77.283 * [progress]: [Phase 1 of 3] Setting up.
0.002 * * * [progress]: [1/2] Preparing points
0.171 * * * [progress]: [2/2] Setting up program.
0.179 * [progress]: [Phase 2 of 3] Improving.
0.180 * [simplify]: Simplifying:
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.180 * * [simplify]: iteration 0: 13 enodes
0.187 * * [simplify]: iteration 1: 29 enodes
0.237 * * [simplify]: iteration 2: 58 enodes
0.268 * * [simplify]: iteration 3: 114 enodes
0.336 * * [simplify]: iteration 4: 285 enodes
0.573 * * [simplify]: iteration 5: 819 enodes
2.663 * * [simplify]: iteration 6: 2725 enodes
4.622 * * [simplify]: iteration complete: 5002 enodes
4.622 * * [simplify]: Extracting #0: cost 1 inf + 0
4.622 * * [simplify]: Extracting #1: cost 107 inf + 0
4.625 * * [simplify]: Extracting #2: cost 441 inf + 1
4.632 * * [simplify]: Extracting #3: cost 1037 inf + 92
4.646 * * [simplify]: Extracting #4: cost 1334 inf + 12205
4.690 * * [simplify]: Extracting #5: cost 655 inf + 86066
4.813 * * [simplify]: Extracting #6: cost 190 inf + 381239
4.977 * * [simplify]: Extracting #7: cost 0 inf + 587702
5.150 * * [simplify]: Extracting #8: cost 0 inf + 570924
5.329 * [simplify]: Simplified to:
  (/ (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))
5.330 * * [progress]: iteration 1 / 4
5.330 * * * [progress]: picking best candidate
5.339 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))>
5.339 * * * [progress]: localizing error
5.390 * * * [progress]: generating rewritten candidates
5.390 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2)
5.435 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1)
5.481 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1)
5.494 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
5.595 * * * [progress]: generating series expansions
5.595 * * * * [progress]: [ 1 / 4 ] generating series at (2 2)
5.596 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
5.596 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
5.596 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
5.596 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
5.597 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
5.597 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
5.597 * [taylor]: Taking taylor expansion of 0.5 in k
5.597 * [backup-simplify]: Simplify 0.5 into 0.5
5.597 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
5.597 * [taylor]: Taking taylor expansion of 1.0 in k
5.597 * [backup-simplify]: Simplify 1.0 into 1.0
5.597 * [taylor]: Taking taylor expansion of k in k
5.597 * [backup-simplify]: Simplify 0 into 0
5.597 * [backup-simplify]: Simplify 1 into 1
5.597 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
5.597 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
5.597 * [taylor]: Taking taylor expansion of 2.0 in k
5.597 * [backup-simplify]: Simplify 2.0 into 2.0
5.597 * [taylor]: Taking taylor expansion of (* n PI) in k
5.597 * [taylor]: Taking taylor expansion of n in k
5.597 * [backup-simplify]: Simplify n into n
5.597 * [taylor]: Taking taylor expansion of PI in k
5.597 * [backup-simplify]: Simplify PI into PI
5.597 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.597 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
5.597 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
5.598 * [backup-simplify]: Simplify (- 0) into 0
5.599 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
5.599 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
5.599 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
5.599 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
5.599 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
5.599 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
5.599 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
5.600 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
5.600 * [taylor]: Taking taylor expansion of 0.5 in n
5.600 * [backup-simplify]: Simplify 0.5 into 0.5
5.600 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
5.600 * [taylor]: Taking taylor expansion of 1.0 in n
5.600 * [backup-simplify]: Simplify 1.0 into 1.0
5.600 * [taylor]: Taking taylor expansion of k in n
5.600 * [backup-simplify]: Simplify k into k
5.600 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
5.600 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
5.600 * [taylor]: Taking taylor expansion of 2.0 in n
5.600 * [backup-simplify]: Simplify 2.0 into 2.0
5.600 * [taylor]: Taking taylor expansion of (* n PI) in n
5.600 * [taylor]: Taking taylor expansion of n in n
5.600 * [backup-simplify]: Simplify 0 into 0
5.600 * [backup-simplify]: Simplify 1 into 1
5.600 * [taylor]: Taking taylor expansion of PI in n
5.600 * [backup-simplify]: Simplify PI into PI
5.601 * [backup-simplify]: Simplify (* 0 PI) into 0
5.601 * [backup-simplify]: Simplify (* 2.0 0) into 0
5.603 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.605 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
5.606 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.606 * [backup-simplify]: Simplify (- k) into (- k)
5.606 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
5.606 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
5.608 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
5.609 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
5.610 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
5.610 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
5.610 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
5.610 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
5.610 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
5.610 * [taylor]: Taking taylor expansion of 0.5 in n
5.610 * [backup-simplify]: Simplify 0.5 into 0.5
5.610 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
5.610 * [taylor]: Taking taylor expansion of 1.0 in n
5.611 * [backup-simplify]: Simplify 1.0 into 1.0
5.611 * [taylor]: Taking taylor expansion of k in n
5.611 * [backup-simplify]: Simplify k into k
5.611 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
5.611 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
5.611 * [taylor]: Taking taylor expansion of 2.0 in n
5.611 * [backup-simplify]: Simplify 2.0 into 2.0
5.611 * [taylor]: Taking taylor expansion of (* n PI) in n
5.611 * [taylor]: Taking taylor expansion of n in n
5.611 * [backup-simplify]: Simplify 0 into 0
5.611 * [backup-simplify]: Simplify 1 into 1
5.611 * [taylor]: Taking taylor expansion of PI in n
5.611 * [backup-simplify]: Simplify PI into PI
5.611 * [backup-simplify]: Simplify (* 0 PI) into 0
5.612 * [backup-simplify]: Simplify (* 2.0 0) into 0
5.614 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.616 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
5.617 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.617 * [backup-simplify]: Simplify (- k) into (- k)
5.617 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
5.617 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
5.619 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
5.620 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
5.621 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
5.622 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
5.622 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
5.622 * [taylor]: Taking taylor expansion of 0.5 in k
5.622 * [backup-simplify]: Simplify 0.5 into 0.5
5.622 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
5.622 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
5.622 * [taylor]: Taking taylor expansion of 1.0 in k
5.622 * [backup-simplify]: Simplify 1.0 into 1.0
5.622 * [taylor]: Taking taylor expansion of k in k
5.622 * [backup-simplify]: Simplify 0 into 0
5.622 * [backup-simplify]: Simplify 1 into 1
5.622 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
5.622 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
5.622 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
5.622 * [taylor]: Taking taylor expansion of 2.0 in k
5.622 * [backup-simplify]: Simplify 2.0 into 2.0
5.622 * [taylor]: Taking taylor expansion of PI in k
5.622 * [backup-simplify]: Simplify PI into PI
5.623 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.624 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.625 * [taylor]: Taking taylor expansion of (log n) in k
5.625 * [taylor]: Taking taylor expansion of n in k
5.625 * [backup-simplify]: Simplify n into n
5.625 * [backup-simplify]: Simplify (log n) into (log n)
5.625 * [backup-simplify]: Simplify (- 0) into 0
5.626 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
5.627 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
5.629 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
5.630 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
5.632 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
5.633 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
5.635 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.637 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
5.639 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
5.639 * [backup-simplify]: Simplify (- 0) into 0
5.640 * [backup-simplify]: Simplify (+ 0 0) into 0
5.640 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
5.642 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
5.643 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
5.645 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.645 * [taylor]: Taking taylor expansion of 0 in k
5.645 * [backup-simplify]: Simplify 0 into 0
5.645 * [backup-simplify]: Simplify 0 into 0
5.646 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
5.648 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
5.649 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
5.650 * [backup-simplify]: Simplify (+ 0 0) into 0
5.650 * [backup-simplify]: Simplify (- 1) into -1
5.651 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.652 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
5.655 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
5.658 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
5.662 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
5.663 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.665 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.668 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
5.669 * [backup-simplify]: Simplify (- 0) into 0
5.669 * [backup-simplify]: Simplify (+ 0 0) into 0
5.670 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
5.672 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
5.673 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
5.676 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.676 * [taylor]: Taking taylor expansion of 0 in k
5.676 * [backup-simplify]: Simplify 0 into 0
5.676 * [backup-simplify]: Simplify 0 into 0
5.676 * [backup-simplify]: Simplify 0 into 0
5.677 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
5.681 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
5.683 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
5.683 * [backup-simplify]: Simplify (+ 0 0) into 0
5.684 * [backup-simplify]: Simplify (- 0) into 0
5.684 * [backup-simplify]: Simplify (+ 0 0) into 0
5.686 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
5.689 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
5.693 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
5.699 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
5.710 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
5.711 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))
5.711 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
5.711 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
5.711 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
5.711 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
5.711 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
5.711 * [taylor]: Taking taylor expansion of 0.5 in k
5.711 * [backup-simplify]: Simplify 0.5 into 0.5
5.711 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
5.711 * [taylor]: Taking taylor expansion of 1.0 in k
5.712 * [backup-simplify]: Simplify 1.0 into 1.0
5.712 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.712 * [taylor]: Taking taylor expansion of k in k
5.712 * [backup-simplify]: Simplify 0 into 0
5.712 * [backup-simplify]: Simplify 1 into 1
5.712 * [backup-simplify]: Simplify (/ 1 1) into 1
5.712 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
5.712 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
5.712 * [taylor]: Taking taylor expansion of 2.0 in k
5.712 * [backup-simplify]: Simplify 2.0 into 2.0
5.712 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.712 * [taylor]: Taking taylor expansion of PI in k
5.712 * [backup-simplify]: Simplify PI into PI
5.712 * [taylor]: Taking taylor expansion of n in k
5.713 * [backup-simplify]: Simplify n into n
5.713 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.713 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
5.713 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
5.713 * [backup-simplify]: Simplify (- 1) into -1
5.714 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.714 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
5.714 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
5.715 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
5.715 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
5.715 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
5.715 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
5.715 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
5.715 * [taylor]: Taking taylor expansion of 0.5 in n
5.715 * [backup-simplify]: Simplify 0.5 into 0.5
5.715 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
5.715 * [taylor]: Taking taylor expansion of 1.0 in n
5.715 * [backup-simplify]: Simplify 1.0 into 1.0
5.715 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.715 * [taylor]: Taking taylor expansion of k in n
5.715 * [backup-simplify]: Simplify k into k
5.715 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.715 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
5.715 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
5.715 * [taylor]: Taking taylor expansion of 2.0 in n
5.716 * [backup-simplify]: Simplify 2.0 into 2.0
5.716 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.716 * [taylor]: Taking taylor expansion of PI in n
5.716 * [backup-simplify]: Simplify PI into PI
5.716 * [taylor]: Taking taylor expansion of n in n
5.716 * [backup-simplify]: Simplify 0 into 0
5.716 * [backup-simplify]: Simplify 1 into 1
5.716 * [backup-simplify]: Simplify (/ PI 1) into PI
5.717 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.718 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.718 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.718 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
5.718 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
5.720 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.721 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
5.723 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
5.723 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
5.723 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
5.723 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
5.723 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
5.723 * [taylor]: Taking taylor expansion of 0.5 in n
5.723 * [backup-simplify]: Simplify 0.5 into 0.5
5.723 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
5.723 * [taylor]: Taking taylor expansion of 1.0 in n
5.723 * [backup-simplify]: Simplify 1.0 into 1.0
5.723 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.723 * [taylor]: Taking taylor expansion of k in n
5.723 * [backup-simplify]: Simplify k into k
5.723 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.723 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
5.723 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
5.723 * [taylor]: Taking taylor expansion of 2.0 in n
5.723 * [backup-simplify]: Simplify 2.0 into 2.0
5.723 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.724 * [taylor]: Taking taylor expansion of PI in n
5.724 * [backup-simplify]: Simplify PI into PI
5.724 * [taylor]: Taking taylor expansion of n in n
5.724 * [backup-simplify]: Simplify 0 into 0
5.724 * [backup-simplify]: Simplify 1 into 1
5.724 * [backup-simplify]: Simplify (/ PI 1) into PI
5.725 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.726 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.726 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.726 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
5.726 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
5.728 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.730 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
5.731 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
5.731 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
5.732 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
5.732 * [taylor]: Taking taylor expansion of 0.5 in k
5.732 * [backup-simplify]: Simplify 0.5 into 0.5
5.732 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
5.732 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
5.732 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
5.732 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
5.732 * [taylor]: Taking taylor expansion of 2.0 in k
5.732 * [backup-simplify]: Simplify 2.0 into 2.0
5.732 * [taylor]: Taking taylor expansion of PI in k
5.732 * [backup-simplify]: Simplify PI into PI
5.732 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.733 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.733 * [taylor]: Taking taylor expansion of (log n) in k
5.734 * [taylor]: Taking taylor expansion of n in k
5.734 * [backup-simplify]: Simplify n into n
5.734 * [backup-simplify]: Simplify (log n) into (log n)
5.734 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
5.734 * [taylor]: Taking taylor expansion of 1.0 in k
5.734 * [backup-simplify]: Simplify 1.0 into 1.0
5.734 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.734 * [taylor]: Taking taylor expansion of k in k
5.734 * [backup-simplify]: Simplify 0 into 0
5.734 * [backup-simplify]: Simplify 1 into 1
5.734 * [backup-simplify]: Simplify (/ 1 1) into 1
5.734 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.735 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
5.736 * [backup-simplify]: Simplify (- 1) into -1
5.737 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.738 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
5.739 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
5.741 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
5.742 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
5.744 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.744 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
5.746 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
5.747 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.747 * [backup-simplify]: Simplify (- 0) into 0
5.748 * [backup-simplify]: Simplify (+ 0 0) into 0
5.748 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
5.750 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.751 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
5.753 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.753 * [taylor]: Taking taylor expansion of 0 in k
5.754 * [backup-simplify]: Simplify 0 into 0
5.754 * [backup-simplify]: Simplify 0 into 0
5.754 * [backup-simplify]: Simplify 0 into 0
5.755 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.756 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
5.759 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
5.760 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.760 * [backup-simplify]: Simplify (- 0) into 0
5.761 * [backup-simplify]: Simplify (+ 0 0) into 0
5.767 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
5.769 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.771 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
5.774 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.774 * [taylor]: Taking taylor expansion of 0 in k
5.774 * [backup-simplify]: Simplify 0 into 0
5.774 * [backup-simplify]: Simplify 0 into 0
5.774 * [backup-simplify]: Simplify 0 into 0
5.774 * [backup-simplify]: Simplify 0 into 0
5.776 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.777 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.783 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
5.784 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.784 * [backup-simplify]: Simplify (- 0) into 0
5.785 * [backup-simplify]: Simplify (+ 0 0) into 0
5.786 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
5.788 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.790 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
5.793 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
5.793 * [taylor]: Taking taylor expansion of 0 in k
5.793 * [backup-simplify]: Simplify 0 into 0
5.793 * [backup-simplify]: Simplify 0 into 0
5.794 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
5.795 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))
5.795 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
5.795 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
5.795 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
5.795 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
5.795 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
5.795 * [taylor]: Taking taylor expansion of 0.5 in k
5.795 * [backup-simplify]: Simplify 0.5 into 0.5
5.795 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
5.795 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.795 * [taylor]: Taking taylor expansion of k in k
5.796 * [backup-simplify]: Simplify 0 into 0
5.796 * [backup-simplify]: Simplify 1 into 1
5.796 * [backup-simplify]: Simplify (/ 1 1) into 1
5.796 * [taylor]: Taking taylor expansion of 1.0 in k
5.796 * [backup-simplify]: Simplify 1.0 into 1.0
5.796 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
5.796 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
5.796 * [taylor]: Taking taylor expansion of -2.0 in k
5.796 * [backup-simplify]: Simplify -2.0 into -2.0
5.796 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.796 * [taylor]: Taking taylor expansion of PI in k
5.796 * [backup-simplify]: Simplify PI into PI
5.796 * [taylor]: Taking taylor expansion of n in k
5.796 * [backup-simplify]: Simplify n into n
5.796 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.796 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
5.797 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
5.797 * [backup-simplify]: Simplify (+ 1 0) into 1
5.798 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
5.798 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
5.798 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
5.798 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
5.798 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
5.798 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
5.798 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
5.798 * [taylor]: Taking taylor expansion of 0.5 in n
5.798 * [backup-simplify]: Simplify 0.5 into 0.5
5.798 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
5.798 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.798 * [taylor]: Taking taylor expansion of k in n
5.798 * [backup-simplify]: Simplify k into k
5.798 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.798 * [taylor]: Taking taylor expansion of 1.0 in n
5.798 * [backup-simplify]: Simplify 1.0 into 1.0
5.798 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
5.798 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
5.799 * [taylor]: Taking taylor expansion of -2.0 in n
5.799 * [backup-simplify]: Simplify -2.0 into -2.0
5.799 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.799 * [taylor]: Taking taylor expansion of PI in n
5.799 * [backup-simplify]: Simplify PI into PI
5.799 * [taylor]: Taking taylor expansion of n in n
5.799 * [backup-simplify]: Simplify 0 into 0
5.799 * [backup-simplify]: Simplify 1 into 1
5.799 * [backup-simplify]: Simplify (/ PI 1) into PI
5.800 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
5.801 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
5.801 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
5.801 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
5.803 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
5.804 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
5.805 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
5.805 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
5.805 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
5.805 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
5.805 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
5.805 * [taylor]: Taking taylor expansion of 0.5 in n
5.805 * [backup-simplify]: Simplify 0.5 into 0.5
5.805 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
5.805 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.805 * [taylor]: Taking taylor expansion of k in n
5.805 * [backup-simplify]: Simplify k into k
5.805 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.806 * [taylor]: Taking taylor expansion of 1.0 in n
5.806 * [backup-simplify]: Simplify 1.0 into 1.0
5.806 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
5.806 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
5.806 * [taylor]: Taking taylor expansion of -2.0 in n
5.806 * [backup-simplify]: Simplify -2.0 into -2.0
