 * [backup-simplify]: Simplify (/ PI 1) into PI 10.830 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 10.830 * [taylor]: Taking taylor expansion of 2.0 in n 10.830 * [backup-simplify]: Simplify 2.0 into 2.0 10.830 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.830 * [taylor]: Taking taylor expansion of PI in n 10.830 * [backup-simplify]: Simplify PI into PI 10.830 * [taylor]: Taking taylor expansion of n in n 10.830 * [backup-simplify]: Simplify 0 into 0 10.830 * [backup-simplify]: Simplify 1 into 1 10.830 * [backup-simplify]: Simplify (/ PI 1) into PI 10.831 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.832 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 10.833 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.833 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 10.833 * [backup-simplify]: Simplify 0 into 0 10.835 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.836 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.836 * [backup-simplify]: Simplify 0 into 0 10.837 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.838 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.839 * [backup-simplify]: Simplify 0 into 0 10.840 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.841 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 10.841 * [backup-simplify]: Simplify 0 into 0 10.843 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.845 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 10.845 * [backup-simplify]: Simplify 0 into 0 10.846 * [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 10.848 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 10.848 * [backup-simplify]: Simplify 0 into 0 10.849 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI)) 10.850 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n)) 10.850 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0 10.850 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.850 * [taylor]: Taking taylor expansion of -2.0 in n 10.850 * [backup-simplify]: Simplify -2.0 into -2.0 10.850 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.850 * [taylor]: Taking taylor expansion of PI in n 10.850 * [backup-simplify]: Simplify PI into PI 10.850 * [taylor]: Taking taylor expansion of n in n 10.850 * [backup-simplify]: Simplify 0 into 0 10.850 * [backup-simplify]: Simplify 1 into 1 10.851 * [backup-simplify]: Simplify (/ PI 1) into PI 10.851 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 10.851 * [taylor]: Taking taylor expansion of -2.0 in n 10.851 * [backup-simplify]: Simplify -2.0 into -2.0 10.851 * [taylor]: Taking taylor expansion of (/ PI n) in n 10.851 * [taylor]: Taking taylor expansion of PI in n 10.851 * [backup-simplify]: Simplify PI into PI 10.851 * [taylor]: Taking taylor expansion of n in n 10.851 * [backup-simplify]: Simplify 0 into 0 10.851 * [backup-simplify]: Simplify 1 into 1 10.852 * [backup-simplify]: Simplify (/ PI 1) into PI 10.853 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.853 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 10.854 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 10.855 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 10.855 * [backup-simplify]: Simplify 0 into 0 10.856 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.858 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 10.858 * [backup-simplify]: Simplify 0 into 0 10.859 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.861 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 10.861 * [backup-simplify]: Simplify 0 into 0 10.862 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.864 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0 10.865 * [backup-simplify]: Simplify 0 into 0 10.866 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 10.868 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0 10.868 * [backup-simplify]: Simplify 0 into 0 10.870 * [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 10.872 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0 10.872 * [backup-simplify]: Simplify 0 into 0 10.872 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI)) 10.873 * * * [progress]: simplifying candidates 10.883 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 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 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(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))) 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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)) 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(+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (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)) 10.899 * * [simplify]: Extracting # 0 : cost 0 10.899 * * [simplify]: Extracting # 1 : cost 0 10.900 * * [simplify]: Extracting # 2 : cost 0 10.901 * * [simplify]: Extracting # 3 : cost 0 10.901 * * [simplify]: Extracting # 4 : cost 0 10.902 * * [simplify]: Extracting # 5 : cost 0 10.903 * * [simplify]: Extracting # 6 : cost 0 10.904 * * [simplify]: Extracting # 7 : cost 0 10.905 * * [simplify]: Extracting # 8 : cost 0 10.906 * * [simplify]: Extracting # 9 : cost 0 10.907 * * [simplify]: Extracting # 10 : cost 0 10.908 * * [simplify]: Extracting # 11 : cost 0 10.909 * * [simplify]: Extracting # 12 : cost 0 10.910 * * [simplify]: iteration 0 : 319 enodes (cost 5430 ) 11.105 * * [simplify]: Extracting # 0 : cost 0 11.108 * * [simplify]: Extracting # 1 : cost 0 11.111 * * [simplify]: Extracting # 2 : cost 0 11.114 * * [simplify]: Extracting # 3 : cost 0 11.116 * * [simplify]: Extracting # 4 : cost 0 11.119 * * [simplify]: Extracting # 5 : cost 0 11.122 * * [simplify]: Extracting # 6 : cost 0 11.124 * * [simplify]: iteration 1 : 1041 enodes (cost 4550 ) 11.618 * * [simplify]: Extracting # 0 : cost 0 11.629 * * [simplify]: Extracting # 1 : cost 0 11.641 * * [simplify]: Extracting # 2 : cost 0 11.659 * * [simplify]: Extracting # 3 : cost 0 11.670 * * [simplify]: Extracting # 4 : cost 0 11.682 * * [simplify]: iteration done: 5000 enodes (cost 4056 ) 11.686 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 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)) (* (log (* (* 2.0 PI) n)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (/ 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(* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n)) (pow (* (* n PI) 2.0) 3) (sqrt (* (* n PI) 2.0)) (sqrt (* (* n PI) 2.0)) (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (* (* 2.0 PI) (sqrt n)) (* 2.0 PI) (* PI n) (- (fma (* 0.03125 (pow k 2)) (* (pow (log (* 2.0 PI)) 2) (pow (* (* n PI) 2.0) 0.25)) (+ (pow (* (* n PI) 2.0) 0.25) (fma (* (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (* n PI) 2.0) 0.25)) (log n)) 0.0625 (* (* (pow (log n) 2) (* (pow k 2) (pow (* (* n PI) 2.0) 0.25))) 0.03125)))) (* (* 0.25 k) (+ (* (pow (* (* n PI) 2.0) 0.25) (log n)) (* (pow (* (* n PI) 2.0) 0.25) (log (* 2.0 PI)))))) (pow (pow (* (* n PI) 2.0) 0.25) (- 1.0 k)) (pow (exp 0.25) (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))) (- (fma (* 0.03125 (pow k 2)) (* (pow (log (* 2.0 PI)) 2) (pow (* (* n PI) 2.0) 0.25)) (+ (pow (* (* n PI) 2.0) 0.25) (fma (* (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (* n PI) 2.0) 0.25)) (log n)) 0.0625 (* (* (pow (log n) 2) (* (pow k 2) (pow (* (* n PI) 2.0) 0.25))) 0.03125)))) (* (* 0.25 k) (+ (* (pow (* (* n PI) 2.0) 0.25) (log n)) (* (pow (* (* n PI) 2.0) 0.25) (log (* 2.0 PI)))))) (pow (pow (* (* n PI) 2.0) 0.25) (- 1.0 k)) (pow (exp 0.25) (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))) (- (+ (pow (pow (* (* n PI) 2.0) 0.25) 2) (fma (* k (* k (* (* (log n) (pow (pow (* (* n PI) 2.0) 0.25) 2)) (log (* 2.0 PI))))) 0.25 (* (* 0.125 (pow k 2)) (+ (* (pow (log n) 2) (pow (pow (* (* n PI) 2.0) 0.25) 2)) (* (pow (pow (* (* n PI) 2.0) 0.25) 2) (pow (log (* 2.0 PI)) 2)))))) (* (* k (+ (* (log (* 2.0 PI)) (pow (pow (* (* n PI) 2.0) 0.25) 2)) (* (log n) (pow (pow (* (* n PI) 2.0) 0.25) 2)))) 0.5)) (pow (pow (pow (* (* n PI) 2.0) 0.25) (- 1.0 k)) 2) (pow (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) 2) (* (* n PI) 2.0) (* (* n PI) 2.0) (* (* n PI) 2.0) 11.689 * * * [progress]: adding candidates to table 12.826 * * [progress]: iteration 4 / 4 12.826 * * * [progress]: picking best candidate 12.848 * * * * [pick]: Picked # 12.848 * * * [progress]: localizing error 12.894 * * * [progress]: generating rewritten candidates 12.894 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 2 1) 12.942 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 2 2) 13.131 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 2 2 1 2) 13.132 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 2 2 1 1 2 2) 13.147 * * * [progress]: generating series expansions 13.147 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 2 1) 13.148 * [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))) 13.148 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 13.148 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 13.148 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 13.149 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 13.149 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 13.149 * [taylor]: Taking taylor expansion of 0.25 in k 13.149 * [backup-simplify]: Simplify 0.25 into 0.25 13.149 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.149 * [taylor]: Taking taylor expansion of 1.0 in k 13.149 * [backup-simplify]: Simplify 1.0 into 1.0 13.149 * [taylor]: Taking taylor expansion of k in k 13.149 * [backup-simplify]: Simplify 0 into 0 13.149 * [backup-simplify]: Simplify 1 into 1 13.149 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 13.149 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 13.149 * [taylor]: Taking taylor expansion of 2.0 in k 13.149 * [backup-simplify]: Simplify 2.0 into 2.0 13.149 * [taylor]: Taking taylor expansion of (* n PI) in k 13.149 * [taylor]: Taking taylor expansion of n in k 13.149 * [backup-simplify]: Simplify n into n 13.149 * [taylor]: Taking taylor expansion of PI in k 13.149 * [backup-simplify]: Simplify PI into PI 13.149 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.149 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 13.149 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 13.150 * [backup-simplify]: Simplify (- 0) into 0 13.150 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.151 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 13.151 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 13.151 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 13.151 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 13.151 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 13.151 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 13.151 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 13.151 * [taylor]: Taking taylor expansion of 0.25 in n 13.151 * [backup-simplify]: Simplify 0.25 into 0.25 13.151 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 13.151 * [taylor]: Taking taylor expansion of 1.0 in n 13.151 * [backup-simplify]: Simplify 1.0 into 1.0 13.151 * [taylor]: Taking taylor expansion of k in n 13.151 * [backup-simplify]: Simplify k into k 13.151 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 13.151 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 13.151 * [taylor]: Taking taylor expansion of 2.0 in n 13.152 * [backup-simplify]: Simplify 2.0 into 2.0 13.152 * [taylor]: Taking taylor expansion of (* n PI) in n 13.152 * [taylor]: Taking taylor expansion of n in n 13.152 * [backup-simplify]: Simplify 0 into 0 13.152 * [backup-simplify]: Simplify 1 into 1 13.152 * [taylor]: Taking taylor expansion of PI in n 13.152 * [backup-simplify]: Simplify PI into PI 13.152 * [backup-simplify]: Simplify (* 0 PI) into 0 13.153 * [backup-simplify]: Simplify (* 2.0 0) into 0 13.154 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.156 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 13.157 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.157 * [backup-simplify]: Simplify (- k) into (- k) 13.157 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 13.157 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 13.159 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.160 * [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)))) 13.162 * [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))))) 13.162 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 13.162 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 13.162 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 13.162 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 13.162 * [taylor]: Taking taylor expansion of 0.25 in n 13.162 * [backup-simplify]: Simplify 0.25 into 0.25 13.162 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 13.162 * [taylor]: Taking taylor expansion of 1.0 in n 13.162 * [backup-simplify]: Simplify 1.0 into 1.0 13.162 * [taylor]: Taking taylor expansion of k in n 13.162 * [backup-simplify]: Simplify k into k 13.162 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 13.162 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 13.162 * [taylor]: Taking taylor expansion of 2.0 in n 13.162 * [backup-simplify]: Simplify 2.0 into 2.0 13.162 * [taylor]: Taking taylor expansion of (* n PI) in n 13.162 * [taylor]: Taking taylor expansion of n in n 13.162 * [backup-simplify]: Simplify 0 into 0 13.162 * [backup-simplify]: Simplify 1 into 1 13.162 * [taylor]: Taking taylor expansion of PI in n 13.162 * [backup-simplify]: Simplify PI into PI 13.163 * [backup-simplify]: Simplify (* 0 PI) into 0 13.163 * [backup-simplify]: Simplify (* 2.0 0) into 0 13.165 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.167 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 13.168 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.168 * [backup-simplify]: Simplify (- k) into (- k) 13.168 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 13.168 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 13.169 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.170 * [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)))) 13.172 * [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))))) 13.172 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 13.172 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 13.172 * [taylor]: Taking taylor expansion of 0.25 in k 13.172 * [backup-simplify]: Simplify 0.25 into 0.25 13.172 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 13.172 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.172 * [taylor]: Taking taylor expansion of 1.0 in k 13.172 * [backup-simplify]: Simplify 1.0 into 1.0 13.172 * [taylor]: Taking taylor expansion of k in k 13.172 * [backup-simplify]: Simplify 0 into 0 13.172 * [backup-simplify]: Simplify 1 into 1 13.172 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 13.172 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 13.172 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 13.172 * [taylor]: Taking taylor expansion of 2.0 in k 13.172 * [backup-simplify]: Simplify 2.0 into 2.0 13.172 * [taylor]: Taking taylor expansion of PI in k 13.172 * [backup-simplify]: Simplify PI into PI 13.173 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.174 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.174 * [taylor]: Taking taylor expansion of (log n) in k 13.174 * [taylor]: Taking taylor expansion of n in k 13.174 * [backup-simplify]: Simplify n into n 13.174 * [backup-simplify]: Simplify (log n) into (log n) 13.175 * [backup-simplify]: Simplify (- 0) into 0 13.175 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.176 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 13.177 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 13.178 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 13.179 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 13.181 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 13.182 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.183 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 13.185 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.185 * [backup-simplify]: Simplify (- 0) into 0 13.186 * [backup-simplify]: Simplify (+ 0 0) into 0 13.186 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 13.188 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.189 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 13.191 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.191 * [taylor]: Taking taylor expansion of 0 in k 13.191 * [backup-simplify]: Simplify 0 into 0 13.191 * [backup-simplify]: Simplify 0 into 0 13.192 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.194 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.195 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 13.195 * [backup-simplify]: Simplify (+ 0 0) into 0 13.195 * [backup-simplify]: Simplify (- 1) into -1 13.196 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.197 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 13.199 * [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)))) 13.201 * [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)))))) 13.203 * [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)))))) 13.204 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.204 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.206 * [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 13.206 * [backup-simplify]: Simplify (- 0) into 0 13.207 * [backup-simplify]: Simplify (+ 0 0) into 0 13.207 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 13.208 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.209 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 13.210 * [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 13.210 * [taylor]: Taking taylor expansion of 0 in k 13.210 * [backup-simplify]: Simplify 0 into 0 13.210 * [backup-simplify]: Simplify 0 into 0 13.210 * [backup-simplify]: Simplify 0 into 0 13.211 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.213 * [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 13.214 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 13.214 * [backup-simplify]: Simplify (+ 0 0) into 0 13.215 * [backup-simplify]: Simplify (- 0) into 0 13.215 * [backup-simplify]: Simplify (+ 0 0) into 0 13.216 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 13.218 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 13.220 * [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))))) 13.223 * [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))))) 13.233 * [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)))))) 13.234 * [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)))) 13.234 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 13.234 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 13.234 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 13.234 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 13.234 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 13.234 * [taylor]: Taking taylor expansion of 0.25 in k 13.234 * [backup-simplify]: Simplify 0.25 into 0.25 13.234 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.234 * [taylor]: Taking taylor expansion of 1.0 in k 13.234 * [backup-simplify]: Simplify 1.0 into 1.0 13.234 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.234 * [taylor]: Taking taylor expansion of k in k 13.234 * [backup-simplify]: Simplify 0 into 0 13.234 * [backup-simplify]: Simplify 1 into 1 13.235 * [backup-simplify]: Simplify (/ 1 1) into 1 13.235 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 13.235 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 13.235 * [taylor]: Taking taylor expansion of 2.0 in k 13.235 * [backup-simplify]: Simplify 2.0 into 2.0 13.235 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.235 * [taylor]: Taking taylor expansion of PI in k 13.235 * [backup-simplify]: Simplify PI into PI 13.235 * [taylor]: Taking taylor expansion of n in k 13.235 * [backup-simplify]: Simplify n into n 13.235 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.235 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 13.235 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 13.236 * [backup-simplify]: Simplify (- 1) into -1 13.236 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.236 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 13.237 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 13.237 * [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))))) 13.237 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 13.237 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 13.237 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 13.237 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 13.237 * [taylor]: Taking taylor expansion of 0.25 in n 13.237 * [backup-simplify]: Simplify 0.25 into 0.25 13.237 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.237 * [taylor]: Taking taylor expansion of 1.0 in n 13.237 * [backup-simplify]: Simplify 1.0 into 1.0 13.237 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.237 * [taylor]: Taking taylor expansion of k in n 13.237 * [backup-simplify]: Simplify k into k 13.237 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.237 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.238 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.238 * [taylor]: Taking taylor expansion of 2.0 in n 13.238 * [backup-simplify]: Simplify 2.0 into 2.0 13.238 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.238 * [taylor]: Taking taylor expansion of PI in n 13.238 * [backup-simplify]: Simplify PI into PI 13.238 * [taylor]: Taking taylor expansion of n in n 13.238 * [backup-simplify]: Simplify 0 into 0 13.238 * [backup-simplify]: Simplify 1 into 1 13.245 * [backup-simplify]: Simplify (/ PI 1) into PI 13.246 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.247 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.247 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.247 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.247 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 13.249 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.250 * [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)))) 13.251 * [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))))) 13.252 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 13.252 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 13.252 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 13.252 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 13.252 * [taylor]: Taking taylor expansion of 0.25 in n 13.252 * [backup-simplify]: Simplify 0.25 into 0.25 13.252 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.252 * [taylor]: Taking taylor expansion of 1.0 in n 13.252 * [backup-simplify]: Simplify 1.0 into 1.0 13.252 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.252 * [taylor]: Taking taylor expansion of k in n 13.252 * [backup-simplify]: Simplify k into k 13.252 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.252 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.252 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.252 * [taylor]: Taking taylor expansion of 2.0 in n 13.252 * [backup-simplify]: Simplify 2.0 into 2.0 13.252 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.252 * [taylor]: Taking taylor expansion of PI in n 13.252 * [backup-simplify]: Simplify PI into PI 13.252 * [taylor]: Taking taylor expansion of n in n 13.252 * [backup-simplify]: Simplify 0 into 0 13.252 * [backup-simplify]: Simplify 1 into 1 13.253 * [backup-simplify]: Simplify (/ PI 1) into PI 13.253 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.254 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.255 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.255 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.255 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 13.256 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.258 * [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)))) 13.259 * [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))))) 13.259 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 13.259 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 13.259 * [taylor]: Taking taylor expansion of 0.25 in k 13.259 * [backup-simplify]: Simplify 0.25 into 0.25 13.259 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 13.259 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 13.259 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 13.259 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 13.259 * [taylor]: Taking taylor expansion of 2.0 in k 13.259 * [backup-simplify]: Simplify 2.0 into 2.0 13.259 * [taylor]: Taking taylor expansion of PI in k 13.259 * [backup-simplify]: Simplify PI into PI 13.260 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.261 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.261 * [taylor]: Taking taylor expansion of (log n) in k 13.261 * [taylor]: Taking taylor expansion of n in k 13.261 * [backup-simplify]: Simplify n into n 13.261 * [backup-simplify]: Simplify (log n) into (log n) 13.261 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.261 * [taylor]: Taking taylor expansion of 1.0 in k 13.261 * [backup-simplify]: Simplify 1.0 into 1.0 13.262 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.262 * [taylor]: Taking taylor expansion of k in k 13.262 * [backup-simplify]: Simplify 0 into 0 13.262 * [backup-simplify]: Simplify 1 into 1 13.262 * [backup-simplify]: Simplify (/ 1 1) into 1 13.262 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.263 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 13.264 * [backup-simplify]: Simplify (- 1) into -1 13.264 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.266 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 13.267 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 13.269 * [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))))) 13.271 * [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))))) 13.272 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.272 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.274 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.274 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.275 * [backup-simplify]: Simplify (- 0) into 0 13.275 * [backup-simplify]: Simplify (+ 0 0) into 0 13.276 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 13.277 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.279 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 13.281 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.281 * [taylor]: Taking taylor expansion of 0 in k 13.281 * [backup-simplify]: Simplify 0 into 0 13.281 * [backup-simplify]: Simplify 0 into 0 13.281 * [backup-simplify]: Simplify 0 into 0 13.282 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.283 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.287 * [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 13.287 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.287 * [backup-simplify]: Simplify (- 0) into 0 13.288 * [backup-simplify]: Simplify (+ 0 0) into 0 13.289 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 13.290 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.291 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 13.292 * [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 13.292 * [taylor]: Taking taylor expansion of 0 in k 13.292 * [backup-simplify]: Simplify 0 into 0 13.292 * [backup-simplify]: Simplify 0 into 0 13.292 * [backup-simplify]: Simplify 0 into 0 13.292 * [backup-simplify]: Simplify 0 into 0 13.293 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.294 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.297 * [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 13.297 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.297 * [backup-simplify]: Simplify (- 0) into 0 13.298 * [backup-simplify]: Simplify (+ 0 0) into 0 13.298 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 13.299 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.300 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 13.302 * [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 13.302 * [taylor]: Taking taylor expansion of 0 in k 13.302 * [backup-simplify]: Simplify 0 into 0 13.302 * [backup-simplify]: Simplify 0 into 0 13.303 * [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)))) 13.303 * [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))) 13.303 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 13.303 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 13.304 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k 13.304 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k 13.304 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 13.304 * [taylor]: Taking taylor expansion of 0.25 in k 13.304 * [backup-simplify]: Simplify 0.25 into 0.25 13.304 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.304 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.304 * [taylor]: Taking taylor expansion of k in k 13.304 * [backup-simplify]: Simplify 0 into 0 13.304 * [backup-simplify]: Simplify 1 into 1 13.304 * [backup-simplify]: Simplify (/ 1 1) into 1 13.304 * [taylor]: Taking taylor expansion of 1.0 in k 13.304 * [backup-simplify]: Simplify 1.0 into 1.0 13.304 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k 13.304 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k 13.304 * [taylor]: Taking taylor expansion of -2.0 in k 13.304 * [backup-simplify]: Simplify -2.0 into -2.0 13.304 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.304 * [taylor]: Taking taylor expansion of PI in k 13.304 * [backup-simplify]: Simplify PI into PI 13.304 * [taylor]: Taking taylor expansion of n in k 13.304 * [backup-simplify]: Simplify n into n 13.304 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.304 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n)) 13.304 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 13.305 * [backup-simplify]: Simplify (+ 1 0) into 1 13.305 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 13.305 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 13.305 * [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)))))) 13.305 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 13.305 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 13.305 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 13.305 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 13.305 * [taylor]: Taking taylor expansion of 0.25 in n 13.305 * [backup-simplify]: Simplify 0.25 into 0.25 13.305 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.305 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.305 * [taylor]: Taking taylor expansion of k in n 13.305 * [backup-simplify]: Simplify k into k 13.305 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.305 * [taylor]: Taking taylor expansion of 1.0 in n 13.305 * [backup-simplify]: Simplify 1.0 into 1.0 13.305 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 13.305 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.305 * [taylor]: Taking taylor expansion of -2.0 in n 13.306 * [backup-simplify]: Simplify -2.0 into -2.0 13.306 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.306 * [taylor]: Taking taylor expansion of PI in n 13.306 * [backup-simplify]: Simplify PI into PI 13.306 * [taylor]: Taking taylor expansion of n in n 13.306 * [backup-simplify]: Simplify 0 into 0 13.306 * [backup-simplify]: Simplify 1 into 1 13.306 * [backup-simplify]: Simplify (/ PI 1) into PI 13.306 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.307 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.307 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.307 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 13.308 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.309 * [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)))) 13.309 * [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))))) 13.309 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 13.309 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n 13.309 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n 13.309 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 13.309 * [taylor]: Taking taylor expansion of 0.25 in n 13.309 * [backup-simplify]: Simplify 0.25 into 0.25 13.310 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.310 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.310 * [taylor]: Taking taylor expansion of k in n 13.310 * [backup-simplify]: Simplify k into k 13.310 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.310 * [taylor]: Taking taylor expansion of 1.0 in n 13.310 * [backup-simplify]: Simplify 1.0 into 1.0 13.310 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n 13.310 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n 13.310 * [taylor]: Taking taylor expansion of -2.0 in n 13.310 * [backup-simplify]: Simplify -2.0 into -2.0 13.310 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.310 * [taylor]: Taking taylor expansion of PI in n 13.310 * [backup-simplify]: Simplify PI into PI 13.310 * [taylor]: Taking taylor expansion of n in n 13.310 * [backup-simplify]: Simplify 0 into 0 13.310 * [backup-simplify]: Simplify 1 into 1 13.310 * [backup-simplify]: Simplify (/ PI 1) into PI 13.310 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.311 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.311 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.311 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 13.312 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.313 * [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)))) 13.314 * [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))))) 13.314 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 13.314 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 13.314 * [taylor]: Taking taylor expansion of 0.25 in k 13.314 * [backup-simplify]: Simplify 0.25 into 0.25 13.314 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 13.314 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.314 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.314 * [taylor]: Taking taylor expansion of k in k 13.314 * [backup-simplify]: Simplify 0 into 0 13.314 * [backup-simplify]: Simplify 1 into 1 13.314 * [backup-simplify]: Simplify (/ 1 1) into 1 13.314 * [taylor]: Taking taylor expansion of 1.0 in k 13.314 * [backup-simplify]: Simplify 1.0 into 1.0 13.314 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 13.314 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 13.314 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 13.314 * [taylor]: Taking taylor expansion of -2.0 in k 13.314 * [backup-simplify]: Simplify -2.0 into -2.0 13.314 * [taylor]: Taking taylor expansion of PI in k 13.314 * [backup-simplify]: Simplify PI into PI 13.315 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.315 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.315 * [taylor]: Taking taylor expansion of (log n) in k 13.315 * [taylor]: Taking taylor expansion of n in k 13.315 * [backup-simplify]: Simplify n into n 13.315 * [backup-simplify]: Simplify (log n) into (log n) 13.316 * [backup-simplify]: Simplify (+ 1 0) into 1 13.316 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.316 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 13.317 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 13.318 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 13.319 * [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))))) 13.321 * [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))))) 13.322 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.323 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0 13.324 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 13.325 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.325 * [backup-simplify]: Simplify (+ 0 0) into 0 13.326 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 13.327 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.328 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 13.330 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.330 * [taylor]: Taking taylor expansion of 0 in k 13.330 * [backup-simplify]: Simplify 0 into 0 13.331 * [backup-simplify]: Simplify 0 into 0 13.331 * [backup-simplify]: Simplify 0 into 0 13.332 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.333 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.336 * [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 13.337 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.337 * [backup-simplify]: Simplify (+ 0 0) into 0 13.338 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 13.340 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.341 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 13.344 * [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 13.344 * [taylor]: Taking taylor expansion of 0 in k 13.344 * [backup-simplify]: Simplify 0 into 0 13.344 * [backup-simplify]: Simplify 0 into 0 13.344 * [backup-simplify]: Simplify 0 into 0 13.344 * [backup-simplify]: Simplify 0 into 0 13.345 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.346 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.352 * [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 13.353 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.353 * [backup-simplify]: Simplify (+ 0 0) into 0 13.354 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 13.356 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.358 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 13.361 * [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 13.361 * [taylor]: Taking taylor expansion of 0 in k 13.361 * [backup-simplify]: Simplify 0 into 0 13.361 * [backup-simplify]: Simplify 0 into 0 13.362 * [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)))))) 13.362 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 2 2) 13.363 * [backup-simplify]: Simplify (pow (* (* (* 2.0 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (/ (- 1.0 k) 2.0) 2)) into (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) 13.363 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in (n k) around 0 13.364 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in k 13.364 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k 13.364 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k 13.364 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in k 13.364 * [taylor]: Taking taylor expansion of 0.25 in k 13.364 * [backup-simplify]: Simplify 0.25 into 0.25 13.364 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.364 * [taylor]: Taking taylor expansion of 1.0 in k 13.364 * [backup-simplify]: Simplify 1.0 into 1.0 13.364 * [taylor]: Taking taylor expansion of k in k 13.364 * [backup-simplify]: Simplify 0 into 0 13.364 * [backup-simplify]: Simplify 1 into 1 13.364 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k 13.364 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k 13.364 * [taylor]: Taking taylor expansion of 2.0 in k 13.364 * [backup-simplify]: Simplify 2.0 into 2.0 13.364 * [taylor]: Taking taylor expansion of (* n PI) in k 13.364 * [taylor]: Taking taylor expansion of n in k 13.364 * [backup-simplify]: Simplify n into n 13.364 * [taylor]: Taking taylor expansion of PI in k 13.364 * [backup-simplify]: Simplify PI into PI 13.364 * [backup-simplify]: Simplify (* n PI) into (* n PI) 13.364 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI)) 