5.806 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.806 * [taylor]: Taking taylor expansion of PI in n
5.806 * [backup-simplify]: Simplify PI into PI
5.806 * [taylor]: Taking taylor expansion of n in n
5.806 * [backup-simplify]: Simplify 0 into 0
5.806 * [backup-simplify]: Simplify 1 into 1
5.806 * [backup-simplify]: Simplify (/ PI 1) into PI
5.807 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
5.808 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
5.808 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
5.808 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
5.810 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
5.811 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
5.812 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
5.812 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
5.812 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
5.812 * [taylor]: Taking taylor expansion of 0.5 in k
5.812 * [backup-simplify]: Simplify 0.5 into 0.5
5.812 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
5.813 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
5.813 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.813 * [taylor]: Taking taylor expansion of k in k
5.813 * [backup-simplify]: Simplify 0 into 0
5.813 * [backup-simplify]: Simplify 1 into 1
5.813 * [backup-simplify]: Simplify (/ 1 1) into 1
5.813 * [taylor]: Taking taylor expansion of 1.0 in k
5.813 * [backup-simplify]: Simplify 1.0 into 1.0
5.813 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
5.813 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
5.813 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
5.813 * [taylor]: Taking taylor expansion of -2.0 in k
5.813 * [backup-simplify]: Simplify -2.0 into -2.0
5.813 * [taylor]: Taking taylor expansion of PI in k
5.813 * [backup-simplify]: Simplify PI into PI
5.814 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
5.815 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
5.815 * [taylor]: Taking taylor expansion of (log n) in k
5.815 * [taylor]: Taking taylor expansion of n in k
5.815 * [backup-simplify]: Simplify n into n
5.815 * [backup-simplify]: Simplify (log n) into (log n)
5.816 * [backup-simplify]: Simplify (+ 1 0) into 1
5.816 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.817 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
5.818 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
5.820 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
5.821 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
5.822 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
5.823 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.824 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
5.826 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
5.826 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.826 * [backup-simplify]: Simplify (+ 0 0) into 0
5.827 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
5.829 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
5.830 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
5.832 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.832 * [taylor]: Taking taylor expansion of 0 in k
5.832 * [backup-simplify]: Simplify 0 into 0
5.832 * [backup-simplify]: Simplify 0 into 0
5.832 * [backup-simplify]: Simplify 0 into 0
5.834 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.835 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
5.838 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
5.839 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.839 * [backup-simplify]: Simplify (+ 0 0) into 0
5.840 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
5.841 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
5.843 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
5.846 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.846 * [taylor]: Taking taylor expansion of 0 in k
5.846 * [backup-simplify]: Simplify 0 into 0
5.846 * [backup-simplify]: Simplify 0 into 0
5.846 * [backup-simplify]: Simplify 0 into 0
5.846 * [backup-simplify]: Simplify 0 into 0
5.848 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.849 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.855 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0
5.856 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.856 * [backup-simplify]: Simplify (+ 0 0) into 0
5.857 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
5.859 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
5.861 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
5.864 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
5.864 * [taylor]: Taking taylor expansion of 0 in k
5.864 * [backup-simplify]: Simplify 0 into 0
5.864 * [backup-simplify]: Simplify 0 into 0
5.866 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
5.866 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1)
5.867 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
5.867 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
5.867 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
5.867 * [taylor]: Taking taylor expansion of 2.0 in n
5.867 * [backup-simplify]: Simplify 2.0 into 2.0
5.867 * [taylor]: Taking taylor expansion of (* n PI) in n
5.867 * [taylor]: Taking taylor expansion of n in n
5.867 * [backup-simplify]: Simplify 0 into 0
5.867 * [backup-simplify]: Simplify 1 into 1
5.867 * [taylor]: Taking taylor expansion of PI in n
5.867 * [backup-simplify]: Simplify PI into PI
5.867 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
5.868 * [taylor]: Taking taylor expansion of 2.0 in n
5.868 * [backup-simplify]: Simplify 2.0 into 2.0
5.868 * [taylor]: Taking taylor expansion of (* n PI) in n
5.868 * [taylor]: Taking taylor expansion of n in n
5.868 * [backup-simplify]: Simplify 0 into 0
5.868 * [backup-simplify]: Simplify 1 into 1
5.868 * [taylor]: Taking taylor expansion of PI in n
5.868 * [backup-simplify]: Simplify PI into PI
5.869 * [backup-simplify]: Simplify (* 0 PI) into 0
5.869 * [backup-simplify]: Simplify (* 2.0 0) into 0
5.869 * [backup-simplify]: Simplify 0 into 0
5.871 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.873 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
5.873 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.874 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.876 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
5.876 * [backup-simplify]: Simplify 0 into 0
5.878 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.879 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.879 * [backup-simplify]: Simplify 0 into 0
5.881 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.883 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
5.883 * [backup-simplify]: Simplify 0 into 0
5.884 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.886 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
5.886 * [backup-simplify]: Simplify 0 into 0
5.889 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.891 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
5.891 * [backup-simplify]: Simplify 0 into 0
5.893 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
5.896 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
5.896 * [backup-simplify]: Simplify 0 into 0
5.897 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
5.898 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
5.898 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
5.898 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
5.898 * [taylor]: Taking taylor expansion of 2.0 in n
5.898 * [backup-simplify]: Simplify 2.0 into 2.0
5.898 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.898 * [taylor]: Taking taylor expansion of PI in n
5.898 * [backup-simplify]: Simplify PI into PI
5.898 * [taylor]: Taking taylor expansion of n in n
5.898 * [backup-simplify]: Simplify 0 into 0
5.898 * [backup-simplify]: Simplify 1 into 1
5.899 * [backup-simplify]: Simplify (/ PI 1) into PI
5.899 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
5.899 * [taylor]: Taking taylor expansion of 2.0 in n
5.899 * [backup-simplify]: Simplify 2.0 into 2.0
5.899 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.899 * [taylor]: Taking taylor expansion of PI in n
5.899 * [backup-simplify]: Simplify PI into PI
5.899 * [taylor]: Taking taylor expansion of n in n
5.899 * [backup-simplify]: Simplify 0 into 0
5.899 * [backup-simplify]: Simplify 1 into 1
5.900 * [backup-simplify]: Simplify (/ PI 1) into PI
5.900 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.901 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.902 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.903 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
5.903 * [backup-simplify]: Simplify 0 into 0
5.905 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.906 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
5.906 * [backup-simplify]: Simplify 0 into 0
5.908 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.910 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.910 * [backup-simplify]: Simplify 0 into 0
5.911 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.913 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.913 * [backup-simplify]: Simplify 0 into 0
5.914 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.916 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.916 * [backup-simplify]: Simplify 0 into 0
5.917 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.919 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.919 * [backup-simplify]: Simplify 0 into 0
5.920 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
5.920 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
5.920 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
5.920 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
5.920 * [taylor]: Taking taylor expansion of -2.0 in n
5.920 * [backup-simplify]: Simplify -2.0 into -2.0
5.920 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.920 * [taylor]: Taking taylor expansion of PI in n
5.920 * [backup-simplify]: Simplify PI into PI
5.920 * [taylor]: Taking taylor expansion of n in n
5.921 * [backup-simplify]: Simplify 0 into 0
5.921 * [backup-simplify]: Simplify 1 into 1
5.921 * [backup-simplify]: Simplify (/ PI 1) into PI
5.921 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
5.921 * [taylor]: Taking taylor expansion of -2.0 in n
5.921 * [backup-simplify]: Simplify -2.0 into -2.0
5.921 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.921 * [taylor]: Taking taylor expansion of PI in n
5.921 * [backup-simplify]: Simplify PI into PI
5.921 * [taylor]: Taking taylor expansion of n in n
5.921 * [backup-simplify]: Simplify 0 into 0
5.921 * [backup-simplify]: Simplify 1 into 1
5.922 * [backup-simplify]: Simplify (/ PI 1) into PI
5.923 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
5.923 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
5.924 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.925 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
5.925 * [backup-simplify]: Simplify 0 into 0
5.926 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.927 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
5.927 * [backup-simplify]: Simplify 0 into 0
5.929 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.930 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.930 * [backup-simplify]: Simplify 0 into 0
5.931 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.932 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.933 * [backup-simplify]: Simplify 0 into 0
5.934 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.935 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.935 * [backup-simplify]: Simplify 0 into 0
5.937 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.944 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.944 * [backup-simplify]: Simplify 0 into 0
5.945 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
5.945 * * * * [progress]: [ 3 / 4 ] generating series at (2 1)
5.945 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k)))
5.945 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0
5.945 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
5.945 * [taylor]: Taking taylor expansion of 1.0 in k
5.946 * [backup-simplify]: Simplify 1.0 into 1.0
5.946 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.946 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.946 * [taylor]: Taking taylor expansion of k in k
5.946 * [backup-simplify]: Simplify 0 into 0
5.946 * [backup-simplify]: Simplify 1 into 1
5.946 * [backup-simplify]: Simplify (/ 1 1) into 1
5.947 * [backup-simplify]: Simplify (sqrt 0) into 0
5.949 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.949 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
5.949 * [taylor]: Taking taylor expansion of 1.0 in k
5.949 * [backup-simplify]: Simplify 1.0 into 1.0
5.949 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.949 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.949 * [taylor]: Taking taylor expansion of k in k
5.949 * [backup-simplify]: Simplify 0 into 0
5.949 * [backup-simplify]: Simplify 1 into 1
5.950 * [backup-simplify]: Simplify (/ 1 1) into 1
5.950 * [backup-simplify]: Simplify (sqrt 0) into 0
5.951 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.952 * [backup-simplify]: Simplify (* 1.0 0) into 0
5.952 * [backup-simplify]: Simplify 0 into 0
5.953 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
5.954 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
5.955 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
5.958 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.960 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
5.960 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
5.961 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.965 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.968 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
5.968 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
5.970 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0)))))
5.970 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k))
5.970 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0
5.970 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
5.970 * [taylor]: Taking taylor expansion of 1.0 in k
5.970 * [backup-simplify]: Simplify 1.0 into 1.0
5.970 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.970 * [taylor]: Taking taylor expansion of k in k
5.970 * [backup-simplify]: Simplify 0 into 0
5.970 * [backup-simplify]: Simplify 1 into 1
5.971 * [backup-simplify]: Simplify (sqrt 0) into 0
5.972 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.972 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
5.972 * [taylor]: Taking taylor expansion of 1.0 in k
5.972 * [backup-simplify]: Simplify 1.0 into 1.0
5.972 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.972 * [taylor]: Taking taylor expansion of k in k
5.972 * [backup-simplify]: Simplify 0 into 0
5.972 * [backup-simplify]: Simplify 1 into 1
5.973 * [backup-simplify]: Simplify (sqrt 0) into 0
5.974 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.975 * [backup-simplify]: Simplify (* 1.0 0) into 0
5.975 * [backup-simplify]: Simplify 0 into 0
5.976 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
5.977 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
5.979 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.981 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
5.982 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
5.986 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.989 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
5.989 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
5.991 * [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))))))))
5.991 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k)))
5.991 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0
5.991 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
5.991 * [taylor]: Taking taylor expansion of 1.0 in k
5.991 * [backup-simplify]: Simplify 1.0 into 1.0
5.991 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.991 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.991 * [taylor]: Taking taylor expansion of -1 in k
5.991 * [backup-simplify]: Simplify -1 into -1
5.991 * [taylor]: Taking taylor expansion of k in k
5.991 * [backup-simplify]: Simplify 0 into 0
5.991 * [backup-simplify]: Simplify 1 into 1
5.992 * [backup-simplify]: Simplify (/ -1 1) into -1
5.992 * [backup-simplify]: Simplify (sqrt 0) into 0
5.994 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.994 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
5.994 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
5.994 * [taylor]: Taking taylor expansion of 1.0 in k
5.994 * [backup-simplify]: Simplify 1.0 into 1.0
5.994 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.994 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.994 * [taylor]: Taking taylor expansion of -1 in k
5.994 * [backup-simplify]: Simplify -1 into -1
5.994 * [taylor]: Taking taylor expansion of k in k
5.994 * [backup-simplify]: Simplify 0 into 0
5.994 * [backup-simplify]: Simplify 1 into 1
5.995 * [backup-simplify]: Simplify (/ -1 1) into -1
5.995 * [backup-simplify]: Simplify (sqrt 0) into 0
5.996 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.997 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
5.997 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.998 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
6.001 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.004 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
6.004 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
6.005 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.009 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.013 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
6.014 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
6.015 * [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)))))
6.015 * * * * [progress]: [ 4 / 4 ] generating series at (2)
6.016 * [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)))))
6.016 * [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
6.016 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n
6.016 * [taylor]: Taking taylor expansion of 1.0 in n
6.016 * [backup-simplify]: Simplify 1.0 into 1.0
6.016 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n
6.016 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
6.016 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.016 * [taylor]: Taking taylor expansion of k in n
6.016 * [backup-simplify]: Simplify k into k
6.016 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.016 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
6.016 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.016 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
6.016 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
6.016 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
6.016 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
6.017 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
6.017 * [taylor]: Taking taylor expansion of 0.5 in n
6.017 * [backup-simplify]: Simplify 0.5 into 0.5
6.017 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
6.017 * [taylor]: Taking taylor expansion of 1.0 in n
6.017 * [backup-simplify]: Simplify 1.0 into 1.0
6.017 * [taylor]: Taking taylor expansion of k in n
6.017 * [backup-simplify]: Simplify k into k
6.017 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
6.017 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
6.017 * [taylor]: Taking taylor expansion of 2.0 in n
6.017 * [backup-simplify]: Simplify 2.0 into 2.0
6.017 * [taylor]: Taking taylor expansion of (* n PI) in n
6.017 * [taylor]: Taking taylor expansion of n in n
6.017 * [backup-simplify]: Simplify 0 into 0
6.017 * [backup-simplify]: Simplify 1 into 1
6.017 * [taylor]: Taking taylor expansion of PI in n
6.017 * [backup-simplify]: Simplify PI into PI
6.018 * [backup-simplify]: Simplify (* 0 PI) into 0
6.018 * [backup-simplify]: Simplify (* 2.0 0) into 0
6.020 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.021 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
6.022 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.022 * [backup-simplify]: Simplify (- k) into (- k)
6.022 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
6.022 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
6.024 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
6.025 * [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))))
6.026 * [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)))))
6.026 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
6.026 * [taylor]: Taking taylor expansion of 1.0 in k
6.026 * [backup-simplify]: Simplify 1.0 into 1.0
6.026 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
6.027 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
6.027 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.027 * [taylor]: Taking taylor expansion of k in k
6.027 * [backup-simplify]: Simplify 0 into 0
6.027 * [backup-simplify]: Simplify 1 into 1
6.027 * [backup-simplify]: Simplify (/ 1 1) into 1
6.027 * [backup-simplify]: Simplify (sqrt 0) into 0
6.029 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.029 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
6.029 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
6.029 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
6.029 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
6.029 * [taylor]: Taking taylor expansion of 0.5 in k
6.029 * [backup-simplify]: Simplify 0.5 into 0.5
6.029 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
6.029 * [taylor]: Taking taylor expansion of 1.0 in k
6.029 * [backup-simplify]: Simplify 1.0 into 1.0
6.029 * [taylor]: Taking taylor expansion of k in k
6.029 * [backup-simplify]: Simplify 0 into 0
6.029 * [backup-simplify]: Simplify 1 into 1
6.029 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
6.029 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
6.029 * [taylor]: Taking taylor expansion of 2.0 in k
6.029 * [backup-simplify]: Simplify 2.0 into 2.0
6.029 * [taylor]: Taking taylor expansion of (* n PI) in k
6.029 * [taylor]: Taking taylor expansion of n in k
6.029 * [backup-simplify]: Simplify n into n
6.029 * [taylor]: Taking taylor expansion of PI in k
6.029 * [backup-simplify]: Simplify PI into PI
6.029 * [backup-simplify]: Simplify (* n PI) into (* n PI)
6.029 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
6.030 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
6.030 * [backup-simplify]: Simplify (- 0) into 0
6.030 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
6.031 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
6.031 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
6.031 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
6.031 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
6.031 * [taylor]: Taking taylor expansion of 1.0 in k
6.031 * [backup-simplify]: Simplify 1.0 into 1.0
6.031 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
6.031 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
6.031 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.031 * [taylor]: Taking taylor expansion of k in k
6.031 * [backup-simplify]: Simplify 0 into 0
6.032 * [backup-simplify]: Simplify 1 into 1
6.032 * [backup-simplify]: Simplify (/ 1 1) into 1
6.032 * [backup-simplify]: Simplify (sqrt 0) into 0
6.034 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.034 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
6.034 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
6.034 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
6.034 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
6.034 * [taylor]: Taking taylor expansion of 0.5 in k
6.034 * [backup-simplify]: Simplify 0.5 into 0.5
6.034 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
6.034 * [taylor]: Taking taylor expansion of 1.0 in k
6.034 * [backup-simplify]: Simplify 1.0 into 1.0
6.034 * [taylor]: Taking taylor expansion of k in k
6.034 * [backup-simplify]: Simplify 0 into 0
6.034 * [backup-simplify]: Simplify 1 into 1
6.034 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
6.034 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
6.034 * [taylor]: Taking taylor expansion of 2.0 in k
6.034 * [backup-simplify]: Simplify 2.0 into 2.0
6.034 * [taylor]: Taking taylor expansion of (* n PI) in k
6.034 * [taylor]: Taking taylor expansion of n in k
6.034 * [backup-simplify]: Simplify n into n
6.034 * [taylor]: Taking taylor expansion of PI in k
6.034 * [backup-simplify]: Simplify PI into PI
6.034 * [backup-simplify]: Simplify (* n PI) into (* n PI)
6.034 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
6.035 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
6.035 * [backup-simplify]: Simplify (- 0) into 0
6.035 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
6.036 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
6.036 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
6.036 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
6.037 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0
6.037 * [backup-simplify]: Simplify (* 1.0 0) into 0
6.037 * [taylor]: Taking taylor expansion of 0 in n
6.037 * [backup-simplify]: Simplify 0 into 0
6.037 * [backup-simplify]: Simplify 0 into 0
6.038 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
6.038 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0
6.039 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0
6.039 * [backup-simplify]: Simplify (- 1) into -1
6.040 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.041 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5)
6.042 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI)))))
6.043 * [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)))
6.045 * [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)))
6.047 * [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)))
6.047 * [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
6.047 * [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
6.047 * [taylor]: Taking taylor expansion of +nan.0 in n
6.047 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.047 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
6.047 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
6.047 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
6.047 * [taylor]: Taking taylor expansion of 0.5 in n
6.047 * [backup-simplify]: Simplify 0.5 into 0.5
6.047 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
6.047 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
6.047 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
6.047 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
6.047 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
6.047 * [taylor]: Taking taylor expansion of 1.0 in n
6.047 * [backup-simplify]: Simplify 1.0 into 1.0
6.047 * [taylor]: Taking taylor expansion of (log PI) in n
6.047 * [taylor]: Taking taylor expansion of PI in n
6.047 * [backup-simplify]: Simplify PI into PI
6.048 * [backup-simplify]: Simplify (log PI) into (log PI)
6.049 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
6.051 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
6.051 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
6.051 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
6.051 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
6.051 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
6.051 * [taylor]: Taking taylor expansion of 1.0 in n
6.051 * [backup-simplify]: Simplify 1.0 into 1.0
6.051 * [taylor]: Taking taylor expansion of (log n) in n
6.051 * [taylor]: Taking taylor expansion of n in n
6.051 * [backup-simplify]: Simplify 0 into 0
6.051 * [backup-simplify]: Simplify 1 into 1
6.051 * [backup-simplify]: Simplify (log 1) into 0
6.052 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
6.052 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
6.052 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
6.052 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
6.052 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
6.052 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
6.052 * [taylor]: Taking taylor expansion of 1.0 in n
6.052 * [backup-simplify]: Simplify 1.0 into 1.0
6.052 * [taylor]: Taking taylor expansion of (log 2.0) in n
6.052 * [taylor]: Taking taylor expansion of 2.0 in n
6.052 * [backup-simplify]: Simplify 2.0 into 2.0
6.053 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
6.053 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
6.055 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
6.056 * [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)
6.057 * [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)
6.058 * [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))
6.059 * [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)))
6.061 * [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)
6.063 * [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))
6.064 * [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)))
6.066 * [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)))
6.066 * [backup-simplify]: Simplify 0 into 0
6.067 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
6.068 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
6.070 * [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
6.070 * [backup-simplify]: Simplify (- 0) into 0
6.070 * [backup-simplify]: Simplify (+ 0 0) into 0
6.072 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0
6.073 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0
6.074 * [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)))
6.075 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
6.078 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.082 * [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))))))))
6.088 * [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))))))))
6.088 * [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
6.088 * [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
6.088 * [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
6.088 * [taylor]: Taking taylor expansion of +nan.0 in n
6.088 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.088 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
6.088 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
6.088 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
6.088 * [taylor]: Taking taylor expansion of 0.5 in n
6.088 * [backup-simplify]: Simplify 0.5 into 0.5
6.088 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
6.088 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
6.088 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
6.088 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
6.088 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
6.089 * [taylor]: Taking taylor expansion of 1.0 in n
6.089 * [backup-simplify]: Simplify 1.0 into 1.0
6.089 * [taylor]: Taking taylor expansion of (log PI) in n
6.089 * [taylor]: Taking taylor expansion of PI in n
6.089 * [backup-simplify]: Simplify PI into PI
6.089 * [backup-simplify]: Simplify (log PI) into (log PI)
6.090 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
6.092 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
6.092 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
6.092 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
6.092 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
6.092 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
6.092 * [taylor]: Taking taylor expansion of 1.0 in n
6.092 * [backup-simplify]: Simplify 1.0 into 1.0
6.092 * [taylor]: Taking taylor expansion of (log n) in n
6.092 * [taylor]: Taking taylor expansion of n in n
6.092 * [backup-simplify]: Simplify 0 into 0
6.092 * [backup-simplify]: Simplify 1 into 1
6.093 * [backup-simplify]: Simplify (log 1) into 0
6.093 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
6.093 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
6.093 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
6.093 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
6.093 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
6.093 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
6.093 * [taylor]: Taking taylor expansion of 1.0 in n
6.093 * [backup-simplify]: Simplify 1.0 into 1.0
6.093 * [taylor]: Taking taylor expansion of (log 2.0) in n
6.093 * [taylor]: Taking taylor expansion of 2.0 in n
6.093 * [backup-simplify]: Simplify 2.0 into 2.0
6.094 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
6.095 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
6.096 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
6.097 * [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)
6.099 * [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)
6.105 * [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))
6.106 * [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)))
6.107 * [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)
6.107 * [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
6.107 * [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
6.107 * [taylor]: Taking taylor expansion of +nan.0 in n
6.107 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.107 * [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
6.107 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
6.107 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
6.107 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
6.107 * [taylor]: Taking taylor expansion of 0.5 in n
6.107 * [backup-simplify]: Simplify 0.5 into 0.5
6.107 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
6.107 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
6.107 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
6.107 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
6.107 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
6.107 * [taylor]: Taking taylor expansion of 1.0 in n
6.107 * [backup-simplify]: Simplify 1.0 into 1.0
6.107 * [taylor]: Taking taylor expansion of (log 2.0) in n
6.107 * [taylor]: Taking taylor expansion of 2.0 in n
6.107 * [backup-simplify]: Simplify 2.0 into 2.0
6.107 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
6.108 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
6.109 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
6.109 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
6.109 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
6.109 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
6.109 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
6.109 * [taylor]: Taking taylor expansion of 1.0 in n
6.109 * [backup-simplify]: Simplify 1.0 into 1.0
6.109 * [taylor]: Taking taylor expansion of (log PI) in n
6.109 * [taylor]: Taking taylor expansion of PI in n
6.109 * [backup-simplify]: Simplify PI into PI
6.109 * [backup-simplify]: Simplify (log PI) into (log PI)
6.110 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
6.111 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
6.111 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
6.111 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
6.111 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
6.111 * [taylor]: Taking taylor expansion of 1.0 in n
6.111 * [backup-simplify]: Simplify 1.0 into 1.0
6.111 * [taylor]: Taking taylor expansion of (log n) in n
6.111 * [taylor]: Taking taylor expansion of n in n
6.111 * [backup-simplify]: Simplify 0 into 0
6.111 * [backup-simplify]: Simplify 1 into 1
6.111 * [backup-simplify]: Simplify (log 1) into 0
6.112 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
6.112 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
6.112 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
6.113 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
6.114 * [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)
6.115 * [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))
6.116 * [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)))
6.118 * [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)
6.118 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
6.118 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
6.118 * [taylor]: Taking taylor expansion of 2.0 in n
6.118 * [backup-simplify]: Simplify 2.0 into 2.0
6.118 * [taylor]: Taking taylor expansion of (* n PI) in n
6.118 * [taylor]: Taking taylor expansion of n in n
6.118 * [backup-simplify]: Simplify 0 into 0
6.118 * [backup-simplify]: Simplify 1 into 1
6.118 * [taylor]: Taking taylor expansion of PI in n
6.118 * [backup-simplify]: Simplify PI into PI
6.119 * [backup-simplify]: Simplify (* 0 PI) into 0
6.119 * [backup-simplify]: Simplify (* 2.0 0) into 0
6.121 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.122 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
6.123 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.125 * [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))
6.126 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
6.129 * [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))
6.132 * [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)))
6.136 * [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))))))
6.142 * [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))))))))
6.148 * [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))))))))
6.154 * [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))))))))
6.156 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0
6.157 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0
6.158 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0
6.159 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
6.160 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
6.160 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0
6.161 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0
6.162 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0
6.163 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
6.164 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0
6.166 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
6.168 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0
6.172 * [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
6.174 * [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
6.175 * [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
6.177 * [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
6.177 * [backup-simplify]: Simplify (- 0) into 0
6.177 * [backup-simplify]: Simplify 0 into 0
6.177 * [backup-simplify]: Simplify 0 into 0
6.177 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
6.178 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
6.180 * [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
6.180 * [backup-simplify]: Simplify (- 0) into 0
6.180 * [backup-simplify]: Simplify (+ 0 0) into 0
6.182 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0
6.183 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0
6.185 * [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)))
6.186 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.190 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.195 * [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))))))))
6.206 * [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))))))))
6.207 * [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
6.207 * [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
6.207 * [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
6.207 * [taylor]: Taking taylor expansion of +nan.0 in n
6.207 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.207 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n
6.207 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n
6.207 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n
6.207 * [taylor]: Taking taylor expansion of 0.5 in n
6.207 * [backup-simplify]: Simplify 0.5 into 0.5
6.207 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n
6.207 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n
6.207 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
6.207 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
6.207 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
6.207 * [taylor]: Taking taylor expansion of 1.0 in n
6.207 * [backup-simplify]: Simplify 1.0 into 1.0
6.207 * [taylor]: Taking taylor expansion of (log 2.0) in n
6.207 * [taylor]: Taking taylor expansion of 2.0 in n
6.207 * [backup-simplify]: Simplify 2.0 into 2.0
6.208 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
6.208 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
6.210 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
6.210 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n
6.210 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
6.210 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
6.210 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
6.210 * [taylor]: Taking taylor expansion of 1.0 in n
6.210 * [backup-simplify]: Simplify 1.0 into 1.0
6.210 * [taylor]: Taking taylor expansion of (log n) in n
6.210 * [taylor]: Taking taylor expansion of n in n
6.210 * [backup-simplify]: Simplify 0 into 0
6.210 * [backup-simplify]: Simplify 1 into 1
6.210 * [backup-simplify]: Simplify (log 1) into 0
6.211 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
6.211 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
6.211 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
6.211 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
6.211 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
6.211 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
6.211 * [taylor]: Taking taylor expansion of 1.0 in n
6.211 * [backup-simplify]: Simplify 1.0 into 1.0
6.211 * [taylor]: Taking taylor expansion of (log PI) in n
6.211 * [taylor]: Taking taylor expansion of PI in n
6.211 * [backup-simplify]: Simplify PI into PI
6.211 * [backup-simplify]: Simplify (log PI) into (log PI)
6.212 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
6.214 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
6.215 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
6.216 * [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)
6.217 * [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))
6.219 * [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)))
6.220 * [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)
6.220 * [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
6.220 * [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
6.220 * [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
6.220 * [taylor]: Taking taylor expansion of +nan.0 in n
6.220 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.220 * [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
6.220 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
6.220 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
6.221 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
6.221 * [taylor]: Taking taylor expansion of 0.5 in n
6.221 * [backup-simplify]: Simplify 0.5 into 0.5
6.221 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
6.221 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
6.221 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
6.221 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
6.221 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
6.221 * [taylor]: Taking taylor expansion of 1.0 in n
6.221 * [backup-simplify]: Simplify 1.0 into 1.0
6.221 * [taylor]: Taking taylor expansion of (log 2.0) in n
6.221 * [taylor]: Taking taylor expansion of 2.0 in n
6.221 * [backup-simplify]: Simplify 2.0 into 2.0
6.221 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
6.223 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
6.224 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
6.224 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
6.224 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
6.224 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
6.225 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
6.225 * [taylor]: Taking taylor expansion of 1.0 in n
6.225 * [backup-simplify]: Simplify 1.0 into 1.0
6.225 * [taylor]: Taking taylor expansion of (log PI) in n
6.225 * [taylor]: Taking taylor expansion of PI in n
6.225 * [backup-simplify]: Simplify PI into PI
6.225 * [backup-simplify]: Simplify (log PI) into (log PI)
6.226 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
6.228 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
6.228 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
6.228 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
6.228 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
6.228 * [taylor]: Taking taylor expansion of 1.0 in n
6.228 * [backup-simplify]: Simplify 1.0 into 1.0
6.228 * [taylor]: Taking taylor expansion of (log n) in n
6.228 * [taylor]: Taking taylor expansion of n in n
6.228 * [backup-simplify]: Simplify 0 into 0
6.228 * [backup-simplify]: Simplify 1 into 1
6.228 * [backup-simplify]: Simplify (log 1) into 0
6.229 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
6.229 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
6.229 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
6.229 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
6.231 * [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)
6.232 * [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))
6.233 * [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)))
6.235 * [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)
6.235 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
6.235 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
6.235 * [taylor]: Taking taylor expansion of 2.0 in n
6.235 * [backup-simplify]: Simplify 2.0 into 2.0
6.235 * [taylor]: Taking taylor expansion of (* n PI) in n
6.235 * [taylor]: Taking taylor expansion of n in n
6.235 * [backup-simplify]: Simplify 0 into 0
6.235 * [backup-simplify]: Simplify 1 into 1
6.235 * [taylor]: Taking taylor expansion of PI in n
6.235 * [backup-simplify]: Simplify PI into PI
6.236 * [backup-simplify]: Simplify (* 0 PI) into 0
6.236 * [backup-simplify]: Simplify (* 2.0 0) into 0
6.238 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.239 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
6.240 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.240 * [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
6.240 * [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
6.240 * [taylor]: Taking taylor expansion of +nan.0 in n
6.240 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.240 * [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
6.240 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
6.240 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
6.240 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
6.240 * [taylor]: Taking taylor expansion of 0.5 in n
6.241 * [backup-simplify]: Simplify 0.5 into 0.5
6.241 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
6.241 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
6.241 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
6.241 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
6.241 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
6.241 * [taylor]: Taking taylor expansion of 1.0 in n
6.241 * [backup-simplify]: Simplify 1.0 into 1.0
6.241 * [taylor]: Taking taylor expansion of (log 2.0) in n
6.241 * [taylor]: Taking taylor expansion of 2.0 in n
6.241 * [backup-simplify]: Simplify 2.0 into 2.0
6.242 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
6.244 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
6.246 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
6.246 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
6.246 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
6.246 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
6.246 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
6.246 * [taylor]: Taking taylor expansion of 1.0 in n
6.246 * [backup-simplify]: Simplify 1.0 into 1.0
6.246 * [taylor]: Taking taylor expansion of (log PI) in n
6.246 * [taylor]: Taking taylor expansion of PI in n
6.246 * [backup-simplify]: Simplify PI into PI
6.247 * [backup-simplify]: Simplify (log PI) into (log PI)
6.248 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
6.250 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
6.250 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
6.250 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
6.250 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
6.250 * [taylor]: Taking taylor expansion of 1.0 in n
6.250 * [backup-simplify]: Simplify 1.0 into 1.0
6.250 * [taylor]: Taking taylor expansion of (log n) in n
6.250 * [taylor]: Taking taylor expansion of n in n
6.250 * [backup-simplify]: Simplify 0 into 0
6.250 * [backup-simplify]: Simplify 1 into 1
6.250 * [backup-simplify]: Simplify (log 1) into 0
6.251 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
6.251 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
6.251 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
6.252 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
6.258 * [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)
6.259 * [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))
6.261 * [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)))
6.262 * [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)
6.262 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n
6.262 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
6.262 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
6.262 * [taylor]: Taking taylor expansion of 2.0 in n
6.262 * [backup-simplify]: Simplify 2.0 into 2.0
6.262 * [taylor]: Taking taylor expansion of (* n PI) in n
6.262 * [taylor]: Taking taylor expansion of n in n
6.262 * [backup-simplify]: Simplify 0 into 0
6.262 * [backup-simplify]: Simplify 1 into 1
6.263 * [taylor]: Taking taylor expansion of PI in n
6.263 * [backup-simplify]: Simplify PI into PI
6.263 * [backup-simplify]: Simplify (* 0 PI) into 0
6.263 * [backup-simplify]: Simplify (* 2.0 0) into 0
6.265 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.267 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
6.268 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.269 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
6.271 * [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))
6.272 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
6.274 * [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))
6.277 * [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)))
6.278 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
6.280 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
6.282 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2)
6.286 * [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))
6.288 * [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)))