13.364 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI))) 13.365 * [backup-simplify]: Simplify (- 0) into 0 13.365 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.366 * [backup-simplify]: Simplify (* 0.25 1.0) into 0.25 13.366 * [backup-simplify]: Simplify (* 0.25 (log (* 2.0 (* n PI)))) into (* 0.25 (log (* 2.0 (* n PI)))) 13.366 * [backup-simplify]: Simplify (exp (* 0.25 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.25) 13.366 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 13.366 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 13.366 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 13.366 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 13.366 * [taylor]: Taking taylor expansion of 0.25 in n 13.366 * [backup-simplify]: Simplify 0.25 into 0.25 13.366 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 13.366 * [taylor]: Taking taylor expansion of 1.0 in n 13.366 * [backup-simplify]: Simplify 1.0 into 1.0 13.366 * [taylor]: Taking taylor expansion of k in n 13.366 * [backup-simplify]: Simplify k into k 13.366 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 13.367 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 13.367 * [taylor]: Taking taylor expansion of 2.0 in n 13.367 * [backup-simplify]: Simplify 2.0 into 2.0 13.367 * [taylor]: Taking taylor expansion of (* n PI) in n 13.367 * [taylor]: Taking taylor expansion of n in n 13.367 * [backup-simplify]: Simplify 0 into 0 13.367 * [backup-simplify]: Simplify 1 into 1 13.367 * [taylor]: Taking taylor expansion of PI in n 13.367 * [backup-simplify]: Simplify PI into PI 13.367 * [backup-simplify]: Simplify (* 0 PI) into 0 13.368 * [backup-simplify]: Simplify (* 2.0 0) into 0 13.369 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.371 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 13.372 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.372 * [backup-simplify]: Simplify (- k) into (- k) 13.372 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 13.372 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 13.374 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.375 * [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)))) 13.376 * [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))))) 13.376 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.25 (- 1.0 k))) in n 13.376 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n 13.376 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n 13.376 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 k)) in n 13.376 * [taylor]: Taking taylor expansion of 0.25 in n 13.376 * [backup-simplify]: Simplify 0.25 into 0.25 13.376 * [taylor]: Taking taylor expansion of (- 1.0 k) in n 13.377 * [taylor]: Taking taylor expansion of 1.0 in n 13.377 * [backup-simplify]: Simplify 1.0 into 1.0 13.377 * [taylor]: Taking taylor expansion of k in n 13.377 * [backup-simplify]: Simplify k into k 13.377 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n 13.377 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n 13.377 * [taylor]: Taking taylor expansion of 2.0 in n 13.377 * [backup-simplify]: Simplify 2.0 into 2.0 13.377 * [taylor]: Taking taylor expansion of (* n PI) in n 13.377 * [taylor]: Taking taylor expansion of n in n 13.377 * [backup-simplify]: Simplify 0 into 0 13.377 * [backup-simplify]: Simplify 1 into 1 13.377 * [taylor]: Taking taylor expansion of PI in n 13.377 * [backup-simplify]: Simplify PI into PI 13.377 * [backup-simplify]: Simplify (* 0 PI) into 0 13.378 * [backup-simplify]: Simplify (* 2.0 0) into 0 13.379 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI 13.382 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI) 13.383 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.383 * [backup-simplify]: Simplify (- k) into (- k) 13.383 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k) 13.383 * [backup-simplify]: Simplify (* 0.25 (- 1.0 k)) into (* 0.25 (- 1.0 k)) 13.384 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.385 * [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)))) 13.385 * [backup-simplify]: Simplify (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 13.386 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k 13.386 * [taylor]: Taking taylor expansion of (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k 13.386 * [taylor]: Taking taylor expansion of 0.25 in k 13.386 * [backup-simplify]: Simplify 0.25 into 0.25 13.386 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k 13.386 * [taylor]: Taking taylor expansion of (- 1.0 k) in k 13.386 * [taylor]: Taking taylor expansion of 1.0 in k 13.386 * [backup-simplify]: Simplify 1.0 into 1.0 13.386 * [taylor]: Taking taylor expansion of k in k 13.386 * [backup-simplify]: Simplify 0 into 0 13.386 * [backup-simplify]: Simplify 1 into 1 13.386 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k 13.386 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 13.386 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 13.386 * [taylor]: Taking taylor expansion of 2.0 in k 13.386 * [backup-simplify]: Simplify 2.0 into 2.0 13.386 * [taylor]: Taking taylor expansion of PI in k 13.386 * [backup-simplify]: Simplify PI into PI 13.386 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.387 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.387 * [taylor]: Taking taylor expansion of (log n) in k 13.387 * [taylor]: Taking taylor expansion of n in k 13.387 * [backup-simplify]: Simplify n into n 13.387 * [backup-simplify]: Simplify (log n) into (log n) 13.387 * [backup-simplify]: Simplify (- 0) into 0 13.387 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0 13.388 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n)) 13.389 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n))) 13.389 * [backup-simplify]: Simplify (* 0.25 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.25 (+ (log (* 2.0 PI)) (log n))) 13.390 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 13.391 * [backup-simplify]: Simplify (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) 13.391 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0 13.392 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0 13.393 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.393 * [backup-simplify]: Simplify (- 0) into 0 13.393 * [backup-simplify]: Simplify (+ 0 0) into 0 13.394 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 k))) into 0 13.395 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.395 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0 13.396 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.396 * [taylor]: Taking taylor expansion of 0 in k 13.396 * [backup-simplify]: Simplify 0 into 0 13.396 * [backup-simplify]: Simplify 0 into 0 13.397 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.398 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.398 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0 13.399 * [backup-simplify]: Simplify (+ 0 0) into 0 13.399 * [backup-simplify]: Simplify (- 1) into -1 13.399 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.400 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n))) 13.401 * [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)))) 13.403 * [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)))))) 13.405 * [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)))))) 13.406 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0 13.407 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0 13.408 * [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 13.409 * [backup-simplify]: Simplify (- 0) into 0 13.409 * [backup-simplify]: Simplify (+ 0 0) into 0 13.409 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0 13.410 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n)) 13.411 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 13.413 * [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 13.413 * [taylor]: Taking taylor expansion of 0 in k 13.413 * [backup-simplify]: Simplify 0 into 0 13.413 * [backup-simplify]: Simplify 0 into 0 13.413 * [backup-simplify]: Simplify 0 into 0 13.413 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.415 * [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 13.416 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0 13.416 * [backup-simplify]: Simplify (+ 0 0) into 0 13.417 * [backup-simplify]: Simplify (- 0) into 0 13.417 * [backup-simplify]: Simplify (+ 0 0) into 0 13.418 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0 13.420 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0 13.422 * [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))))) 13.425 * [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))))) 13.431 * [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)))))) 13.432 * [backup-simplify]: Simplify (pow (* (* (* 2.0 PI) (* (cbrt (/ 1 n)) (cbrt (/ 1 n)))) (cbrt (/ 1 n))) (/ (/ (- 1.0 (/ 1 k)) 2.0) 2)) into (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) 13.432 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in (n k) around 0 13.432 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in k 13.432 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k 13.432 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k 13.432 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in k 13.432 * [taylor]: Taking taylor expansion of 0.25 in k 13.432 * [backup-simplify]: Simplify 0.25 into 0.25 13.432 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.432 * [taylor]: Taking taylor expansion of 1.0 in k 13.432 * [backup-simplify]: Simplify 1.0 into 1.0 13.432 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.432 * [taylor]: Taking taylor expansion of k in k 13.432 * [backup-simplify]: Simplify 0 into 0 13.433 * [backup-simplify]: Simplify 1 into 1 13.433 * [backup-simplify]: Simplify (/ 1 1) into 1 13.433 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k 13.433 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k 13.433 * [taylor]: Taking taylor expansion of 2.0 in k 13.433 * [backup-simplify]: Simplify 2.0 into 2.0 13.433 * [taylor]: Taking taylor expansion of (/ PI n) in k 13.433 * [taylor]: Taking taylor expansion of PI in k 13.433 * [backup-simplify]: Simplify PI into PI 13.433 * [taylor]: Taking taylor expansion of n in k 13.433 * [backup-simplify]: Simplify n into n 13.433 * [backup-simplify]: Simplify (/ PI n) into (/ PI n) 13.433 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n)) 13.433 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n))) 13.433 * [backup-simplify]: Simplify (- 1) into -1 13.434 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.434 * [backup-simplify]: Simplify (* 0.25 -1) into -0.25 13.434 * [backup-simplify]: Simplify (* -0.25 (log (* 2.0 (/ PI n)))) into (* -0.25 (log (* 2.0 (/ PI n)))) 13.434 * [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))))) 13.434 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 13.434 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 13.434 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 13.434 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 13.434 * [taylor]: Taking taylor expansion of 0.25 in n 13.434 * [backup-simplify]: Simplify 0.25 into 0.25 13.434 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.434 * [taylor]: Taking taylor expansion of 1.0 in n 13.434 * [backup-simplify]: Simplify 1.0 into 1.0 13.434 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.434 * [taylor]: Taking taylor expansion of k in n 13.434 * [backup-simplify]: Simplify k into k 13.434 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.434 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.434 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.434 * [taylor]: Taking taylor expansion of 2.0 in n 13.434 * [backup-simplify]: Simplify 2.0 into 2.0 13.434 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.435 * [taylor]: Taking taylor expansion of PI in n 13.435 * [backup-simplify]: Simplify PI into PI 13.435 * [taylor]: Taking taylor expansion of n in n 13.435 * [backup-simplify]: Simplify 0 into 0 13.435 * [backup-simplify]: Simplify 1 into 1 13.435 * [backup-simplify]: Simplify (/ PI 1) into PI 13.435 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.436 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.436 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.436 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.436 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 13.437 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.438 * [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)))) 13.439 * [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))))) 13.439 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.25 (- 1.0 (/ 1 k)))) in n 13.439 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n 13.439 * [taylor]: Taking taylor expansion of (* (* 0.25 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n 13.439 * [taylor]: Taking taylor expansion of (* 0.25 (- 1.0 (/ 1 k))) in n 13.439 * [taylor]: Taking taylor expansion of 0.25 in n 13.439 * [backup-simplify]: Simplify 0.25 into 0.25 13.439 