6.291 * [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))))))))
6.302 * [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))))))))))))
6.317 * [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))))))))))))
6.331 * [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))))))))))))))
6.346 * [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))))))))))))))
6.362 * [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))))))))))))))
6.386 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (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))))))))))))))))))))))
6.387 * [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))))))
6.387 * [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
6.388 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n
6.388 * [taylor]: Taking taylor expansion of 1.0 in n
6.388 * [backup-simplify]: Simplify 1.0 into 1.0
6.388 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
6.388 * [taylor]: Taking taylor expansion of (sqrt k) in n
6.388 * [taylor]: Taking taylor expansion of k in n
6.388 * [backup-simplify]: Simplify k into k
6.388 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
6.388 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
6.388 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
6.388 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
6.388 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
6.388 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
6.388 * [taylor]: Taking taylor expansion of 0.5 in n
6.388 * [backup-simplify]: Simplify 0.5 into 0.5
6.388 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
6.388 * [taylor]: Taking taylor expansion of 1.0 in n
6.388 * [backup-simplify]: Simplify 1.0 into 1.0
6.388 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.388 * [taylor]: Taking taylor expansion of k in n
6.388 * [backup-simplify]: Simplify k into k
6.388 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.388 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
6.388 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
6.388 * [taylor]: Taking taylor expansion of 2.0 in n
6.388 * [backup-simplify]: Simplify 2.0 into 2.0
6.388 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.388 * [taylor]: Taking taylor expansion of PI in n
6.389 * [backup-simplify]: Simplify PI into PI
6.389 * [taylor]: Taking taylor expansion of n in n
6.389 * [backup-simplify]: Simplify 0 into 0
6.389 * [backup-simplify]: Simplify 1 into 1
6.389 * [backup-simplify]: Simplify (/ PI 1) into PI
6.390 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
6.391 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.391 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.391 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
6.391 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
6.392 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
6.394 * [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))))
6.395 * [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)))))
6.395 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
6.395 * [taylor]: Taking taylor expansion of 1.0 in k
6.395 * [backup-simplify]: Simplify 1.0 into 1.0
6.395 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
6.395 * [taylor]: Taking taylor expansion of (sqrt k) in k
6.395 * [taylor]: Taking taylor expansion of k in k
6.395 * [backup-simplify]: Simplify 0 into 0
6.395 * [backup-simplify]: Simplify 1 into 1
6.400 * [backup-simplify]: Simplify (sqrt 0) into 0
6.402 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.402 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
6.402 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
6.402 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
6.402 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
6.402 * [taylor]: Taking taylor expansion of 0.5 in k
6.402 * [backup-simplify]: Simplify 0.5 into 0.5
6.402 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
6.402 * [taylor]: Taking taylor expansion of 1.0 in k
6.402 * [backup-simplify]: Simplify 1.0 into 1.0
6.402 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.402 * [taylor]: Taking taylor expansion of k in k
6.402 * [backup-simplify]: Simplify 0 into 0
6.402 * [backup-simplify]: Simplify 1 into 1
6.402 * [backup-simplify]: Simplify (/ 1 1) into 1
6.402 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
6.402 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
6.402 * [taylor]: Taking taylor expansion of 2.0 in k
6.402 * [backup-simplify]: Simplify 2.0 into 2.0
6.402 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.403 * [taylor]: Taking taylor expansion of PI in k
6.403 * [backup-simplify]: Simplify PI into PI
6.403 * [taylor]: Taking taylor expansion of n in k
6.403 * [backup-simplify]: Simplify n into n
6.403 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.403 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
6.403 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
6.403 * [backup-simplify]: Simplify (- 1) into -1
6.404 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.404 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
6.404 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
6.404 * [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)))))
6.405 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
6.405 * [taylor]: Taking taylor expansion of 1.0 in k
6.405 * [backup-simplify]: Simplify 1.0 into 1.0
6.405 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
6.405 * [taylor]: Taking taylor expansion of (sqrt k) in k
6.405 * [taylor]: Taking taylor expansion of k in k
6.405 * [backup-simplify]: Simplify 0 into 0
6.405 * [backup-simplify]: Simplify 1 into 1
6.406 * [backup-simplify]: Simplify (sqrt 0) into 0
6.407 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.407 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
6.407 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
6.408 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
6.408 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
6.408 * [taylor]: Taking taylor expansion of 0.5 in k
6.408 * [backup-simplify]: Simplify 0.5 into 0.5
6.408 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
6.408 * [taylor]: Taking taylor expansion of 1.0 in k
6.408 * [backup-simplify]: Simplify 1.0 into 1.0
6.408 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.408 * [taylor]: Taking taylor expansion of k in k
6.408 * [backup-simplify]: Simplify 0 into 0
6.408 * [backup-simplify]: Simplify 1 into 1
6.408 * [backup-simplify]: Simplify (/ 1 1) into 1
6.408 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
6.408 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
6.408 * [taylor]: Taking taylor expansion of 2.0 in k
6.409 * [backup-simplify]: Simplify 2.0 into 2.0
6.409 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.409 * [taylor]: Taking taylor expansion of PI in k
6.409 * [backup-simplify]: Simplify PI into PI
6.409 * [taylor]: Taking taylor expansion of n in k
6.409 * [backup-simplify]: Simplify n into n
6.409 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.409 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
6.409 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
6.409 * [backup-simplify]: Simplify (- 1) into -1
6.410 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.410 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
6.411 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
6.411 * [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)))))
6.411 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0
6.412 * [backup-simplify]: Simplify (* 1.0 0) into 0
6.412 * [taylor]: Taking taylor expansion of 0 in n
6.412 * [backup-simplify]: Simplify 0 into 0
6.412 * [backup-simplify]: Simplify 0 into 0
6.413 * [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)))))))
6.414 * [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)))))))
6.414 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
6.414 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
6.414 * [taylor]: Taking taylor expansion of +nan.0 in n
6.414 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.414 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
6.414 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
6.414 * [taylor]: Taking taylor expansion of 0.5 in n
6.414 * [backup-simplify]: Simplify 0.5 into 0.5
6.414 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
6.414 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
6.414 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
6.415 * [taylor]: Taking taylor expansion of 2.0 in n
6.415 * [backup-simplify]: Simplify 2.0 into 2.0
6.415 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.415 * [taylor]: Taking taylor expansion of PI in n
6.415 * [backup-simplify]: Simplify PI into PI
6.415 * [taylor]: Taking taylor expansion of n in n
6.415 * [backup-simplify]: Simplify 0 into 0
6.415 * [backup-simplify]: Simplify 1 into 1
6.416 * [backup-simplify]: Simplify (/ PI 1) into PI
6.416 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
6.417 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.417 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
6.417 * [taylor]: Taking taylor expansion of 1.0 in n
6.417 * [backup-simplify]: Simplify 1.0 into 1.0
6.417 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.417 * [taylor]: Taking taylor expansion of k in n
6.417 * [backup-simplify]: Simplify k into k
6.417 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.418 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
6.418 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.418 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
6.419 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
6.420 * [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))))
6.422 * [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)))))
6.423 * [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))))))
6.424 * [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)))))))
6.426 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
6.426 * [backup-simplify]: Simplify 0 into 0
6.429 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.431 * [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)))))))
6.433 * [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)))))))
6.433 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
6.433 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
6.433 * [taylor]: Taking taylor expansion of +nan.0 in n
6.433 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.433 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
6.433 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
6.433 * [taylor]: Taking taylor expansion of 0.5 in n
6.433 * [backup-simplify]: Simplify 0.5 into 0.5
6.433 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
6.433 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
6.433 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
6.433 * [taylor]: Taking taylor expansion of 2.0 in n
6.433 * [backup-simplify]: Simplify 2.0 into 2.0
6.433 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.433 * [taylor]: Taking taylor expansion of PI in n
6.433 * [backup-simplify]: Simplify PI into PI
6.433 * [taylor]: Taking taylor expansion of n in n
6.433 * [backup-simplify]: Simplify 0 into 0
6.433 * [backup-simplify]: Simplify 1 into 1
6.434 * [backup-simplify]: Simplify (/ PI 1) into PI
6.434 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
6.435 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.435 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
6.435 * [taylor]: Taking taylor expansion of 1.0 in n
6.435 * [backup-simplify]: Simplify 1.0 into 1.0
6.436 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.436 * [taylor]: Taking taylor expansion of k in n
6.436 * [backup-simplify]: Simplify k into k
6.436 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.437 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
6.437 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.437 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
6.438 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
6.440 * [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))))
6.441 * [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)))))
6.441 * [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))))))
6.442 * [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)))))))
6.443 * [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)))))))
6.445 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
6.445 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) 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 1) (+ (* PI (/ 0 1)))) into 0
6.447 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
6.449 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
6.451 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0
6.452 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0
6.454 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
6.456 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0
6.456 * [backup-simplify]: Simplify (- 0) into 0
6.456 * [backup-simplify]: Simplify 0 into 0
6.457 * [backup-simplify]: Simplify 0 into 0
6.460 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.461 * [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)))))))
6.463 * [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)))))))
6.463 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
6.463 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
6.463 * [taylor]: Taking taylor expansion of +nan.0 in n
6.463 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.463 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
6.463 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
6.463 * [taylor]: Taking taylor expansion of 0.5 in n
6.463 * [backup-simplify]: Simplify 0.5 into 0.5
6.463 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
6.463 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
6.463 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
6.463 * [taylor]: Taking taylor expansion of 2.0 in n
6.463 * [backup-simplify]: Simplify 2.0 into 2.0
6.463 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.463 * [taylor]: Taking taylor expansion of PI in n
6.463 * [backup-simplify]: Simplify PI into PI
6.464 * [taylor]: Taking taylor expansion of n in n
6.464 * [backup-simplify]: Simplify 0 into 0
6.464 * [backup-simplify]: Simplify 1 into 1
6.464 * [backup-simplify]: Simplify (/ PI 1) into PI
6.465 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
6.466 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.466 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
6.466 * [taylor]: Taking taylor expansion of 1.0 in n
6.466 * [backup-simplify]: Simplify 1.0 into 1.0
6.466 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.467 * [taylor]: Taking taylor expansion of k in n
6.467 * [backup-simplify]: Simplify k into k
6.467 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.468 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
6.468 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.468 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
6.469 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
6.471 * [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))))
6.472 * [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)))))
6.473 * [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))))))
6.475 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
6.477 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
6.483 * [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))))))))
6.485 * [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))))
6.485 * [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
6.485 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
6.485 * [taylor]: Taking taylor expansion of 1.0 in n
6.485 * [backup-simplify]: Simplify 1.0 into 1.0
6.485 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
6.485 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
6.485 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
6.485 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
6.485 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
6.485 * [taylor]: Taking taylor expansion of 0.5 in n
6.485 * [backup-simplify]: Simplify 0.5 into 0.5
6.485 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
6.485 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.485 * [taylor]: Taking taylor expansion of k in n
6.485 * [backup-simplify]: Simplify k into k
6.485 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.485 * [taylor]: Taking taylor expansion of 1.0 in n
6.485 * [backup-simplify]: Simplify 1.0 into 1.0
6.485 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
6.485 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
6.485 * [taylor]: Taking taylor expansion of -2.0 in n
6.485 * [backup-simplify]: Simplify -2.0 into -2.0
6.485 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.485 * [taylor]: Taking taylor expansion of PI in n
6.485 * [backup-simplify]: Simplify PI into PI
6.485 * [taylor]: Taking taylor expansion of n in n
6.486 * [backup-simplify]: Simplify 0 into 0
6.486 * [backup-simplify]: Simplify 1 into 1
6.486 * [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) 1.0) into (+ (/ 1 k) 1.0)
6.488 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
6.489 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.490 * [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))))
6.492 * [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)))))
6.492 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
6.492 * [taylor]: Taking taylor expansion of (/ -1 k) in n
6.492 * [taylor]: Taking taylor expansion of -1 in n
6.492 * [backup-simplify]: Simplify -1 into -1
6.492 * [taylor]: Taking taylor expansion of k in n
6.492 * [backup-simplify]: Simplify k into k
6.492 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
6.492 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
6.492 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
6.492 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
6.493 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))
6.493 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
6.493 * [taylor]: Taking taylor expansion of 1.0 in k
6.494 * [backup-simplify]: Simplify 1.0 into 1.0
6.494 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
6.494 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
6.494 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
6.494 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
6.494 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
6.494 * [taylor]: Taking taylor expansion of 0.5 in k
6.494 * [backup-simplify]: Simplify 0.5 into 0.5
6.494 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
6.494 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.494 * [taylor]: Taking taylor expansion of k in k
6.494 * [backup-simplify]: Simplify 0 into 0
6.494 * [backup-simplify]: Simplify 1 into 1
6.494 * [backup-simplify]: Simplify (/ 1 1) into 1
6.494 * [taylor]: Taking taylor expansion of 1.0 in k
6.494 * [backup-simplify]: Simplify 1.0 into 1.0
6.494 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
6.494 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
6.494 * [taylor]: Taking taylor expansion of -2.0 in k
6.494 * [backup-simplify]: Simplify -2.0 into -2.0
6.494 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.494 * [taylor]: Taking taylor expansion of PI in k
6.494 * [backup-simplify]: Simplify PI into PI
6.495 * [taylor]: Taking taylor expansion of n in k
6.495 * [backup-simplify]: Simplify n into n
6.495 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.495 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
6.495 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
6.495 * [backup-simplify]: Simplify (+ 1 0) into 1
6.496 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
6.496 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
6.496 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
6.496 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
6.496 * [taylor]: Taking taylor expansion of (/ -1 k) in k
6.496 * [taylor]: Taking taylor expansion of -1 in k
6.496 * [backup-simplify]: Simplify -1 into -1
6.496 * [taylor]: Taking taylor expansion of k in k
6.496 * [backup-simplify]: Simplify 0 into 0
6.496 * [backup-simplify]: Simplify 1 into 1
6.497 * [backup-simplify]: Simplify (/ -1 1) into -1
6.497 * [backup-simplify]: Simplify (sqrt 0) into 0
6.498 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
6.499 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))
6.499 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
6.499 * [taylor]: Taking taylor expansion of 1.0 in k
6.499 * [backup-simplify]: Simplify 1.0 into 1.0
6.499 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
6.499 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
6.499 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
6.499 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
6.499 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
6.499 * [taylor]: Taking taylor expansion of 0.5 in k
6.499 * [backup-simplify]: Simplify 0.5 into 0.5
6.499 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
6.499 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.499 * [taylor]: Taking taylor expansion of k in k
6.499 * [backup-simplify]: Simplify 0 into 0
6.499 * [backup-simplify]: Simplify 1 into 1
6.499 * [backup-simplify]: Simplify (/ 1 1) into 1
6.499 * [taylor]: Taking taylor expansion of 1.0 in k
6.499 * [backup-simplify]: Simplify 1.0 into 1.0
6.499 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
6.500 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
6.500 * [taylor]: Taking taylor expansion of -2.0 in k
6.500 * [backup-simplify]: Simplify -2.0 into -2.0
6.500 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.500 * [taylor]: Taking taylor expansion of PI in k
6.500 * [backup-simplify]: Simplify PI into PI
6.500 * [taylor]: Taking taylor expansion of n in k
6.500 * [backup-simplify]: Simplify n into n
6.500 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.500 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
6.500 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
6.500 * [backup-simplify]: Simplify (+ 1 0) into 1
6.501 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
6.501 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
6.501 * [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))))))
6.501 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
6.501 * [taylor]: Taking taylor expansion of (/ -1 k) in k
6.501 * [taylor]: Taking taylor expansion of -1 in k
6.501 * [backup-simplify]: Simplify -1 into -1
6.501 * [taylor]: Taking taylor expansion of k in k
6.501 * [backup-simplify]: Simplify 0 into 0
6.501 * [backup-simplify]: Simplify 1 into 1
6.502 * [backup-simplify]: Simplify (/ -1 1) into -1
6.502 * [backup-simplify]: Simplify (sqrt 0) into 0
6.503 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
6.504 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))
6.504 * [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)))))))
6.504 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
6.504 * [taylor]: Taking taylor expansion of +nan.0 in n
6.504 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.504 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
6.504 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
6.504 * [taylor]: Taking taylor expansion of 0.5 in n
6.504 * [backup-simplify]: Simplify 0.5 into 0.5
6.504 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
6.504 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
6.504 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.504 * [taylor]: Taking taylor expansion of k in n
6.504 * [backup-simplify]: Simplify k into k
6.504 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.504 * [taylor]: Taking taylor expansion of 1.0 in n
6.504 * [backup-simplify]: Simplify 1.0 into 1.0
6.504 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
6.505 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
6.505 * [taylor]: Taking taylor expansion of -2.0 in n
6.505 * [backup-simplify]: Simplify -2.0 into -2.0
6.505 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.505 * [taylor]: Taking taylor expansion of PI in n
6.505 * [backup-simplify]: Simplify PI into PI
6.505 * [taylor]: Taking taylor expansion of n in n
6.505 * [backup-simplify]: Simplify 0 into 0
6.505 * [backup-simplify]: Simplify 1 into 1
6.505 * [backup-simplify]: Simplify (/ PI 1) into PI
6.506 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
6.507 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
6.507 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
6.508 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.509 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
6.510 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
6.511 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
6.513 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
6.514 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
6.515 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
6.518 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.519 * [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))))))))
6.519 * [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))))))))
6.519 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
6.519 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
6.519 * [taylor]: Taking taylor expansion of +nan.0 in n
6.519 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.519 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
6.519 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
6.519 * [taylor]: Taking taylor expansion of 0.5 in n
6.520 * [backup-simplify]: Simplify 0.5 into 0.5
6.520 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
6.520 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
6.520 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.520 * [taylor]: Taking taylor expansion of k in n
6.520 * [backup-simplify]: Simplify k into k
6.520 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.520 * [taylor]: Taking taylor expansion of 1.0 in n
6.520 * [backup-simplify]: Simplify 1.0 into 1.0
6.520 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
6.520 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
6.520 * [taylor]: Taking taylor expansion of -2.0 in n
6.520 * [backup-simplify]: Simplify -2.0 into -2.0
6.520 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.520 * [taylor]: Taking taylor expansion of PI in n
6.520 * [backup-simplify]: Simplify PI into PI
6.520 * [taylor]: Taking taylor expansion of n in n
6.520 * [backup-simplify]: Simplify 0 into 0
6.520 * [backup-simplify]: Simplify 1 into 1
6.521 * [backup-simplify]: Simplify (/ PI 1) into PI
6.521 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
6.522 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
6.522 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
6.523 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.524 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
6.525 * [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))))
6.526 * [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)))))
6.527 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
6.527 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
6.528 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
6.529 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.529 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
6.530 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
6.530 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.531 * [backup-simplify]: Simplify (+ 0 0) into 0
6.531 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.533 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
6.534 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0
6.535 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
6.536 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0
6.536 * [backup-simplify]: Simplify 0 into 0
6.537 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.539 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.541 * [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))))))))
6.542 * [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))))))))
6.542 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
6.542 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
6.542 * [taylor]: Taking taylor expansion of +nan.0 in n
6.542 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.542 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
6.542 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
6.542 * [taylor]: Taking taylor expansion of 0.5 in n
6.542 * [backup-simplify]: Simplify 0.5 into 0.5
6.542 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
6.542 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
6.542 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.542 * [taylor]: Taking taylor expansion of k in n
6.542 * [backup-simplify]: Simplify k into k
6.542 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.542 * [taylor]: Taking taylor expansion of 1.0 in n
6.542 * [backup-simplify]: Simplify 1.0 into 1.0
6.542 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
6.542 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
6.542 * [taylor]: Taking taylor expansion of -2.0 in n
6.543 * [backup-simplify]: Simplify -2.0 into -2.0
6.543 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.543 * [taylor]: Taking taylor expansion of PI in n
6.543 * [backup-simplify]: Simplify PI into PI
6.543 * [taylor]: Taking taylor expansion of n in n
6.543 * [backup-simplify]: Simplify 0 into 0
6.543 * [backup-simplify]: Simplify 1 into 1
6.543 * [backup-simplify]: Simplify (/ PI 1) into PI
6.544 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
6.548 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
6.549 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
6.550 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.551 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
6.552 * [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))))
6.553 * [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)))))
6.554 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
6.556 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
6.557 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
6.561 * [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))))))))))))
6.562 * * * [progress]: simplifying candidates
6.566 * [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) 2.0)))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
  (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
  (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0)))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
  (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))))))
6.576 * * [simplify]: iteration 0: 369 enodes
6.803 * * [simplify]: iteration 1: 1028 enodes
7.686 * * [simplify]: iteration 2: 3472 enodes
10.036 * * [simplify]: iteration complete: 5001 enodes
10.036 * * [simplify]: Extracting #0: cost 125 inf + 0
10.039 * * [simplify]: Extracting #1: cost 638 inf + 43
10.047 * * [simplify]: Extracting #2: cost 1159 inf + 2395
10.067 * * [simplify]: Extracting #3: cost 1111 inf + 44265
10.121 * * [simplify]: Extracting #4: cost 745 inf + 188861
10.245 * * [simplify]: Extracting #5: cost 365 inf + 413031
10.408 * * [simplify]: Extracting #6: cost 115 inf + 617063
10.647 * * [simplify]: Extracting #7: cost 10 inf + 711172
10.943 * * [simplify]: Extracting #8: cost 0 inf + 719728
11.231 * * [simplify]: Extracting #9: cost 0 inf + 719393
11.509 * [simplify]: Simplified to:
  (expm1 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (pow (* 2.0 (* n PI)) (/ 1.0 2.0))
  (pow (* 2.0 (* n PI)) (/ k 2.0))
  (pow (* 2.0 (* n PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* 2.0 (* n PI)) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* 2.0 (* n PI)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0))))
  (pow (* 2.0 (* n PI)) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* 2.0 (* n PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* 2.0 (* n PI)) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* 2.0 (* n PI)) (sqrt (- 1.0 k)))
  (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0)))
  (* 2.0 (* n PI))
  (pow (* 2.0 (* n PI)) (/ (/ (+ (sqrt k) (sqrt 1.0)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* 2.0 (* n PI)) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0)))
  (pow (* 2.0 (* n PI)) (+ (sqrt k) (sqrt 1.0)))
  (pow (* 2.0 (* n PI)) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0)))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (pow (* 2.0 (* n PI)) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (exp (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (pow (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) 1/2))
  (pow (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) 1/2))
  (expm1 (* 2.0 (* n PI)))
  (log1p (* 2.0 (* n PI)))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (log (* 2.0 (* n PI)))
  (log (* 2.0 (* n PI)))
  (log (* 2.0 (* n PI)))
  (exp (* 2.0 (* n PI)))
  (* (* (* 2.0 PI) (* (* n (* 2.0 PI)) (* n (* 2.0 PI)))) n)
  (* (* (* 2.0 PI) (* (* n (* 2.0 PI)) (* n (* 2.0 PI)))) n)
  (* (cbrt (* 2.0 (* n PI))) (cbrt (* 2.0 (* n PI))))
  (cbrt (* 2.0 (* n PI)))
  (* (* (* 2.0 PI) (* (* n (* 2.0 PI)) (* n (* 2.0 PI)))) n)
  (sqrt (* 2.0 (* n PI)))
  (sqrt (* 2.0 (* n PI)))
  (* 2.0 (* (* PI (cbrt n)) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* 2.0 PI)
  (* n PI)
  (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)))
  (/ (* 1.0 (/ (* 1.0 1.0) k)) (sqrt k))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (/ (* 1.0 (/ (* 1.0 1.0) k)) (sqrt k))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (- 1.0)
  (- (sqrt k))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (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) (/ (sqrt (sqrt k)) (cbrt 1.0)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt 1.0)))
  (/ (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 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (log1p (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* 2.0 (* n PI))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (exp (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (* (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (/ (sqrt k) (/ 1.0 k))))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (* (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (/ (sqrt k) (/ 1.0 k))))
  (* (cbrt (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (cbrt (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (* (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (/ (sqrt k) (/ 1.0 k))))
  (sqrt (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (* (pow (* 2.0 (* n PI)) (/ 1.0 2.0)) 1.0)
  (* (sqrt k) (pow (* 2.0 (* n PI)) (/ k 2.0)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (pow (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) 1/2)) (sqrt (/ 1.0 (sqrt k))))
  (* (pow (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) 1/2)) (sqrt (/ 1.0 (sqrt k))))
  (/ (* (sqrt 1.0) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) 1/2))) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) 1/2))) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) 1/2))) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) 1/2))) (sqrt (sqrt k)))
  (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))
  (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt k) (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (sqrt k))
  (* (pow (* 2.0 (* n PI)) (* (/ (- 1.0 k) 2.0) 1/2)) (/ 1.0 (sqrt k)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (cbrt (/ 1.0 (sqrt k))))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (/ 1.0 (sqrt k))))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt (cbrt k))))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt k)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt k)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (cbrt (sqrt k))))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt (cbrt k)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (* (sqrt 1.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (cbrt (sqrt k))))
  (/ (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt (cbrt k)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (sqrt k))))
  (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt (sqrt k))))
  (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k))
  (/ (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (sqrt k))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (* (pow (* 2.0 (* n PI)) (/ 1.0 2.0)) (/ 1.0 (sqrt k)))
  (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (- (fma (* 0.125 (* k k)) (fma (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (log (* 2.0 PI))) (log (* 2.0 PI)) (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (log n) (log n)))) (fma 0.25 (* (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (log (* 2.0 PI))) (* (log n) (* k k))) (exp (* (log (* 2.0 (* n PI))) 0.5)))) (* (fma (* k (exp (* (log (* 2.0 (* n PI))) 0.5))) (log (* 2.0 PI)) (* (* k (exp (* (log (* 2.0 (* n PI))) 0.5))) (log n))) 0.5))
  (exp (* (* (log (* 2.0 (* n PI))) 0.5) (- 1.0 k)))
  (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* (- 1.0 k) 0.5)))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (- (fma k +nan.0 +nan.0) (* (* k k) +nan.0)))
  (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ +nan.0 (* k (* k k)))))
  (- (- (/ +nan.0 (* k k)) (- (/ +nan.0 k) +nan.0)))
  (fma (* +nan.0 (* (* k (log (* 2.0 PI))) (* k (log (* 2.0 PI))))) (- (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5)) (- (fma (* +nan.0 (* (* k k) (log (* 2.0 PI)))) (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5) (* (* (* +nan.0 (* (* k k) (log (* 2.0 PI)))) (log n)) (- (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5)))) (fma (* (* (log n) (* k k)) +nan.0) (- (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5)) (fma k (* (* (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5) (log (* 2.0 PI))) +nan.0) (fma (* +nan.0 (* (* k (log n)) (* k (log n)))) (- (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5)) (fma +nan.0 (- (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5)) (fma +nan.0 (fma (* k k) (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5) (* (- k) (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5))) (* (* +nan.0 (* k (log n))) (pow (* (* (pow PI 1.0) (pow 2.0 1.0)) (pow n 1.0)) 0.5)))))))))
  (fma (/ (exp (* (* (log (* 2.0 (* n PI))) 0.5) (- 1.0 k))) (* k (* k k))) (- +nan.0) (fma (/ (exp (* (* (log (* 2.0 (* n PI))) 0.5) (- 1.0 k))) k) +nan.0 (* (/ (- +nan.0) k) (/ (exp (* (* (log (* 2.0 (* n PI))) 0.5) (- 1.0 k))) k))))
  (fma +nan.0 (- (/ (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* (- 1.0 k) 0.5))) k)) (- (* (/ (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* (- 1.0 k) 0.5))) k) (/ +nan.0 k)) (* +nan.0 (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* (- 1.0 k) 0.5))))))
11.533 * * * [progress]: adding candidates to table
12.843 * * [progress]: iteration 2 / 4
12.844 * * * [progress]: picking best candidate
12.950 * * * * [pick]: Picked  #<alt (λ (k n) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))>
12.950 * * * [progress]: localizing error
12.992 * * * [progress]: generating rewritten candidates
12.993 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1 2)
13.036 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 2 1)
13.077 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
13.123 * * * [progress]: generating series expansions
13.123 * * * * [progress]: [ 1 / 3 ] generating series at (2 1 2)
13.124 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
13.124 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
13.124 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
13.124 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
13.124 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
13.124 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
13.124 * [taylor]: Taking taylor expansion of 0.5 in k
13.124 * [backup-simplify]: Simplify 0.5 into 0.5
13.124 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
13.124 * [taylor]: Taking taylor expansion of 1.0 in k
13.124 * [backup-simplify]: Simplify 1.0 into 1.0
13.124 * [taylor]: Taking taylor expansion of k in k
13.124 * [backup-simplify]: Simplify 0 into 0
13.124 * [backup-simplify]: Simplify 1 into 1
13.124 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
13.124 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
13.124 * [taylor]: Taking taylor expansion of 2.0 in k
13.124 * [backup-simplify]: Simplify 2.0 into 2.0
13.124 * [taylor]: Taking taylor expansion of (* n PI) in k
13.125 * [taylor]: Taking taylor expansion of n in k
13.125 * [backup-simplify]: Simplify n into n
13.125 * [taylor]: Taking taylor expansion of PI in k
13.125 * [backup-simplify]: Simplify PI into PI
13.125 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.125 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
13.125 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
13.125 * [backup-simplify]: Simplify (- 0) into 0
13.126 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
13.126 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
13.126 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
13.127 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
13.127 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
13.127 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
13.127 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
13.127 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
13.127 * [taylor]: Taking taylor expansion of 0.5 in n
13.127 * [backup-simplify]: Simplify 0.5 into 0.5
13.127 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
13.127 * [taylor]: Taking taylor expansion of 1.0 in n
13.127 * [backup-simplify]: Simplify 1.0 into 1.0
13.127 * [taylor]: Taking taylor expansion of k in n
13.127 * [backup-simplify]: Simplify k into k
13.127 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
13.127 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.127 * [taylor]: Taking taylor expansion of 2.0 in n
13.127 * [backup-simplify]: Simplify 2.0 into 2.0
13.127 * [taylor]: Taking taylor expansion of (* n PI) in n
13.127 * [taylor]: Taking taylor expansion of n in n
13.127 * [backup-simplify]: Simplify 0 into 0
13.127 * [backup-simplify]: Simplify 1 into 1
13.127 * [taylor]: Taking taylor expansion of PI in n
13.127 * [backup-simplify]: Simplify PI into PI
13.128 * [backup-simplify]: Simplify (* 0 PI) into 0
13.128 * [backup-simplify]: Simplify (* 2.0 0) into 0
13.130 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.131 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
13.132 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.132 * [backup-simplify]: Simplify (- k) into (- k)
13.132 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
13.133 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
13.134 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.135 * [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))))
13.136 * [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)))))
13.136 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
13.136 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
13.137 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
13.137 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
13.137 * [taylor]: Taking taylor expansion of 0.5 in n
13.137 * [backup-simplify]: Simplify 0.5 into 0.5
13.137 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
13.137 * [taylor]: Taking taylor expansion of 1.0 in n
13.137 * [backup-simplify]: Simplify 1.0 into 1.0
13.137 * [taylor]: Taking taylor expansion of k in n
13.137 * [backup-simplify]: Simplify k into k
13.137 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
13.137 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.137 * [taylor]: Taking taylor expansion of 2.0 in n
13.137 * [backup-simplify]: Simplify 2.0 into 2.0
13.137 * [taylor]: Taking taylor expansion of (* n PI) in n
13.137 * [taylor]: Taking taylor expansion of n in n
13.137 * [backup-simplify]: Simplify 0 into 0
13.137 * [backup-simplify]: Simplify 1 into 1
13.137 * [taylor]: Taking taylor expansion of PI in n
13.137 * [backup-simplify]: Simplify PI into PI
13.137 * [backup-simplify]: Simplify (* 0 PI) into 0
13.138 * [backup-simplify]: Simplify (* 2.0 0) into 0
13.139 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.141 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
13.142 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.142 * [backup-simplify]: Simplify (- k) into (- k)
13.142 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
13.142 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
13.143 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.145 * [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))))
13.146 * [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)))))
13.146 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
13.146 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
13.146 * [taylor]: Taking taylor expansion of 0.5 in k
13.146 * [backup-simplify]: Simplify 0.5 into 0.5
13.146 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
13.146 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
13.146 * [taylor]: Taking taylor expansion of 1.0 in k
13.146 * [backup-simplify]: Simplify 1.0 into 1.0
13.146 * [taylor]: Taking taylor expansion of k in k
13.147 * [backup-simplify]: Simplify 0 into 0
13.147 * [backup-simplify]: Simplify 1 into 1
13.147 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
13.147 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
13.147 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
13.147 * [taylor]: Taking taylor expansion of 2.0 in k
13.147 * [backup-simplify]: Simplify 2.0 into 2.0
13.147 * [taylor]: Taking taylor expansion of PI in k
13.147 * [backup-simplify]: Simplify PI into PI
13.147 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.148 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.149 * [taylor]: Taking taylor expansion of (log n) in k
13.149 * [taylor]: Taking taylor expansion of n in k
13.149 * [backup-simplify]: Simplify n into n
13.149 * [backup-simplify]: Simplify (log n) into (log n)
13.149 * [backup-simplify]: Simplify (- 0) into 0
13.149 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
13.150 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
13.151 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
13.152 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
13.153 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
13.155 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
13.156 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.157 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
13.159 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.159 * [backup-simplify]: Simplify (- 0) into 0
13.159 * [backup-simplify]: Simplify (+ 0 0) into 0
13.160 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
13.162 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.163 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
13.165 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.165 * [taylor]: Taking taylor expansion of 0 in k
13.165 * [backup-simplify]: Simplify 0 into 0
13.165 * [backup-simplify]: Simplify 0 into 0
13.165 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
13.167 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.168 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
13.168 * [backup-simplify]: Simplify (+ 0 0) into 0
13.169 * [backup-simplify]: Simplify (- 1) into -1
13.169 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.171 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
13.173 * [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))))
13.176 * [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))))))
13.179 * [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))))))
13.180 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.181 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.189 * [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
13.190 * [backup-simplify]: Simplify (- 0) into 0
13.190 * [backup-simplify]: Simplify (+ 0 0) into 0
13.191 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
13.192 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.194 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
13.196 * [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
13.196 * [taylor]: Taking taylor expansion of 0 in k
13.196 * [backup-simplify]: Simplify 0 into 0
13.196 * [backup-simplify]: Simplify 0 into 0
13.196 * [backup-simplify]: Simplify 0 into 0
13.197 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.201 * [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
13.203 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
13.203 * [backup-simplify]: Simplify (+ 0 0) into 0
13.203 * [backup-simplify]: Simplify (- 0) into 0
13.204 * [backup-simplify]: Simplify (+ 0 0) into 0
13.205 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
13.208 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.212 * [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))))))
13.218 * [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))))))
13.228 * [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))))))
13.229 * [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))))
13.229 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
13.229 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
13.229 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
13.229 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
13.229 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
13.229 * [taylor]: Taking taylor expansion of 0.5 in k
13.229 * [backup-simplify]: Simplify 0.5 into 0.5
13.229 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
13.229 * [taylor]: Taking taylor expansion of 1.0 in k
13.229 * [backup-simplify]: Simplify 1.0 into 1.0
13.229 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.229 * [taylor]: Taking taylor expansion of k in k
13.229 * [backup-simplify]: Simplify 0 into 0
13.229 * [backup-simplify]: Simplify 1 into 1
13.230 * [backup-simplify]: Simplify (/ 1 1) into 1
13.230 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
13.230 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
13.230 * [taylor]: Taking taylor expansion of 2.0 in k
13.230 * [backup-simplify]: Simplify 2.0 into 2.0
13.230 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.230 * [taylor]: Taking taylor expansion of PI in k