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n 13.439 * [taylor]: Taking taylor expansion of 1.0 in n 13.439 * [backup-simplify]: Simplify 1.0 into 1.0 13.439 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.439 * [taylor]: Taking taylor expansion of k in n 13.439 * [backup-simplify]: Simplify k into k 13.439 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.439 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n 13.439 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n 13.439 * [taylor]: Taking taylor expansion of 2.0 in n 13.439 * [backup-simplify]: Simplify 2.0 into 2.0 13.439 * [taylor]: Taking taylor expansion of (/ PI n) in n 13.440 * [taylor]: Taking taylor expansion of PI in n 13.440 * [backup-simplify]: Simplify PI into PI 13.440 * [taylor]: Taking taylor expansion of n in n 13.440 * [backup-simplify]: Simplify 0 into 0 13.440 * [backup-simplify]: Simplify 1 into 1 13.440 * [backup-simplify]: Simplify (/ PI 1) into PI 13.441 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.442 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.442 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k)) 13.442 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k)) 13.442 * [backup-simplify]: Simplify (* 0.25 (- 1.0 (/ 1 k))) into (* 0.25 (- 1.0 (/ 1 k))) 13.443 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.444 * [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)))) 13.445 * [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))))) 13.446 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k 13.446 * [taylor]: Taking taylor expansion of (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k 13.446 * [taylor]: Taking taylor expansion of 0.25 in k 13.446 * [backup-simplify]: Simplify 0.25 into 0.25 13.446 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k 13.446 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k 13.446 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k 13.446 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k 13.446 * [taylor]: Taking taylor expansion of 2.0 in k 13.446 * [backup-simplify]: Simplify 2.0 into 2.0 13.446 * [taylor]: Taking taylor expansion of PI in k 13.446 * [backup-simplify]: Simplify PI into PI 13.446 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI) 13.447 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI)) 13.447 * [taylor]: Taking taylor expansion of (log n) in k 13.448 * [taylor]: Taking taylor expansion of n in k 13.448 * [backup-simplify]: Simplify n into n 13.448 * [backup-simplify]: Simplify (log n) into (log n) 13.448 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k 13.448 * [taylor]: Taking taylor expansion of 1.0 in k 13.448 * [backup-simplify]: Simplify 1.0 into 1.0 13.448 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.448 * [taylor]: Taking taylor expansion of k in k 13.448 * [backup-simplify]: Simplify 0 into 0 13.448 * [backup-simplify]: Simplify 1 into 1 13.448 * [backup-simplify]: Simplify (/ 1 1) into 1 13.448 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.449 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n)) 13.450 * [backup-simplify]: Simplify (- 1) into -1 13.450 * [backup-simplify]: Simplify (+ 0 -1) into -1 13.451 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n))) 13.452 * [backup-simplify]: Simplify (* 0.25 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.25 (- (log (* 2.0 PI)) (log n))) 13.453 * [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))))) 13.454 * [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))))) 13.455 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0 13.456 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0 13.457 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0 13.457 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.458 * [backup-simplify]: Simplify (- 0) into 0 13.458 * [backup-simplify]: Simplify (+ 0 0) into 0 13.459 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (- 1.0 (/ 1 k)))) into 0 13.460 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.461 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0 13.463 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.463 * [taylor]: Taking taylor expansion of 0 in k 13.463 * [backup-simplify]: Simplify 0 into 0 13.463 * [backup-simplify]: Simplify 0 into 0 13.463 * [backup-simplify]: Simplify 0 into 0 13.464 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.465 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0 13.468 * [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 13.468 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.469 * [backup-simplify]: Simplify (- 0) into 0 13.469 * [backup-simplify]: Simplify (+ 0 0) into 0 13.470 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0 13.472 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.473 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0 13.476 * [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 13.476 * [taylor]: Taking taylor expansion of 0 in k 13.476 * [backup-simplify]: Simplify 0 into 0 13.476 * [backup-simplify]: Simplify 0 into 0 13.476 * [backup-simplify]: Simplify 0 into 0 13.476 * [backup-simplify]: Simplify 0 into 0 13.477 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.478 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.484 * [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 13.484 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.485 * [backup-simplify]: Simplify (- 0) into 0 13.485 * [backup-simplify]: Simplify (+ 0 0) into 0 13.494 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0 13.496 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n)) 13.498 * [backup-simplify]: Simplify (+ (* (* 0.25 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0 13.501 * [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 13.501 * [taylor]: Taking taylor expansion of 0 in k 13.501 * [backup-simplify]: Simplify 0 into 0 13.501 * [backup-simplify]: Simplify 0 into 0 13.502 * [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)))) 13.504 * [backup-simplify]: Simplify (pow (* (* (* 2.0 PI) (* (cbrt (/ 1 (- n))) (cbrt (/ 1 (- n))))) (cbrt (/ 1 (- n)))) (/ (/ (- 1.0 (/ 1 (- k))) 2.0) 2)) into (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.25 (+ (/ 1 k) 1.0))) 13.504 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.25 (+ (/ 1 k) 1.0))) in (n k) around 0 13.504 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.25 (+ (/ 1 k) 1.0))) in k 13.504 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in k 13.504 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in k 13.504 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in k 13.504 * [taylor]: Taking taylor expansion of 0.25 in k 13.504 * [backup-simplify]: Simplify 0.25 into 0.25 13.504 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.504 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.504 * [taylor]: Taking taylor expansion of k in k 13.504 * [backup-simplify]: Simplify 0 into 0 13.504 * [backup-simplify]: Simplify 1 into 1 13.505 * [backup-simplify]: Simplify (/ 1 1) into 1 13.505 * [taylor]: Taking taylor expansion of 1.0 in k 13.505 * [backup-simplify]: Simplify 1.0 into 1.0 13.505 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in k 13.505 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in k 13.505 * [taylor]: Taking taylor expansion of 2.0 in k 13.505 * [backup-simplify]: Simplify 2.0 into 2.0 13.505 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in k 13.505 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in k 13.505 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in k 13.505 * [taylor]: Taking taylor expansion of (cbrt -1) in k 13.505 * [taylor]: Taking taylor expansion of -1 in k 13.505 * [backup-simplify]: Simplify -1 into -1 13.506 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 13.506 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 13.506 * [taylor]: Taking taylor expansion of PI in k 13.506 * [backup-simplify]: Simplify PI into PI 13.506 * [taylor]: Taking taylor expansion of n in k 13.506 * [backup-simplify]: Simplify n into n 13.507 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 13.508 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 13.509 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 13.510 * [backup-simplify]: Simplify (/ (* -1 PI) n) into (* -1 (/ PI n)) 13.510 * [backup-simplify]: Simplify (* 2.0 (* -1 (/ PI n))) into (* -2.0 (/ PI n)) 13.510 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n))) 13.510 * [backup-simplify]: Simplify (+ 1 0) into 1 13.510 * [backup-simplify]: Simplify (* 0.25 1) into 0.25 13.511 * [backup-simplify]: Simplify (* 0.25 (log (* -2.0 (/ PI n)))) into (* 0.25 (log (* -2.0 (/ PI n)))) 13.512 * [backup-simplify]: Simplify (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) 13.512 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 13.512 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in n 13.512 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in n 13.512 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 13.512 * [taylor]: Taking taylor expansion of 0.25 in n 13.512 * [backup-simplify]: Simplify 0.25 into 0.25 13.512 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.512 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.513 * [taylor]: Taking taylor expansion of k in n 13.513 * [backup-simplify]: Simplify k into k 13.513 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.513 * [taylor]: Taking taylor expansion of 1.0 in n 13.513 * [backup-simplify]: Simplify 1.0 into 1.0 13.513 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in n 13.513 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in n 13.513 * [taylor]: Taking taylor expansion of 2.0 in n 13.513 * [backup-simplify]: Simplify 2.0 into 2.0 13.513 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in n 13.513 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in n 13.513 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in n 13.513 * [taylor]: Taking taylor expansion of (cbrt -1) in n 13.513 * [taylor]: Taking taylor expansion of -1 in n 13.513 * [backup-simplify]: Simplify -1 into -1 13.513 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 13.514 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 13.514 * [taylor]: Taking taylor expansion of PI in n 13.514 * [backup-simplify]: Simplify PI into PI 13.514 * [taylor]: Taking taylor expansion of n in n 13.514 * [backup-simplify]: Simplify 0 into 0 13.514 * [backup-simplify]: Simplify 1 into 1 13.515 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 13.517 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 13.518 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 13.518 * [backup-simplify]: Simplify (/ (* -1 PI) 1) into (* -1 PI) 13.519 * [backup-simplify]: Simplify (* 2.0 (* -1 PI)) into (* -2.0 PI) 13.520 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.520 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.520 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 13.521 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.521 * [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)))) 13.522 * [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))))) 13.522 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) (* 0.25 (+ (/ 1 k) 1.0))) in n 13.522 * [taylor]: Taking taylor expansion of (exp (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))))) in n 13.522 * [taylor]: Taking taylor expansion of (* (* 0.25 (+ (/ 1 k) 1.0)) (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)))) in n 13.522 * [taylor]: Taking taylor expansion of (* 0.25 (+ (/ 1 k) 1.0)) in n 13.522 * [taylor]: Taking taylor expansion of 0.25 in n 13.522 * [backup-simplify]: Simplify 0.25 into 0.25 13.522 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n 13.522 * [taylor]: Taking taylor expansion of (/ 1 k) in n 13.522 * [taylor]: Taking taylor expansion of k in n 13.522 * [backup-simplify]: Simplify k into k 13.523 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k) 13.523 * [taylor]: Taking taylor expansion of 1.0 in n 13.523 * [backup-simplify]: Simplify 1.0 into 1.0 13.523 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n))) in n 13.523 * [taylor]: Taking taylor expansion of (* 2.0 (/ (* (pow (cbrt -1) 3) PI) n)) in n 13.523 * [taylor]: Taking taylor expansion of 2.0 in n 13.523 * [backup-simplify]: Simplify 2.0 into 2.0 13.523 * [taylor]: Taking taylor expansion of (/ (* (pow (cbrt -1) 3) PI) n) in n 13.523 * [taylor]: Taking taylor expansion of (* (pow (cbrt -1) 3) PI) in n 13.523 * [taylor]: Taking taylor expansion of (pow (cbrt -1) 3) in n 13.523 * [taylor]: Taking taylor expansion of (cbrt -1) in n 13.523 * [taylor]: Taking taylor expansion of -1 in n 13.523 * [backup-simplify]: Simplify -1 into -1 13.523 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 13.523 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 13.523 * [taylor]: Taking taylor expansion of PI in n 13.523 * [backup-simplify]: Simplify PI into PI 13.523 * [taylor]: Taking taylor expansion of n in n 13.524 * [backup-simplify]: Simplify 0 into 0 13.524 * [backup-simplify]: Simplify 1 into 1 13.524 * [backup-simplify]: Simplify (* (cbrt -1) (cbrt -1)) into (pow (cbrt -1) 2) 13.526 * [backup-simplify]: Simplify (* (cbrt -1) (pow (cbrt -1) 2)) into (pow (cbrt -1) 3) 13.527 * [backup-simplify]: Simplify (* (pow (cbrt -1) 3) PI) into (* -1 PI) 13.527 * [backup-simplify]: Simplify (/ (* -1 PI) 1) into (* -1 PI) 13.528 * [backup-simplify]: Simplify (* 2.0 (* -1 PI)) into (* -2.0 PI) 13.529 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.529 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0) 13.529 * [backup-simplify]: Simplify (* 0.25 (+ (/ 1 k) 1.0)) into (* 0.25 (+ (/ 1 k) 1.0)) 13.530 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.530 * [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)))) 13.531 * [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))))) 13.531 * [taylor]: Taking taylor expansion of (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k 13.531 * [taylor]: Taking taylor expansion of (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k 13.531 * [taylor]: Taking taylor expansion of 0.25 in k 13.531 * [backup-simplify]: Simplify 0.25 into 0.25 13.531 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k 13.531 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k 13.531 * [taylor]: Taking taylor expansion of (/ 1 k) in k 13.531 * [taylor]: Taking taylor expansion of k in k 13.531 * [backup-simplify]: Simplify 0 into 0 13.531 * [backup-simplify]: Simplify 1 into 1 13.532 * [backup-simplify]: Simplify (/ 1 1) into 1 13.532 * [taylor]: Taking taylor expansion of 1.0 in k 13.532 * [backup-simplify]: Simplify 1.0 into 1.0 13.532 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k 13.532 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k 13.532 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k 13.532 * [taylor]: Taking taylor expansion of -2.0 in k 13.532 * [backup-simplify]: Simplify -2.0 into -2.0 13.532 * [taylor]: Taking taylor expansion of PI in k 13.532 * [backup-simplify]: Simplify PI into PI 13.532 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI) 13.533 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI)) 13.533 * [taylor]: Taking taylor expansion of (log n) in k 13.533 * [taylor]: Taking taylor expansion of n in k 13.533 * [backup-simplify]: Simplify n into n 13.533 * [backup-simplify]: Simplify (log n) into (log n) 13.533 * [backup-simplify]: Simplify (+ 1 0) into 1 13.533 * [backup-simplify]: Simplify (- (log n)) into (- (log n)) 13.534 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n)) 13.535 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n)) 13.535 * [backup-simplify]: Simplify (* 0.25 (- (log (* -2.0 PI)) (log n))) into (* 0.25 (- (log (* -2.0 PI)) (log n))) 13.536 * [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))))) 13.537 * [backup-simplify]: Simplify (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) 13.537 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (cbrt -1))) into 0 13.538 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow (cbrt -1) 2))) into 0 13.539 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (* 0 PI)) into 0 13.539 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)))) into 0 13.540 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* -1 PI))) into 0 13.541 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0 13.541 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0 13.541 * [backup-simplify]: Simplify (+ 0 0) into 0 13.541 * [backup-simplify]: Simplify (+ (* 0.25 0) (* 0 (+ (/ 1 k) 1.0))) into 0 13.542 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.543 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0 13.544 * [backup-simplify]: Simplify (* (exp (* 0.25 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0 13.544 * [taylor]: Taking taylor expansion of 0 in k 13.544 * [backup-simplify]: Simplify 0 into 0 13.544 * [backup-simplify]: Simplify 0 into 0 13.544 * [backup-simplify]: Simplify 0 into 0 13.546 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 13.547 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (cbrt -1)))) into 0 13.548 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow (cbrt -1) 2)))) into 0 13.549 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (+ (* 0 0) (* 0 PI))) into 0 13.551 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.552 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* -1 PI)))) into 0 13.555 * [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 13.556 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.556 * [backup-simplify]: Simplify (+ 0 0) into 0 13.557 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0 13.558 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.560 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0 13.562 * [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 13.563 * [taylor]: Taking taylor expansion of 0 in k 13.563 * [backup-simplify]: Simplify 0 into 0 13.563 * [backup-simplify]: Simplify 0 into 0 13.563 * [backup-simplify]: Simplify 0 into 0 13.563 * [backup-simplify]: Simplify 0 into 0 13.564 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 13.565 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (cbrt -1))))) into 0 13.567 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (cbrt -1) 2))))) into 0 13.569 * [backup-simplify]: Simplify (+ (* (pow (cbrt -1) 3) 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0 13.570 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* (* -1 PI) (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.572 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* -1 PI))))) into 0 13.578 * [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 13.578 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0 13.579 * [backup-simplify]: Simplify (+ 0 0) into 0 13.580 * [backup-simplify]: Simplify (+ (* 0.25 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0 13.581 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n)) 13.584 * [backup-simplify]: Simplify (+ (* (* 0.25 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0 13.586 * [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 13.586 * [taylor]: Taking taylor expansion of 0 in k 13.586 * [backup-simplify]: Simplify 0 into 0 13.587 * [backup-simplify]: Simplify 0 into 0 13.588 * [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)))))) 13.588 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 2 2 1 2) 13.588 * [backup-simplify]: Simplify (cbrt n) into (pow n 1/3) 13.588 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 13.588 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 13.588 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 13.588 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 13.588 * [taylor]: Taking taylor expansion of 1/3 in n 13.588 * [backup-simplify]: Simplify 1/3 into 1/3 13.588 * [taylor]: Taking taylor expansion of (log n) in n 13.588 * [taylor]: Taking taylor expansion of n in n 13.588 * [backup-simplify]: Simplify 0 into 0 13.588 * [backup-simplify]: Simplify 1 into 1 13.589 * [backup-simplify]: Simplify (log 1) into 0 13.589 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.589 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 13.589 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 13.589 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 13.589 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 13.589 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 13.589 * [taylor]: Taking taylor expansion of 1/3 in n 13.589 * [backup-simplify]: Simplify 1/3 into 1/3 13.590 * [taylor]: Taking taylor expansion of (log n) in n 13.590 * [taylor]: Taking taylor expansion of n in n 13.590 * [backup-simplify]: Simplify 0 into 0 13.590 * [backup-simplify]: Simplify 1 into 1 13.590 * [backup-simplify]: Simplify (log 1) into 0 13.590 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.590 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 13.591 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 13.591 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 13.592 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 13.593 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.593 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (log n))) into 0 13.594 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 13.594 * [backup-simplify]: Simplify 0 into 0 13.597 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 13.597 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.598 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log n)))) into 0 13.599 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.600 * [backup-simplify]: Simplify 0 into 0 13.605 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 13.605 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.607 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 13.608 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.608 * [backup-simplify]: Simplify 0 into 0 13.620 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 13.624 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.625 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))) into 0 13.627 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.627 * [backup-simplify]: Simplify 0 into 0 13.636 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 13.636 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.638 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))))) into 0 13.639 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.640 * [backup-simplify]: Simplify 0 into 0 13.667 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 13.667 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.669 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))))) into 0 13.672 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.672 * [backup-simplify]: Simplify 0 into 0 13.673 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 13.673 * [backup-simplify]: Simplify (cbrt (/ 1 n)) into (pow (/ 1 n) 1/3) 13.673 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 13.673 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 13.673 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 13.673 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 13.673 * [taylor]: Taking taylor expansion of 1/3 in n 13.673 * [backup-simplify]: Simplify 1/3 into 1/3 13.673 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 13.673 * [taylor]: Taking taylor expansion of (/ 1 n) in n 13.673 * [taylor]: Taking taylor expansion of n in n 13.673 * [backup-simplify]: Simplify 0 into 0 13.673 * [backup-simplify]: Simplify 1 into 1 13.673 * [backup-simplify]: Simplify (/ 1 1) into 1 13.673 * [backup-simplify]: Simplify (log 1) into 0 13.674 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.674 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 13.674 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 13.674 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 13.674 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 13.674 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 13.674 * [taylor]: Taking taylor expansion of 1/3 in n 13.674 * [backup-simplify]: Simplify 1/3 into 1/3 13.674 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 13.674 * [taylor]: Taking taylor expansion of (/ 1 n) in n 13.674 * [taylor]: Taking taylor expansion of n in n 13.674 * [backup-simplify]: Simplify 0 into 0 13.674 * [backup-simplify]: Simplify 1 into 1 13.674 * [backup-simplify]: Simplify (/ 1 1) into 1 13.674 * [backup-simplify]: Simplify (log 1) into 0 13.675 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.675 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 13.675 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 13.675 * [backup-simplify]: Simplify (pow n -1/3) into (pow n -1/3) 13.675 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 13.676 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 13.676 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.677 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 13.677 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 13.677 * [backup-simplify]: Simplify 0 into 0 13.678 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.679 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 13.680 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.680 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 13.681 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.681 * [backup-simplify]: Simplify 0 into 0 13.681 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.684 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 13.685 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.685 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 13.686 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.686 * [backup-simplify]: Simplify 0 into 0 13.687 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.693 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 13.693 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.694 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 13.695 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.695 * [backup-simplify]: Simplify 0 into 0 13.696 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.712 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 13.713 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.715 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 13.719 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.719 * [backup-simplify]: Simplify 0 into 0 13.720 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.757 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 13.758 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.760 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 13.766 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.766 * [backup-simplify]: Simplify 0 into 0 13.766 * [backup-simplify]: Simplify (pow (/ 1 n) -1/3) into (pow (/ 1 n) -1/3) 13.767 * [backup-simplify]: Simplify (cbrt (/ 1 (- n))) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 13.767 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 13.767 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 13.767 * [taylor]: Taking taylor expansion of (cbrt -1) in n 13.767 * [taylor]: Taking taylor expansion of -1 in n 13.767 * [backup-simplify]: Simplify -1 into -1 13.768 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 13.768 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 13.768 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 13.768 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 13.768 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 13.768 * [taylor]: Taking taylor expansion of 1/3 in n 13.769 * [backup-simplify]: Simplify 1/3 into 1/3 13.769 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 13.769 * [taylor]: Taking taylor expansion of (/ 1 n) in n 13.769 * [taylor]: Taking taylor expansion of n in n 13.769 * [backup-simplify]: Simplify 0 into 0 13.769 * [backup-simplify]: Simplify 1 into 1 13.769 * [backup-simplify]: Simplify (/ 1 1) into 1 13.769 * [backup-simplify]: Simplify (log 1) into 0 13.770 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.770 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 13.770 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 13.770 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 13.770 * [taylor]: Taking taylor expansion of (cbrt -1) in n 13.770 * [taylor]: Taking taylor expansion of -1 in n 13.770 * [backup-simplify]: Simplify -1 into -1 13.770 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 13.771 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 13.771 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 13.771 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 13.771 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 13.771 * [taylor]: Taking taylor expansion of 1/3 in n 13.771 * [backup-simplify]: Simplify 1/3 into 1/3 13.771 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 13.771 * [taylor]: Taking taylor expansion of (/ 1 n) in n 13.771 * [taylor]: Taking taylor expansion of n in n 13.771 * [backup-simplify]: Simplify 0 into 0 13.771 * [backup-simplify]: Simplify 1 into 1 13.771 * [backup-simplify]: Simplify (/ 1 1) into 1 13.771 * [backup-simplify]: Simplify (log 1) into 0 13.772 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.772 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 13.772 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 13.772 * [backup-simplify]: Simplify (* (cbrt -1) (pow n -1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 13.773 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 n) 1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 13.773 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 13.774 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 13.774 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.774 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 13.775 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 13.775 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow n -1/3))) into 0 13.775 * [backup-simplify]: Simplify 0 into 0 13.776 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.777 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 13.778 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.778 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 13.779 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.780 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 13.780 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow n -1/3)))) into 0 13.780 * [backup-simplify]: Simplify 0 into 0 13.781 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.784 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 13.784 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.785 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 13.786 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.786 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 13.787 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))) into 0 13.787 * [backup-simplify]: Simplify 0 into 0 13.788 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.794 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 13.794 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.795 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 13.796 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.797 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 13.798 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))) into 0 13.799 * [backup-simplify]: Simplify 0 into 0 13.799 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.808 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 13.809 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.810 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 13.812 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.813 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 13.814 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))))) into 0 13.814 * [backup-simplify]: Simplify 0 into 0 13.815 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.846 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 13.847 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.849 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 13.858 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.861 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 13.863 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))))) into 0 13.863 * [backup-simplify]: Simplify 0 into 0 13.864 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 (/ 1 (- n))) 1/3)) into (* (pow (* -1 n) 1/3) (cbrt -1)) 13.864 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 2 2 1 1 2 2) 13.864 * [backup-simplify]: Simplify (cbrt n) into (pow n 1/3) 13.864 * [approximate]: Taking taylor expansion of (pow n 1/3) in (n) around 0 13.864 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 13.864 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 13.865 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 13.865 * [taylor]: Taking taylor expansion of 1/3 in n 13.865 * [backup-simplify]: Simplify 1/3 into 1/3 13.865 * [taylor]: Taking taylor expansion of (log n) in n 13.865 * [taylor]: Taking taylor expansion of n in n 13.865 * [backup-simplify]: Simplify 0 into 0 13.865 * [backup-simplify]: Simplify 1 into 1 13.865 * [backup-simplify]: Simplify (log 1) into 0 13.866 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.866 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 13.866 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 13.866 * [taylor]: Taking taylor expansion of (pow n 1/3) in n 13.866 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log n))) in n 13.866 * [taylor]: Taking taylor expansion of (* 1/3 (log n)) in n 13.866 * [taylor]: Taking taylor expansion of 1/3 in n 13.866 * [backup-simplify]: Simplify 1/3 into 1/3 13.866 * [taylor]: Taking taylor expansion of (log n) in n 13.866 * [taylor]: Taking taylor expansion of n in n 13.866 * [backup-simplify]: Simplify 0 into 0 13.866 * [backup-simplify]: Simplify 1 into 1 13.866 * [backup-simplify]: Simplify (log 1) into 0 13.867 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.867 * [backup-simplify]: Simplify (* 1/3 (log n)) into (* 1/3 (log n)) 13.867 * [backup-simplify]: Simplify (exp (* 1/3 (log n))) into (pow n 1/3) 13.867 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 13.869 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 13.869 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.870 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (log n))) into 0 13.871 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 13.871 * [backup-simplify]: Simplify 0 into 0 13.874 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 13.875 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.876 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (log n)))) into 0 13.878 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.878 * [backup-simplify]: Simplify 0 into 0 13.884 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 13.884 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.885 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))) into 0 13.887 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.887 * [backup-simplify]: Simplify 0 into 0 13.898 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 13.899 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.900 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))) into 0 13.903 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.903 * [backup-simplify]: Simplify 0 into 0 13.922 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 13.922 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.924 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n))))))) into 0 13.928 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.928 * [backup-simplify]: Simplify 0 into 0 13.962 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 13.963 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n) 13.965 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log n)))))))) into 0 13.970 * [backup-simplify]: Simplify (* (exp (* 1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.970 * [backup-simplify]: Simplify 0 into 0 13.970 * [backup-simplify]: Simplify (pow n 1/3) into (pow n 1/3) 13.971 * [backup-simplify]: Simplify (cbrt (/ 1 n)) into (pow (/ 1 n) 1/3) 13.971 * [approximate]: Taking taylor expansion of (pow (/ 1 n) 1/3) in (n) around 0 13.971 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 13.971 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 13.971 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 13.971 * [taylor]: Taking taylor expansion of 1/3 in n 13.971 * [backup-simplify]: Simplify 1/3 into 1/3 13.971 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 13.971 * [taylor]: Taking taylor expansion of (/ 1 n) in n 13.971 * [taylor]: Taking taylor expansion of n in n 13.971 * [backup-simplify]: Simplify 0 into 0 13.971 * [backup-simplify]: Simplify 1 into 1 13.971 * [backup-simplify]: Simplify (/ 1 1) into 1 13.971 * [backup-simplify]: Simplify (log 1) into 0 13.972 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.972 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 13.972 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 13.972 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 13.972 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 13.972 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 13.972 * [taylor]: Taking taylor expansion of 1/3 in n 13.972 * [backup-simplify]: Simplify 1/3 into 1/3 13.972 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 13.972 * [taylor]: Taking taylor expansion of (/ 1 n) in n 13.972 * [taylor]: Taking taylor expansion of n in n 13.972 * [backup-simplify]: Simplify 0 into 0 13.972 * [backup-simplify]: Simplify 1 into 1 13.972 * [backup-simplify]: Simplify (/ 1 1) into 1 13.972 * [backup-simplify]: Simplify (log 1) into 0 13.973 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.973 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 13.973 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 13.973 * [backup-simplify]: Simplify (pow n -1/3) into (pow n -1/3) 13.973 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 13.974 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 13.974 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.975 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 13.975 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 13.975 * [backup-simplify]: Simplify 0 into 0 13.976 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.977 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 13.977 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.978 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 13.979 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.979 * [backup-simplify]: Simplify 0 into 0 13.979 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.982 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 13.982 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.983 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 13.984 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 13.984 * [backup-simplify]: Simplify 