13.230 * [backup-simplify]: Simplify PI into PI
13.230 * [taylor]: Taking taylor expansion of n in k
13.230 * [backup-simplify]: Simplify n into n
13.230 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.230 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
13.230 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
13.230 * [backup-simplify]: Simplify (- 1) into -1
13.231 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.231 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
13.231 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
13.232 * [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)))))
13.232 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
13.232 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
13.232 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
13.232 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
13.232 * [taylor]: Taking taylor expansion of 0.5 in n
13.232 * [backup-simplify]: Simplify 0.5 into 0.5
13.232 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
13.232 * [taylor]: Taking taylor expansion of 1.0 in n
13.232 * [backup-simplify]: Simplify 1.0 into 1.0
13.232 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.232 * [taylor]: Taking taylor expansion of k in n
13.232 * [backup-simplify]: Simplify k into k
13.232 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.232 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
13.232 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.232 * [taylor]: Taking taylor expansion of 2.0 in n
13.232 * [backup-simplify]: Simplify 2.0 into 2.0
13.232 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.232 * [taylor]: Taking taylor expansion of PI in n
13.232 * [backup-simplify]: Simplify PI into PI
13.232 * [taylor]: Taking taylor expansion of n in n
13.232 * [backup-simplify]: Simplify 0 into 0
13.232 * [backup-simplify]: Simplify 1 into 1
13.233 * [backup-simplify]: Simplify (/ PI 1) into PI
13.233 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.234 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.234 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.234 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
13.235 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
13.236 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.237 * [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))))
13.238 * [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)))))
13.238 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
13.238 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
13.238 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
13.238 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
13.238 * [taylor]: Taking taylor expansion of 0.5 in n
13.238 * [backup-simplify]: Simplify 0.5 into 0.5
13.238 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
13.238 * [taylor]: Taking taylor expansion of 1.0 in n
13.239 * [backup-simplify]: Simplify 1.0 into 1.0
13.239 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.239 * [taylor]: Taking taylor expansion of k in n
13.239 * [backup-simplify]: Simplify k into k
13.239 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.239 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
13.239 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.239 * [taylor]: Taking taylor expansion of 2.0 in n
13.239 * [backup-simplify]: Simplify 2.0 into 2.0
13.239 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.239 * [taylor]: Taking taylor expansion of PI in n
13.239 * [backup-simplify]: Simplify PI into PI
13.239 * [taylor]: Taking taylor expansion of n in n
13.239 * [backup-simplify]: Simplify 0 into 0
13.239 * [backup-simplify]: Simplify 1 into 1
13.240 * [backup-simplify]: Simplify (/ PI 1) into PI
13.240 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.241 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.241 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.241 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
13.241 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
13.243 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.244 * [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))))
13.246 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
13.246 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
13.246 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
13.246 * [taylor]: Taking taylor expansion of 0.5 in k
13.246 * [backup-simplify]: Simplify 0.5 into 0.5
13.246 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
13.246 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
13.246 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
13.246 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
13.246 * [taylor]: Taking taylor expansion of 2.0 in k
13.246 * [backup-simplify]: Simplify 2.0 into 2.0
13.246 * [taylor]: Taking taylor expansion of PI in k
13.246 * [backup-simplify]: Simplify PI into PI
13.247 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.248 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.248 * [taylor]: Taking taylor expansion of (log n) in k
13.248 * [taylor]: Taking taylor expansion of n in k
13.248 * [backup-simplify]: Simplify n into n
13.248 * [backup-simplify]: Simplify (log n) into (log n)
13.248 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
13.248 * [taylor]: Taking taylor expansion of 1.0 in k
13.248 * [backup-simplify]: Simplify 1.0 into 1.0
13.248 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.248 * [taylor]: Taking taylor expansion of k in k
13.248 * [backup-simplify]: Simplify 0 into 0
13.248 * [backup-simplify]: Simplify 1 into 1
13.248 * [backup-simplify]: Simplify (/ 1 1) into 1
13.249 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.250 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
13.250 * [backup-simplify]: Simplify (- 1) into -1
13.250 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.252 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
13.253 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
13.254 * [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)))))
13.255 * [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)))))
13.256 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.257 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
13.258 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.258 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.259 * [backup-simplify]: Simplify (- 0) into 0
13.259 * [backup-simplify]: Simplify (+ 0 0) into 0
13.260 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
13.261 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.263 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
13.264 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.265 * [taylor]: Taking taylor expansion of 0 in k
13.265 * [backup-simplify]: Simplify 0 into 0
13.265 * [backup-simplify]: Simplify 0 into 0
13.265 * [backup-simplify]: Simplify 0 into 0
13.266 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.267 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.270 * [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
13.270 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.271 * [backup-simplify]: Simplify (- 0) into 0
13.271 * [backup-simplify]: Simplify (+ 0 0) into 0
13.272 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
13.273 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.274 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
13.277 * [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
13.277 * [taylor]: Taking taylor expansion of 0 in k
13.277 * [backup-simplify]: Simplify 0 into 0
13.277 * [backup-simplify]: Simplify 0 into 0
13.277 * [backup-simplify]: Simplify 0 into 0
13.277 * [backup-simplify]: Simplify 0 into 0
13.278 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.279 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.285 * [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
13.285 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.285 * [backup-simplify]: Simplify (- 0) into 0
13.286 * [backup-simplify]: Simplify (+ 0 0) into 0
13.287 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
13.288 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.290 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
13.292 * [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
13.293 * [taylor]: Taking taylor expansion of 0 in k
13.293 * [backup-simplify]: Simplify 0 into 0
13.293 * [backup-simplify]: Simplify 0 into 0
13.294 * [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))))
13.295 * [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)))
13.295 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
13.295 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
13.295 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
13.295 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
13.295 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
13.295 * [taylor]: Taking taylor expansion of 0.5 in k
13.295 * [backup-simplify]: Simplify 0.5 into 0.5
13.295 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
13.295 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.295 * [taylor]: Taking taylor expansion of k in k
13.295 * [backup-simplify]: Simplify 0 into 0
13.295 * [backup-simplify]: Simplify 1 into 1
13.295 * [backup-simplify]: Simplify (/ 1 1) into 1
13.295 * [taylor]: Taking taylor expansion of 1.0 in k
13.295 * [backup-simplify]: Simplify 1.0 into 1.0
13.295 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
13.295 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
13.295 * [taylor]: Taking taylor expansion of -2.0 in k
13.295 * [backup-simplify]: Simplify -2.0 into -2.0
13.296 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.296 * [taylor]: Taking taylor expansion of PI in k
13.296 * [backup-simplify]: Simplify PI into PI
13.296 * [taylor]: Taking taylor expansion of n in k
13.296 * [backup-simplify]: Simplify n into n
13.296 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.296 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
13.296 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
13.296 * [backup-simplify]: Simplify (+ 1 0) into 1
13.297 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
13.297 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
13.297 * [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))))))
13.297 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
13.297 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
13.297 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
13.297 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
13.297 * [taylor]: Taking taylor expansion of 0.5 in n
13.297 * [backup-simplify]: Simplify 0.5 into 0.5
13.297 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
13.297 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.297 * [taylor]: Taking taylor expansion of k in n
13.297 * [backup-simplify]: Simplify k into k
13.297 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.297 * [taylor]: Taking taylor expansion of 1.0 in n
13.298 * [backup-simplify]: Simplify 1.0 into 1.0
13.298 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
13.298 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.298 * [taylor]: Taking taylor expansion of -2.0 in n
13.298 * [backup-simplify]: Simplify -2.0 into -2.0
13.298 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.298 * [taylor]: Taking taylor expansion of PI in n
13.298 * [backup-simplify]: Simplify PI into PI
13.298 * [taylor]: Taking taylor expansion of n in n
13.298 * [backup-simplify]: Simplify 0 into 0
13.298 * [backup-simplify]: Simplify 1 into 1
13.298 * [backup-simplify]: Simplify (/ PI 1) into PI
13.299 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.301 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.301 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
13.301 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
13.302 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.303 * [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))))
13.305 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
13.305 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
13.305 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
13.305 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
13.305 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
13.305 * [taylor]: Taking taylor expansion of 0.5 in n
13.305 * [backup-simplify]: Simplify 0.5 into 0.5
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
13.305 * [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
13.307 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.307 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.308 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
13.308 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
13.309 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.310 * [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))))
13.311 * [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)))))
13.311 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
13.311 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
13.311 * [taylor]: Taking taylor expansion of 0.5 in k
13.311 * [backup-simplify]: Simplify 0.5 into 0.5
13.311 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
13.311 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
13.311 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.311 * [taylor]: Taking taylor expansion of k in k
13.311 * [backup-simplify]: Simplify 0 into 0
13.311 * [backup-simplify]: Simplify 1 into 1
13.312 * [backup-simplify]: Simplify (/ 1 1) into 1
13.312 * [taylor]: Taking taylor expansion of 1.0 in k
13.312 * [backup-simplify]: Simplify 1.0 into 1.0
13.312 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
13.312 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
13.312 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
13.312 * [taylor]: Taking taylor expansion of -2.0 in k
13.312 * [backup-simplify]: Simplify -2.0 into -2.0
13.312 * [taylor]: Taking taylor expansion of PI in k
13.312 * [backup-simplify]: Simplify PI into PI
13.312 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.313 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.313 * [taylor]: Taking taylor expansion of (log n) in k
13.313 * [taylor]: Taking taylor expansion of n in k
13.313 * [backup-simplify]: Simplify n into n
13.313 * [backup-simplify]: Simplify (log n) into (log n)
13.314 * [backup-simplify]: Simplify (+ 1 0) into 1
13.314 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.315 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
13.316 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
13.317 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
13.318 * [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)))))
13.319 * [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)))))
13.321 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.321 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
13.323 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
13.323 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.324 * [backup-simplify]: Simplify (+ 0 0) into 0
13.325 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
13.326 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.327 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
13.330 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 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
13.330 * [backup-simplify]: Simplify 0 into 0
13.330 * [backup-simplify]: Simplify 0 into 0
13.331 * [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
13.342 * [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
13.342 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.343 * [backup-simplify]: Simplify (+ 0 0) into 0
13.344 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
13.346 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.347 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
13.350 * [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
13.350 * [taylor]: Taking taylor expansion of 0 in k
13.350 * [backup-simplify]: Simplify 0 into 0
13.350 * [backup-simplify]: Simplify 0 into 0
13.350 * [backup-simplify]: Simplify 0 into 0
13.350 * [backup-simplify]: Simplify 0 into 0
13.352 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.353 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.360 * [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
13.360 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.361 * [backup-simplify]: Simplify (+ 0 0) into 0
13.362 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
13.364 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.366 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
13.370 * [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
13.370 * [taylor]: Taking taylor expansion of 0 in k
13.371 * [backup-simplify]: Simplify 0 into 0
13.371 * [backup-simplify]: Simplify 0 into 0
13.372 * [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))))))
13.372 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 2 1)
13.373 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
13.373 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
13.373 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.373 * [taylor]: Taking taylor expansion of 2.0 in n
13.373 * [backup-simplify]: Simplify 2.0 into 2.0
13.373 * [taylor]: Taking taylor expansion of (* n PI) in n
13.373 * [taylor]: Taking taylor expansion of n in n
13.373 * [backup-simplify]: Simplify 0 into 0
13.373 * [backup-simplify]: Simplify 1 into 1
13.373 * [taylor]: Taking taylor expansion of PI in n
13.373 * [backup-simplify]: Simplify PI into PI
13.373 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.373 * [taylor]: Taking taylor expansion of 2.0 in n
13.373 * [backup-simplify]: Simplify 2.0 into 2.0
13.373 * [taylor]: Taking taylor expansion of (* n PI) in n
13.373 * [taylor]: Taking taylor expansion of n in n
13.373 * [backup-simplify]: Simplify 0 into 0
13.374 * [backup-simplify]: Simplify 1 into 1
13.374 * [taylor]: Taking taylor expansion of PI in n
13.374 * [backup-simplify]: Simplify PI into PI
13.374 * [backup-simplify]: Simplify (* 0 PI) into 0
13.375 * [backup-simplify]: Simplify (* 2.0 0) into 0
13.375 * [backup-simplify]: Simplify 0 into 0
13.376 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.378 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
13.379 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.380 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.381 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
13.381 * [backup-simplify]: Simplify 0 into 0
13.382 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.383 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.383 * [backup-simplify]: Simplify 0 into 0
13.385 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.386 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
13.387 * [backup-simplify]: Simplify 0 into 0
13.388 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.390 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
13.390 * [backup-simplify]: Simplify 0 into 0
13.392 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.394 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
13.394 * [backup-simplify]: Simplify 0 into 0
13.396 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
13.398 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
13.398 * [backup-simplify]: Simplify 0 into 0
13.399 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
13.400 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
13.400 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
13.400 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.400 * [taylor]: Taking taylor expansion of 2.0 in n
13.400 * [backup-simplify]: Simplify 2.0 into 2.0
13.400 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.400 * [taylor]: Taking taylor expansion of PI in n
13.400 * [backup-simplify]: Simplify PI into PI
13.400 * [taylor]: Taking taylor expansion of n in n
13.400 * [backup-simplify]: Simplify 0 into 0
13.400 * [backup-simplify]: Simplify 1 into 1
13.400 * [backup-simplify]: Simplify (/ PI 1) into PI
13.400 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.400 * [taylor]: Taking taylor expansion of 2.0 in n
13.400 * [backup-simplify]: Simplify 2.0 into 2.0
13.400 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.401 * [taylor]: Taking taylor expansion of PI in n
13.401 * [backup-simplify]: Simplify PI into PI
13.401 * [taylor]: Taking taylor expansion of n in n
13.401 * [backup-simplify]: Simplify 0 into 0
13.401 * [backup-simplify]: Simplify 1 into 1
13.401 * [backup-simplify]: Simplify (/ PI 1) into PI
13.402 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.402 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.403 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.404 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
13.404 * [backup-simplify]: Simplify 0 into 0
13.405 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.407 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.407 * [backup-simplify]: Simplify 0 into 0
13.408 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.409 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.409 * [backup-simplify]: Simplify 0 into 0
13.410 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.412 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.412 * [backup-simplify]: Simplify 0 into 0
13.414 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.415 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.415 * [backup-simplify]: Simplify 0 into 0
13.417 * [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
13.419 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.419 * [backup-simplify]: Simplify 0 into 0
13.420 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
13.420 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
13.420 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
13.420 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.421 * [taylor]: Taking taylor expansion of -2.0 in n
13.421 * [backup-simplify]: Simplify -2.0 into -2.0
13.421 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.421 * [taylor]: Taking taylor expansion of PI in n
13.421 * [backup-simplify]: Simplify PI into PI
13.421 * [taylor]: Taking taylor expansion of n in n
13.421 * [backup-simplify]: Simplify 0 into 0
13.421 * [backup-simplify]: Simplify 1 into 1
13.421 * [backup-simplify]: Simplify (/ PI 1) into PI
13.421 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.421 * [taylor]: Taking taylor expansion of -2.0 in n
13.421 * [backup-simplify]: Simplify -2.0 into -2.0
13.421 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.421 * [taylor]: Taking taylor expansion of PI in n
13.421 * [backup-simplify]: Simplify PI into PI
13.421 * [taylor]: Taking taylor expansion of n in n
13.422 * [backup-simplify]: Simplify 0 into 0
13.422 * [backup-simplify]: Simplify 1 into 1
13.422 * [backup-simplify]: Simplify (/ PI 1) into PI
13.423 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.423 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.424 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.425 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
13.425 * [backup-simplify]: Simplify 0 into 0
13.426 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.427 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.427 * [backup-simplify]: Simplify 0 into 0
13.430 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.431 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.431 * [backup-simplify]: Simplify 0 into 0
13.432 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.434 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.434 * [backup-simplify]: Simplify 0 into 0
13.435 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.437 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.437 * [backup-simplify]: Simplify 0 into 0
13.438 * [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
13.440 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.440 * [backup-simplify]: Simplify 0 into 0
13.441 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
13.441 * * * * [progress]: [ 3 / 3 ] generating series at (2)
13.442 * [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))))
13.442 * [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
13.442 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
13.442 * [taylor]: Taking taylor expansion of 1.0 in k
13.442 * [backup-simplify]: Simplify 1.0 into 1.0
13.442 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
13.442 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
13.442 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
13.442 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
13.442 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
13.442 * [taylor]: Taking taylor expansion of 0.5 in k
13.442 * [backup-simplify]: Simplify 0.5 into 0.5
13.442 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
13.442 * [taylor]: Taking taylor expansion of 1.0 in k
13.442 * [backup-simplify]: Simplify 1.0 into 1.0
13.442 * [taylor]: Taking taylor expansion of k in k
13.442 * [backup-simplify]: Simplify 0 into 0
13.442 * [backup-simplify]: Simplify 1 into 1
13.442 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
13.443 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
13.443 * [taylor]: Taking taylor expansion of 2.0 in k
13.443 * [backup-simplify]: Simplify 2.0 into 2.0
13.443 * [taylor]: Taking taylor expansion of (* n PI) in k
13.443 * [taylor]: Taking taylor expansion of n in k
13.443 * [backup-simplify]: Simplify n into n
13.443 * [taylor]: Taking taylor expansion of PI in k
13.443 * [backup-simplify]: Simplify PI into PI
13.443 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.443 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
13.443 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
13.443 * [backup-simplify]: Simplify (- 0) into 0
13.444 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
13.444 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
13.444 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
13.445 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
13.445 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
13.445 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.445 * [taylor]: Taking taylor expansion of k in k
13.445 * [backup-simplify]: Simplify 0 into 0
13.445 * [backup-simplify]: Simplify 1 into 1
13.445 * [backup-simplify]: Simplify (/ 1 1) into 1
13.446 * [backup-simplify]: Simplify (sqrt 0) into 0
13.447 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.447 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
13.447 * [taylor]: Taking taylor expansion of 1.0 in n
13.447 * [backup-simplify]: Simplify 1.0 into 1.0
13.447 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
13.447 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
13.447 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
13.447 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
13.447 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
13.447 * [taylor]: Taking taylor expansion of 0.5 in n
13.447 * [backup-simplify]: Simplify 0.5 into 0.5
13.447 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
13.447 * [taylor]: Taking taylor expansion of 1.0 in n
13.447 * [backup-simplify]: Simplify 1.0 into 1.0
13.447 * [taylor]: Taking taylor expansion of k in n
13.447 * [backup-simplify]: Simplify k into k
13.448 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
13.448 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.448 * [taylor]: Taking taylor expansion of 2.0 in n
13.448 * [backup-simplify]: Simplify 2.0 into 2.0
13.448 * [taylor]: Taking taylor expansion of (* n PI) in n
13.448 * [taylor]: Taking taylor expansion of n in n
13.448 * [backup-simplify]: Simplify 0 into 0
13.448 * [backup-simplify]: Simplify 1 into 1
13.448 * [taylor]: Taking taylor expansion of PI in n
13.448 * [backup-simplify]: Simplify PI into PI
13.448 * [backup-simplify]: Simplify (* 0 PI) into 0
13.449 * [backup-simplify]: Simplify (* 2.0 0) into 0
13.450 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.452 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
13.453 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.453 * [backup-simplify]: Simplify (- k) into (- k)
13.453 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
13.453 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
13.455 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.456 * [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))))
13.457 * [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)))))
13.457 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
13.457 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.457 * [taylor]: Taking taylor expansion of k in n
13.457 * [backup-simplify]: Simplify k into k
13.457 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.458 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
13.458 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.458 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
13.458 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
13.458 * [taylor]: Taking taylor expansion of 1.0 in n
13.458 * [backup-simplify]: Simplify 1.0 into 1.0
13.458 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
13.458 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
13.458 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
13.458 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
13.458 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
13.458 * [taylor]: Taking taylor expansion of 0.5 in n
13.458 * [backup-simplify]: Simplify 0.5 into 0.5
13.458 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
13.458 * [taylor]: Taking taylor expansion of 1.0 in n
13.458 * [backup-simplify]: Simplify 1.0 into 1.0
13.458 * [taylor]: Taking taylor expansion of k in n
13.458 * [backup-simplify]: Simplify k into k
13.458 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
13.458 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.458 * [taylor]: Taking taylor expansion of 2.0 in n
13.458 * [backup-simplify]: Simplify 2.0 into 2.0
13.458 * [taylor]: Taking taylor expansion of (* n PI) in n
13.458 * [taylor]: Taking taylor expansion of n in n
13.458 * [backup-simplify]: Simplify 0 into 0
13.459 * [backup-simplify]: Simplify 1 into 1
13.459 * [taylor]: Taking taylor expansion of PI in n
13.459 * [backup-simplify]: Simplify PI into PI
13.459 * [backup-simplify]: Simplify (* 0 PI) into 0
13.460 * [backup-simplify]: Simplify (* 2.0 0) into 0
13.461 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.463 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
13.464 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.464 * [backup-simplify]: Simplify (- k) into (- k)
13.464 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
13.464 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
13.465 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.467 * [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))))
13.468 * [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)))))
13.468 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
13.468 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.468 * [taylor]: Taking taylor expansion of k in n
13.468 * [backup-simplify]: Simplify k into k
13.468 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.468 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
13.469 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.469 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
13.470 * [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))))))
13.472 * [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)))))))
13.472 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))) in k
13.472 * [taylor]: Taking taylor expansion of 1.0 in k
13.472 * [backup-simplify]: Simplify 1.0 into 1.0
13.472 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) in k
13.472 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
13.472 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.472 * [taylor]: Taking taylor expansion of k in k
13.472 * [backup-simplify]: Simplify 0 into 0
13.472 * [backup-simplify]: Simplify 1 into 1
13.473 * [backup-simplify]: Simplify (/ 1 1) into 1
13.473 * [backup-simplify]: Simplify (sqrt 0) into 0
13.475 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.475 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
13.475 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
13.475 * [taylor]: Taking taylor expansion of 0.5 in k
13.475 * [backup-simplify]: Simplify 0.5 into 0.5
13.475 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
13.475 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
13.475 * [taylor]: Taking taylor expansion of 1.0 in k
13.475 * [backup-simplify]: Simplify 1.0 into 1.0
13.475 * [taylor]: Taking taylor expansion of k in k
13.475 * [backup-simplify]: Simplify 0 into 0
13.475 * [backup-simplify]: Simplify 1 into 1
13.475 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
13.475 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
13.475 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
13.475 * [taylor]: Taking taylor expansion of 2.0 in k
13.475 * [backup-simplify]: Simplify 2.0 into 2.0
13.475 * [taylor]: Taking taylor expansion of PI in k
13.475 * [backup-simplify]: Simplify PI into PI
13.476 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.477 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.477 * [taylor]: Taking taylor expansion of (log n) in k
13.477 * [taylor]: Taking taylor expansion of n in k
13.477 * [backup-simplify]: Simplify n into n
13.477 * [backup-simplify]: Simplify (log n) into (log n)
13.477 * [backup-simplify]: Simplify (- 0) into 0
13.478 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
13.479 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
13.480 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
13.481 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
13.483 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
13.484 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) into 0
13.484 * [backup-simplify]: Simplify (* 1.0 0) into 0
13.484 * [backup-simplify]: Simplify 0 into 0
13.486 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.487 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
13.489 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.489 * [backup-simplify]: Simplify (- 0) into 0
13.490 * [backup-simplify]: Simplify (+ 0 0) into 0
13.490 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
13.492 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.493 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
13.495 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.497 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
13.498 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))))) into 0
13.498 * [taylor]: Taking taylor expansion of 0 in k
13.498 * [backup-simplify]: Simplify 0 into 0
13.499 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
13.501 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.502 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
13.503 * [backup-simplify]: Simplify (+ 0 0) into 0
13.503 * [backup-simplify]: Simplify (- 1) into -1
13.503 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.505 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
13.507 * [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))))
13.516 * [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))))))
13.520 * [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))))))
13.522 * [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))))))
13.523 * [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))))))
13.524 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.524 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
13.526 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.527 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.531 * [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
13.532 * [backup-simplify]: Simplify (- 0) into 0
13.532 * [backup-simplify]: Simplify (+ 0 0) into 0
13.533 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
13.535 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.537 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
13.540 * [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
13.542 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
13.544 * [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
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
13.545 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.549 * [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
13.551 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
13.551 * [backup-simplify]: Simplify (+ 0 0) into 0
13.552 * [backup-simplify]: Simplify (- 0) into 0
13.552 * [backup-simplify]: Simplify (+ 0 0) into 0
13.554 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
13.557 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.561 * [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))))))
13.562 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
13.565 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.575 * [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))))))))
13.582 * [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))))))))
13.587 * [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))))))))
13.588 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.589 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
13.591 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.593 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
13.599 * [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
13.600 * [backup-simplify]: Simplify (- 0) into 0
13.600 * [backup-simplify]: Simplify (+ 0 0) into 0
13.601 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
13.603 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.604 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.607 * [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
13.610 * [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
13.612 * [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
13.612 * [taylor]: Taking taylor expansion of 0 in k
13.612 * [backup-simplify]: Simplify 0 into 0
13.612 * [backup-simplify]: Simplify 0 into 0
13.612 * [backup-simplify]: Simplify 0 into 0
13.614 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.620 * [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
13.623 * [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
13.623 * [backup-simplify]: Simplify (+ 0 0) into 0
13.624 * [backup-simplify]: Simplify (- 0) into 0
13.624 * [backup-simplify]: Simplify (+ 0 0) into 0
13.626 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.630 * [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
13.637 * [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)))))))
13.638 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.643 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.661 * [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))))))))))))))))
13.689 * [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))))))))))))))
13.703 * [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))))))))))))))
13.725 * [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))))))))))))))))))))))))
13.726 * [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))))))
13.726 * [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
13.726 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
13.726 * [taylor]: Taking taylor expansion of 1.0 in k
13.726 * [backup-simplify]: Simplify 1.0 into 1.0
13.726 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
13.726 * [taylor]: Taking taylor expansion of (sqrt k) in k
13.726 * [taylor]: Taking taylor expansion of k in k
13.726 * [backup-simplify]: Simplify 0 into 0
13.726 * [backup-simplify]: Simplify 1 into 1
13.727 * [backup-simplify]: Simplify (sqrt 0) into 0
13.728 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.728 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
13.728 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
13.728 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
13.728 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
13.728 * [taylor]: Taking taylor expansion of 0.5 in k
13.729 * [backup-simplify]: Simplify 0.5 into 0.5
13.729 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
13.729 * [taylor]: Taking taylor expansion of 1.0 in k
13.729 * [backup-simplify]: Simplify 1.0 into 1.0
13.729 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.729 * [taylor]: Taking taylor expansion of k in k
13.729 * [backup-simplify]: Simplify 0 into 0
13.729 * [backup-simplify]: Simplify 1 into 1
13.729 * [backup-simplify]: Simplify (/ 1 1) into 1
13.729 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
13.729 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
13.729 * [taylor]: Taking taylor expansion of 2.0 in k
13.729 * [backup-simplify]: Simplify 2.0 into 2.0
13.729 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.729 * [taylor]: Taking taylor expansion of PI in k
13.729 * [backup-simplify]: Simplify PI into PI
13.729 * [taylor]: Taking taylor expansion of n in k
13.729 * [backup-simplify]: Simplify n into n
13.730 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.730 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
13.730 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
13.730 * [backup-simplify]: Simplify (- 1) into -1
13.731 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.731 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
13.731 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
13.731 * [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)))))
13.732 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n
13.732 * [taylor]: Taking taylor expansion of 1.0 in n
13.732 * [backup-simplify]: Simplify 1.0 into 1.0
13.732 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
13.732 * [taylor]: Taking taylor expansion of (sqrt k) in n
13.732 * [taylor]: Taking taylor expansion of k in n
13.732 * [backup-simplify]: Simplify k into k
13.732 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
13.732 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
13.732 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
13.732 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
13.732 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
13.732 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
13.732 * [taylor]: Taking taylor expansion of 0.5 in n
13.732 * [backup-simplify]: Simplify 0.5 into 0.5
13.732 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
13.732 * [taylor]: Taking taylor expansion of 1.0 in n
13.732 * [backup-simplify]: Simplify 1.0 into 1.0
13.732 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.732 * [taylor]: Taking taylor expansion of k in n
13.732 * [backup-simplify]: Simplify k into k
13.732 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.732 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
13.732 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.732 * [taylor]: Taking taylor expansion of 2.0 in n
13.733 * [backup-simplify]: Simplify 2.0 into 2.0
13.733 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.733 * [taylor]: Taking taylor expansion of PI in n
13.733 * [backup-simplify]: Simplify PI into PI
13.733 * [taylor]: Taking taylor expansion of n in n
13.733 * [backup-simplify]: Simplify 0 into 0
13.733 * [backup-simplify]: Simplify 1 into 1
13.733 * [backup-simplify]: Simplify (/ PI 1) into PI
13.734 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.735 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.735 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.735 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
13.735 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
13.737 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.738 * [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))))
13.740 * [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)))))
13.740 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n
13.740 * [taylor]: Taking taylor expansion of 1.0 in n
13.740 * [backup-simplify]: Simplify 1.0 into 1.0
13.740 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
13.740 * [taylor]: Taking taylor expansion of (sqrt k) in n
13.740 * [taylor]: Taking taylor expansion of k in n
13.740 * [backup-simplify]: Simplify k into k
13.740 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
13.740 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
13.740 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
13.740 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
13.740 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
13.740 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
13.740 * [taylor]: Taking taylor expansion of 0.5 in n
13.740 * [backup-simplify]: Simplify 0.5 into 0.5
13.740 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
13.740 * [taylor]: Taking taylor expansion of 1.0 in n
13.740 * [backup-simplify]: Simplify 1.0 into 1.0
13.740 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.741 * [taylor]: Taking taylor expansion of k in n
13.741 * [backup-simplify]: Simplify k into k
13.741 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.741 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
13.741 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.741 * [taylor]: Taking taylor expansion of 2.0 in n
13.741 * [backup-simplify]: Simplify 2.0 into 2.0
13.741 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.741 * [taylor]: Taking taylor expansion of PI in n
13.741 * [backup-simplify]: Simplify PI into PI
13.741 * [taylor]: Taking taylor expansion of n in n
13.741 * [backup-simplify]: Simplify 0 into 0
13.741 * [backup-simplify]: Simplify 1 into 1
13.742 * [backup-simplify]: Simplify (/ PI 1) into PI
13.742 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.743 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.744 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.744 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
13.744 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
13.745 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.747 * [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))))
13.748 * [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)))))
13.750 * [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))))))
13.752 * [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)))))))
13.752 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) in k
13.752 * [taylor]: Taking taylor expansion of 1.0 in k
13.752 * [backup-simplify]: Simplify 1.0 into 1.0
13.752 * [taylor]: Taking taylor expansion of (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) in k
13.752 * [taylor]: Taking taylor expansion of (sqrt k) in k
13.752 * [taylor]: Taking taylor expansion of k in k
13.752 * [backup-simplify]: Simplify 0 into 0
13.752 * [backup-simplify]: Simplify 1 into 1
13.752 * [backup-simplify]: Simplify (sqrt 0) into 0
13.754 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.754 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
13.754 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
13.754 * [taylor]: Taking taylor expansion of 0.5 in k
13.754 * [backup-simplify]: Simplify 0.5 into 0.5
13.754 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
13.754 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
13.754 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
13.754 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
13.754 * [taylor]: Taking taylor expansion of 2.0 in k
13.754 * [backup-simplify]: Simplify 2.0 into 2.0
13.754 * [taylor]: Taking taylor expansion of PI in k
13.754 * [backup-simplify]: Simplify PI into PI
13.755 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.756 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.756 * [taylor]: Taking taylor expansion of (log n) in k
13.756 * [taylor]: Taking taylor expansion of n in k
13.756 * [backup-simplify]: Simplify n into n
13.756 * [backup-simplify]: Simplify (log n) into (log n)
13.756 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
13.756 * [taylor]: Taking taylor expansion of 1.0 in k
13.756 * [backup-simplify]: Simplify 1.0 into 1.0
13.756 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.756 * [taylor]: Taking taylor expansion of k in k
13.756 * [backup-simplify]: Simplify 0 into 0
13.756 * [backup-simplify]: Simplify 1 into 1
13.757 * [backup-simplify]: Simplify (/ 1 1) into 1
13.757 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.758 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
13.758 * [backup-simplify]: Simplify (- 1) into -1
13.759 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.760 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
13.761 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
13.762 * [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)))))
13.764 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into 0
13.764 * [backup-simplify]: Simplify (* 1.0 0) into 0
13.764 * [backup-simplify]: Simplify 0 into 0
13.765 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.766 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
13.768 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.768 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.768 * [backup-simplify]: Simplify (- 0) into 0
13.769 * [backup-simplify]: Simplify (+ 0 0) into 0
13.769 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
13.771 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.772 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
13.774 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.776 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0
13.778 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0
13.778 * [taylor]: Taking taylor expansion of 0 in k
13.778 * [backup-simplify]: Simplify 0 into 0
13.778 * [backup-simplify]: Simplify 0 into 0
13.780 * [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)))))))
13.782 * [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)))))))
13.784 * [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)))))))
13.785 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.786 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.790 * [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
13.790 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.791 * [backup-simplify]: Simplify (- 0) into 0
13.791 * [backup-simplify]: Simplify (+ 0 0) into 0
13.792 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