0 into 0 13.984 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 13.990 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 13.991 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 13.991 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 13.993 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 13.993 * [backup-simplify]: Simplify 0 into 0 13.994 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.009 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 14.010 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 14.012 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 14.016 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.016 * [backup-simplify]: Simplify 0 into 0 14.018 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.046 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 14.047 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 14.048 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 14.051 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.051 * [backup-simplify]: Simplify 0 into 0 14.051 * [backup-simplify]: Simplify (pow (/ 1 n) -1/3) into (pow (/ 1 n) -1/3) 14.051 * [backup-simplify]: Simplify (cbrt (/ 1 (- n))) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 14.051 * [approximate]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in (n) around 0 14.051 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 14.051 * [taylor]: Taking taylor expansion of (cbrt -1) in n 14.052 * [taylor]: Taking taylor expansion of -1 in n 14.052 * [backup-simplify]: Simplify -1 into -1 14.052 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 14.052 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 14.052 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 14.052 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 14.052 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 14.052 * [taylor]: Taking taylor expansion of 1/3 in n 14.052 * [backup-simplify]: Simplify 1/3 into 1/3 14.052 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 14.052 * [taylor]: Taking taylor expansion of (/ 1 n) in n 14.052 * [taylor]: Taking taylor expansion of n in n 14.053 * [backup-simplify]: Simplify 0 into 0 14.053 * [backup-simplify]: Simplify 1 into 1 14.053 * [backup-simplify]: Simplify (/ 1 1) into 1 14.053 * [backup-simplify]: Simplify (log 1) into 0 14.053 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 14.053 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 14.053 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 14.053 * [taylor]: Taking taylor expansion of (* (cbrt -1) (pow (/ 1 n) 1/3)) in n 14.053 * [taylor]: Taking taylor expansion of (cbrt -1) in n 14.053 * [taylor]: Taking taylor expansion of -1 in n 14.053 * [backup-simplify]: Simplify -1 into -1 14.054 * [backup-simplify]: Simplify (cbrt -1) into (cbrt -1) 14.054 * [backup-simplify]: Simplify (/ 0 (* 3 (cbrt -1))) into 0 14.054 * [taylor]: Taking taylor expansion of (pow (/ 1 n) 1/3) in n 14.054 * [taylor]: Taking taylor expansion of (exp (* 1/3 (log (/ 1 n)))) in n 14.054 * [taylor]: Taking taylor expansion of (* 1/3 (log (/ 1 n))) in n 14.054 * [taylor]: Taking taylor expansion of 1/3 in n 14.054 * [backup-simplify]: Simplify 1/3 into 1/3 14.054 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n 14.054 * [taylor]: Taking taylor expansion of (/ 1 n) in n 14.054 * [taylor]: Taking taylor expansion of n in n 14.054 * [backup-simplify]: Simplify 0 into 0 14.054 * [backup-simplify]: Simplify 1 into 1 14.055 * [backup-simplify]: Simplify (/ 1 1) into 1 14.055 * [backup-simplify]: Simplify (log 1) into 0 14.055 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 14.055 * [backup-simplify]: Simplify (* 1/3 (- (log n))) into (* -1/3 (log n)) 14.055 * [backup-simplify]: Simplify (exp (* -1/3 (log n))) into (pow n -1/3) 14.056 * [backup-simplify]: Simplify (* (cbrt -1) (pow n -1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 14.056 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 n) 1/3)) into (* (cbrt -1) (pow (/ 1 n) 1/3)) 14.057 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0 14.057 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0 14.058 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 14.058 * [backup-simplify]: Simplify (+ (* 1/3 0) (* 0 (- (log n)))) into 0 14.058 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0 14.059 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (* 0 (pow n -1/3))) into 0 14.059 * [backup-simplify]: Simplify 0 into 0 14.059 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.061 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0 14.061 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 14.062 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (* 0 (- (log n))))) into 0 14.062 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.064 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 14.064 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (* 0 (pow n -1/3)))) into 0 14.064 * [backup-simplify]: Simplify 0 into 0 14.065 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.067 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0 14.068 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 14.068 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0 14.069 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.070 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 14.071 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))) into 0 14.071 * [backup-simplify]: Simplify 0 into 0 14.072 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.078 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0 14.078 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 14.079 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))) into 0 14.080 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.081 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 14.083 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))) into 0 14.083 * [backup-simplify]: Simplify 0 into 0 14.084 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.096 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0 14.096 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 14.098 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))))) into 0 14.100 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0 14.100 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)))) (* 3 (cbrt -1))) into 0 14.102 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3))))))) into 0 14.102 * [backup-simplify]: Simplify 0 into 0 14.102 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0 14.123 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0 14.124 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n)) 14.126 * [backup-simplify]: Simplify (+ (* 1/3 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n))))))))) into 0 14.129 * [backup-simplify]: Simplify (* (exp (* -1/3 (log n))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0 14.130 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0 0)) (* 2 (* 0 0 0)) (* 2 (* 0 0 (cbrt -1))))) (* 3 (cbrt -1))) into 0 14.132 * [backup-simplify]: Simplify (+ (* (cbrt -1) 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow n -1/3)))))))) into 0 14.132 * [backup-simplify]: Simplify 0 into 0 14.132 * [backup-simplify]: Simplify (* (cbrt -1) (pow (/ 1 (/ 1 (- n))) 1/3)) into (* (pow (* -1 n) 1/3) (cbrt -1)) 14.132 * * * [progress]: simplifying candidates 14.136 * [simplify]: Simplifying: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 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 (/ (- 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(* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (+ (* 0.03125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (+ (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.0625 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (* 0.03125 (* (pow k 2) (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))) (+ (* 0.25 (* k (* (log (* 2.0 PI)) (exp (* 0.25 (+ (log (* 2.0 PI)) (log n))))))) (* 0.25 (* k (* (exp (* 0.25 (+ (log (* 2.0 PI)) (log n)))) (log n)))))) (exp (* 0.25 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) (pow n 1/3) (pow (/ 1 n) -1/3) (* (pow (* -1 n) 1/3) (cbrt -1)) 14.142 * * [simplify]: Extracting # 0 : cost 0 14.142 * * [simplify]: Extracting # 1 : cost 0 14.142 * * [simplify]: Extracting # 2 : cost 0 14.143 * * [simplify]: Extracting # 3 : cost 0 14.143 * * [simplify]: Extracting # 4 : cost 0 14.144 * * [simplify]: Extracting # 5 : cost 0 14.144 * * [simplify]: Extracting # 6 : cost 0 14.144 * * [simplify]: Extracting # 7 : cost 0 14.145 * * [simplify]: Extracting # 8 : cost 0 14.145 * * [simplify]: Extracting # 9 : cost 0 14.146 * * [simplify]: Extracting # 10 : cost 0 14.146 * * [simplify]: Extracting # 11 : cost 0 14.147 * * [simplify]: Extracting # 12 : cost 0 14.147 * * [simplify]: Extracting # 13 : cost 0 14.148 * * [simplify]: iteration 0 : 327 enodes (cost 3810 ) 14.263 * * [simplify]: Extracting # 0 : cost 0 14.271 * * [simplify]: Extracting # 1 : cost 0 14.275 * * [simplify]: Extracting # 2 : cost 0 14.278 * * [simplify]: Extracting # 3 : cost 0 14.282 * * [simplify]: Extracting # 4 : cost 0 14.283 * * [simplify]: Extracting # 5 : cost 0 14.285 * * [simplify]: Extracting # 6 : cost 0 14.286 * * [simplify]: iteration 1 : 1079 enodes (cost 3555 ) 15.020 * * [simplify]: Extracting # 0 : cost 0 15.030 * * [simplify]: Extracting # 1 : cost 0 15.040 * * [simplify]: Extracting # 2 : cost 0 15.049 * * [simplify]: Extracting # 3 : cost 0 15.059 * * [simplify]: Extracting # 4 : cost 0 15.068 * * [simplify]: Extracting # 5 : cost 0 15.078 * * [simplify]: iteration 2 : 4039 enodes (cost 3142 ) 16.333 * * [simplify]: Extracting # 0 : cost 0 16.359 * * [simplify]: Extracting # 1 : cost 0 16.370 * * [simplify]: Extracting # 2 : cost 0 16.381 * * [simplify]: iteration done: 5000 enodes (cost 2886 ) 16.383 * [simplify]: Simplified to: (expm1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log1p (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (log (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) 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(sqrt 2))) (* (* 2.0 PI) n) (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)))) (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))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt k) (sqrt 1.0)) (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2))) (pow (* (* 2.0 PI) n) (+ (sqrt k) (sqrt 1.0))) (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)))) (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))) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2))) (* (* 2.0 PI) n) (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)) (* (* 2.0 PI) n) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (pow n 2/3) (* 2.0 PI)) (/ (/ (- 1.0 k) 2.0) 2)) (pow (cbrt 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 (pow (* (* PI n) 2.0) (/ (/ (- 1.0 k) 2.0) 2)) 3) (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) 4)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 4)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (pow n 2/3)) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) 1 (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) n (sqrt (cbrt n)) (sqrt (cbrt n)) (expm1 (cbrt n)) (log1p (cbrt n)) (log (cbrt n)) (exp (cbrt n)) (cbrt (pow n 2/3)) (cbrt (cbrt n)) (cbrt (sqrt n)) (cbrt (sqrt n)) 1 (cbrt n) (* (cbrt (cbrt n)) (cbrt (cbrt n))) (cbrt (cbrt n)) n (sqrt (cbrt n)) (sqrt (cbrt n)) (- (fma (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (* (pow (* (* 2.0 PI) n) 0.25) 0.03125) (fma (* (* 0.0625 (pow k 2)) (* (pow (* (* 2.0 PI) n) 0.25) (log (* 2.0 PI)))) (log n) (fma (* (* 0.03125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.25)) (pow (log n) 2) (pow (* (* 2.0 PI) n) 0.25)))) (* (* 0.25 k) (fma (log n) (pow (* (* 2.0 PI) n) 0.25) (* (pow (* (* 2.0 PI) n) 0.25) (log (* 2.0 PI)))))) (pow (pow (* (* 2.0 PI) n) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (fma (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (* (pow (* (* 2.0 PI) n) 0.25) 0.03125) (fma (* (* 0.0625 (pow k 2)) (* (pow (* (* 2.0 PI) n) 0.25) (log (* 2.0 PI)))) (log n) (fma (* (* 0.03125 (pow k 2)) (pow (* (* 2.0 PI) n) 0.25)) (pow (log n) 2) (pow (* (* 2.0 PI) n) 0.25)))) (* (* 0.25 k) (fma (log n) (pow (* (* 2.0 PI) n) 0.25) (* (pow (* (* 2.0 PI) n) 0.25) (log (* 2.0 PI)))))) (pow (pow (* (* 2.0 PI) n) 0.25) (- 1.0 k)) (exp (* 0.25 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (cbrt n) (pow (/ 1 n) -1/3) (* (cbrt (- n)) (cbrt -1)) (cbrt n) (pow (/ 1 n) -1/3) (* (cbrt (- n)) (cbrt -1)) 16.386 * * * [progress]: adding candidates to table 17.663 * [progress]: [Phase 3 of 3] Extracting. 17.663 * * [regime]: Finding splitpoints for: (# # # # # # # # #) 17.666 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k) 17.666 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (# # # # # # # # #) 17.728 * * * * [regimes]: Trying to branch on n from (# # # # # # # # #) 17.803 * * * * [regimes]: Trying to branch on k from (# # # # # # # # #) 17.855 * * * [regime]: Found split indices: #