13.794 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.796 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
13.798 * [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
13.799 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
13.801 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0
13.803 * [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
13.803 * [taylor]: Taking taylor expansion of 0 in k
13.803 * [backup-simplify]: Simplify 0 into 0
13.803 * [backup-simplify]: Simplify 0 into 0
13.803 * [backup-simplify]: Simplify 0 into 0
13.807 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.809 * [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)))))))
13.812 * [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)))))))
13.813 * [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)))))))
13.815 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.817 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.823 * [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
13.824 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.824 * [backup-simplify]: Simplify (- 0) into 0
13.824 * [backup-simplify]: Simplify (+ 0 0) into 0
13.831 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
13.832 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.834 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
13.837 * [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
13.838 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
13.839 * [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
13.842 * [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
13.842 * [taylor]: Taking taylor expansion of 0 in k
13.842 * [backup-simplify]: Simplify 0 into 0
13.842 * [backup-simplify]: Simplify 0 into 0
13.842 * [backup-simplify]: Simplify 0 into 0
13.842 * [backup-simplify]: Simplify 0 into 0
13.846 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.848 * [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)))))))
13.852 * [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)))))))
13.853 * [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)))))))
13.858 * [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))))))))
13.859 * [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))))
13.859 * [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
13.859 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
13.859 * [taylor]: Taking taylor expansion of 1.0 in k
13.860 * [backup-simplify]: Simplify 1.0 into 1.0
13.860 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
13.860 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
13.860 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
13.860 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
13.860 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
13.860 * [taylor]: Taking taylor expansion of 0.5 in k
13.860 * [backup-simplify]: Simplify 0.5 into 0.5
13.860 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
13.860 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.860 * [taylor]: Taking taylor expansion of k in k
13.860 * [backup-simplify]: Simplify 0 into 0
13.860 * [backup-simplify]: Simplify 1 into 1
13.861 * [backup-simplify]: Simplify (/ 1 1) into 1
13.861 * [taylor]: Taking taylor expansion of 1.0 in k
13.861 * [backup-simplify]: Simplify 1.0 into 1.0
13.861 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
13.861 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
13.861 * [taylor]: Taking taylor expansion of -2.0 in k
13.861 * [backup-simplify]: Simplify -2.0 into -2.0
13.861 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.861 * [taylor]: Taking taylor expansion of PI in k
13.861 * [backup-simplify]: Simplify PI into PI
13.861 * [taylor]: Taking taylor expansion of n in k
13.861 * [backup-simplify]: Simplify n into n
13.861 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.861 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
13.861 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
13.862 * [backup-simplify]: Simplify (+ 1 0) into 1
13.862 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
13.862 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
13.863 * [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))))))
13.863 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
13.863 * [taylor]: Taking taylor expansion of (/ -1 k) in k
13.863 * [taylor]: Taking taylor expansion of -1 in k
13.863 * [backup-simplify]: Simplify -1 into -1
13.863 * [taylor]: Taking taylor expansion of k in k
13.863 * [backup-simplify]: Simplify 0 into 0
13.863 * [backup-simplify]: Simplify 1 into 1
13.863 * [backup-simplify]: Simplify (/ -1 1) into -1
13.864 * [backup-simplify]: Simplify (sqrt 0) into 0
13.865 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
13.866 * [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)))))))
13.866 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
13.866 * [taylor]: Taking taylor expansion of 1.0 in n
13.866 * [backup-simplify]: Simplify 1.0 into 1.0
13.866 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
13.866 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
13.866 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
13.866 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
13.866 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
13.866 * [taylor]: Taking taylor expansion of 0.5 in n
13.866 * [backup-simplify]: Simplify 0.5 into 0.5
13.866 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
13.866 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.866 * [taylor]: Taking taylor expansion of k in n
13.866 * [backup-simplify]: Simplify k into k
13.866 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.866 * [taylor]: Taking taylor expansion of 1.0 in n
13.866 * [backup-simplify]: Simplify 1.0 into 1.0
13.866 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
13.866 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.866 * [taylor]: Taking taylor expansion of -2.0 in n
13.866 * [backup-simplify]: Simplify -2.0 into -2.0
13.866 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.866 * [taylor]: Taking taylor expansion of PI in n
13.866 * [backup-simplify]: Simplify PI into PI
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
13.867 * [backup-simplify]: Simplify (/ PI 1) into PI
13.867 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.868 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.869 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
13.869 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
13.870 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.872 * [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))))
13.873 * [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)))))
13.873 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
13.873 * [taylor]: Taking taylor expansion of (/ -1 k) in n
13.873 * [taylor]: Taking taylor expansion of -1 in n
13.873 * [backup-simplify]: Simplify -1 into -1
13.873 * [taylor]: Taking taylor expansion of k in n
13.873 * [backup-simplify]: Simplify k into k
13.873 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
13.873 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
13.873 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
13.874 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
13.875 * [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)))
13.875 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
13.875 * [taylor]: Taking taylor expansion of 1.0 in n
13.875 * [backup-simplify]: Simplify 1.0 into 1.0
13.875 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
13.875 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
13.875 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
13.875 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
13.875 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
13.875 * [taylor]: Taking taylor expansion of 0.5 in n
13.875 * [backup-simplify]: Simplify 0.5 into 0.5
13.875 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
13.875 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.875 * [taylor]: Taking taylor expansion of k in n
13.875 * [backup-simplify]: Simplify k into k
13.875 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.875 * [taylor]: Taking taylor expansion of 1.0 in n
13.876 * [backup-simplify]: Simplify 1.0 into 1.0
13.876 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
13.876 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.876 * [taylor]: Taking taylor expansion of -2.0 in n
13.876 * [backup-simplify]: Simplify -2.0 into -2.0
13.876 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.876 * [taylor]: Taking taylor expansion of PI in n
13.876 * [backup-simplify]: Simplify PI into PI
13.876 * [taylor]: Taking taylor expansion of n in n
13.876 * [backup-simplify]: Simplify 0 into 0
13.876 * [backup-simplify]: Simplify 1 into 1
13.876 * [backup-simplify]: Simplify (/ PI 1) into PI
13.877 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.878 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.878 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
13.878 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
13.879 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.881 * [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))))
13.882 * [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)))))
13.882 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
13.882 * [taylor]: Taking taylor expansion of (/ -1 k) in n
13.882 * [taylor]: Taking taylor expansion of -1 in n
13.882 * [backup-simplify]: Simplify -1 into -1
13.882 * [taylor]: Taking taylor expansion of k in n
13.882 * [backup-simplify]: Simplify k into k
13.882 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
13.882 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
13.882 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
13.882 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
13.884 * [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)))
13.885 * [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))))
13.885 * [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
13.885 * [taylor]: Taking taylor expansion of 1.0 in k
13.885 * [backup-simplify]: Simplify 1.0 into 1.0
13.885 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) in k
13.886 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
13.886 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
13.886 * [taylor]: Taking taylor expansion of 0.5 in k
13.886 * [backup-simplify]: Simplify 0.5 into 0.5
13.886 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
13.886 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
13.886 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.886 * [taylor]: Taking taylor expansion of k in k
13.886 * [backup-simplify]: Simplify 0 into 0
13.886 * [backup-simplify]: Simplify 1 into 1
13.886 * [backup-simplify]: Simplify (/ 1 1) into 1
13.886 * [taylor]: Taking taylor expansion of 1.0 in k
13.886 * [backup-simplify]: Simplify 1.0 into 1.0
13.886 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
13.886 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
13.886 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
13.886 * [taylor]: Taking taylor expansion of -2.0 in k
13.886 * [backup-simplify]: Simplify -2.0 into -2.0
13.886 * [taylor]: Taking taylor expansion of PI in k
13.886 * [backup-simplify]: Simplify PI into PI
13.887 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.888 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.888 * [taylor]: Taking taylor expansion of (log n) in k
13.888 * [taylor]: Taking taylor expansion of n in k
13.888 * [backup-simplify]: Simplify n into n
13.888 * [backup-simplify]: Simplify (log n) into (log n)
13.889 * [backup-simplify]: Simplify (+ 1 0) into 1
13.889 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.890 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
13.891 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
13.892 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
13.893 * [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)))))
13.893 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
13.893 * [taylor]: Taking taylor expansion of (/ -1 k) in k
13.893 * [taylor]: Taking taylor expansion of -1 in k
13.893 * [backup-simplify]: Simplify -1 into -1
13.893 * [taylor]: Taking taylor expansion of k in k
13.893 * [backup-simplify]: Simplify 0 into 0
13.893 * [backup-simplify]: Simplify 1 into 1
13.894 * [backup-simplify]: Simplify (/ -1 1) into -1
13.894 * [backup-simplify]: Simplify (sqrt 0) into 0
13.895 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
13.897 * [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))))))
13.898 * [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))))))
13.900 * [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))))))
13.901 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.901 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
13.903 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
13.904 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.904 * [backup-simplify]: Simplify (+ 0 0) into 0
13.905 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
13.906 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.907 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
13.909 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.911 * [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
13.913 * [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
13.913 * [taylor]: Taking taylor expansion of 0 in k
13.913 * [backup-simplify]: Simplify 0 into 0
13.913 * [backup-simplify]: Simplify 0 into 0
13.914 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
13.917 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.920 * [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)))))))
13.922 * [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)))))))
13.924 * [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)))))))
13.925 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.926 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.930 * [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
13.931 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.931 * [backup-simplify]: Simplify (+ 0 0) into 0
13.939 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
13.941 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.944 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
13.955 * [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
13.956 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.956 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
13.958 * [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
13.982 * [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
13.982 * [taylor]: Taking taylor expansion of 0 in k
13.982 * [backup-simplify]: Simplify 0 into 0
13.982 * [backup-simplify]: Simplify 0 into 0
13.982 * [backup-simplify]: Simplify 0 into 0
13.984 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.991 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.995 * [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)))))))
13.999 * [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)))))))
14.001 * [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)))))))
14.006 * [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))))))))))))
14.006 * * * [progress]: simplifying candidates
14.009 * [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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (log1p (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (- (+ (log 1.0) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k)))
  (- (log (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k)))
  (log (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (exp (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (/ (* (* (* 1.0 1.0) 1.0) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (/ (* (* (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (* (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (- (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- (sqrt k))
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 (sqrt 1))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 1)
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt 1))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1)
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
  (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (+ (* +nan.0 (* (pow k 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))))))
14.021 * * [simplify]: iteration 0: 270 enodes
14.217 * * [simplify]: iteration 1: 765 enodes
14.764 * * [simplify]: iteration 2: 2571 enodes
16.723 * * [simplify]: iteration complete: 5000 enodes
16.723 * * [simplify]: Extracting #0: cost 73 inf + 0
16.726 * * [simplify]: Extracting #1: cost 614 inf + 1
16.734 * * [simplify]: Extracting #2: cost 1151 inf + 2162
16.753 * * [simplify]: Extracting #3: cost 1159 inf + 39680
16.815 * * [simplify]: Extracting #4: cost 715 inf + 204222
16.936 * * [simplify]: Extracting #5: cost 281 inf + 417211
17.121 * * [simplify]: Extracting #6: cost 130 inf + 493304
17.401 * * [simplify]: Extracting #7: cost 58 inf + 529930
17.684 * * [simplify]: Extracting #8: cost 13 inf + 563879
17.941 * * [simplify]: Extracting #9: cost 0 inf + 568587
18.209 * * [simplify]: Extracting #10: cost 0 inf + 565737
18.498 * * [simplify]: Extracting #11: cost 0 inf + 565407
18.790 * [simplify]: Simplified to:
  (expm1 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (pow (* 2.0 (* n PI)) (/ 1.0 2.0))
  (pow (* 2.0 (* n PI)) (/ k 2.0))
  (pow (* 2.0 (* n PI)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* 2.0 (* n PI)) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* 2.0 (* n PI)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0))))
  (pow (* 2.0 (* n PI)) (* (/ (cbrt (- 1.0 k)) (sqrt 2.0)) (cbrt (- 1.0 k))))
  (pow (* 2.0 (* n PI)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* 2.0 (* n PI)) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* 2.0 (* n PI)) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* 2.0 (* n PI)) (sqrt (- 1.0 k)))
  (pow (* 2.0 (* n PI)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0)))
  (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0)))
  (* 2.0 (* n PI))
  (pow (* 2.0 (* n PI)) (/ (/ (+ (sqrt 1.0) (sqrt k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* 2.0 (* n PI)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* 2.0 (* n PI)) (+ (sqrt 1.0) (sqrt k)))
  (pow (* 2.0 (* n PI)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0)))
  (pow (* 2.0 (* n PI)) (/ 1 (sqrt 2.0)))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (pow (* 2.0 (* n PI)) (- 1.0 k))
  (pow (* PI 2.0) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))))
  (exp (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (pow (* 2.0 (* n PI)) (* 1/2 (/ (- 1.0 k) 2.0)))
  (pow (* 2.0 (* n PI)) (* 1/2 (/ (- 1.0 k) 2.0)))
  (expm1 (* 2.0 (* n PI)))
  (log1p (* 2.0 (* n PI)))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (log (* 2.0 (* n PI)))
  (log (* 2.0 (* n PI)))
  (log (* 2.0 (* n PI)))
  (exp (* 2.0 (* n PI)))
  (* (* (* 2.0 (* n PI)) (* 2.0 (* n PI))) (* 2.0 (* n PI)))
  (* (* (* 2.0 (* n PI)) (* 2.0 (* n PI))) (* 2.0 (* n PI)))
  (* (cbrt (* 2.0 (* n PI))) (cbrt (* 2.0 (* n PI))))
  (cbrt (* 2.0 (* n PI)))
  (* (* (* 2.0 (* n PI)) (* 2.0 (* n PI))) (* 2.0 (* n PI)))
  (sqrt (* 2.0 (* n PI)))
  (sqrt (* 2.0 (* n PI)))
  (* (cbrt n) (* (* PI 2.0) (cbrt n)))
  (* (* (sqrt n) 2.0) PI)
  (* PI 2.0)
  (* n PI)
  (expm1 (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (log1p (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI)))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI)))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI)))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI)))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI)))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI)))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI)))))
  (exp (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))))
  (cbrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (- 1.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (- (sqrt k))
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (fabs (cbrt k)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (/ (sqrt k) 1.0) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k))) (/ 1.0 (cbrt (sqrt k))))
  (* (/ 1.0 (fabs (cbrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) 1.0)
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) 1.0)
  (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (sqrt k) (pow (* 2.0 (* n PI)) (/ k 2.0)))
  (fma (* (* k k) 0.125) (fma (* (log (* PI 2.0)) (exp (* (log (* 2.0 (* n PI))) 0.5))) (log (* PI 2.0)) (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (log n) (log n)))) (- (fma (* (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (* k k) (log n))) (log (* PI 2.0))) 0.25 (exp (* (log (* 2.0 (* n PI))) 0.5))) (* 0.5 (* k (fma (log (* PI 2.0)) (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (log n)))))))
  (exp (* 0.5 (* (log (* 2.0 (* n PI))) (- 1.0 k))))
  (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* 0.5 (- 1.0 k))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (fma (* +nan.0 (exp (* (log (* 2.0 (* n PI))) 0.5))) (* k k) (fma (- +nan.0) (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (* k k) (log n))) (fma (* (log (* PI 2.0)) (* k k)) (* +nan.0 (exp (* (log (* 2.0 (* n PI))) 0.5))) (fma (- +nan.0) (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (log n) k)) (- (- (* (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (* k (log (* PI 2.0))) (* k (log (* PI 2.0))))) +nan.0) (* k (* +nan.0 (exp (* (log (* 2.0 (* n PI))) 0.5))))) (fma (* (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (* k k) (log n))) (log (* PI 2.0))) (- +nan.0) (- (fma (* k (log (* PI 2.0))) (* +nan.0 (exp (* (log (* 2.0 (* n PI))) 0.5))) (* +nan.0 (exp (* (log (* 2.0 (* n PI))) 0.5)))) (* +nan.0 (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (* (log n) k) (* (log n) k))))))))))))
  (- (- (* (/ +nan.0 (* k k)) (/ (exp (* 0.5 (* (log (* 2.0 (* n PI))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (log (* 2.0 (* n PI))) (- 1.0 k)))) k)) (* (/ (exp (* 0.5 (* (log (* 2.0 (* n PI))) (- 1.0 k)))) k) (/ +nan.0 k)))))
  (fma +nan.0 (- (/ (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* 0.5 (- 1.0 k)))) k)) (* +nan.0 (- (/ (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* 0.5 (- 1.0 k)))) (* k k)) (exp (* (- (log (* -2.0 PI)) (log (/ -1 n))) (* 0.5 (- 1.0 k)))))))
18.805 * * * [progress]: adding candidates to table
19.597 * * [progress]: iteration 3 / 4
19.597 * * * [progress]: picking best candidate
19.687 * * * * [pick]: Picked  #<alt (λ (k n) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))>
19.687 * * * [progress]: localizing error
19.732 * * * [progress]: generating rewritten candidates
19.732 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2)
19.775 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1)
19.828 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2)
19.854 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
19.939 * * * [progress]: generating series expansions
19.940 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2)
19.941 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
19.941 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
19.941 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
19.941 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
19.941 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
19.941 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
19.941 * [taylor]: Taking taylor expansion of 0.5 in k
19.941 * [backup-simplify]: Simplify 0.5 into 0.5
19.941 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
19.941 * [taylor]: Taking taylor expansion of 1.0 in k
19.941 * [backup-simplify]: Simplify 1.0 into 1.0
19.941 * [taylor]: Taking taylor expansion of k in k
19.941 * [backup-simplify]: Simplify 0 into 0
19.941 * [backup-simplify]: Simplify 1 into 1
19.941 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
19.941 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
19.941 * [taylor]: Taking taylor expansion of 2.0 in k
19.941 * [backup-simplify]: Simplify 2.0 into 2.0
19.941 * [taylor]: Taking taylor expansion of (* n PI) in k
19.942 * [taylor]: Taking taylor expansion of n in k
19.942 * [backup-simplify]: Simplify n into n
19.942 * [taylor]: Taking taylor expansion of PI in k
19.942 * [backup-simplify]: Simplify PI into PI
19.942 * [backup-simplify]: Simplify (* n PI) into (* n PI)
19.942 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
19.942 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
19.942 * [backup-simplify]: Simplify (- 0) into 0
19.943 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
19.943 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
19.943 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
19.944 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
19.944 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
19.944 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
19.944 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
19.944 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
19.944 * [taylor]: Taking taylor expansion of 0.5 in n
19.944 * [backup-simplify]: Simplify 0.5 into 0.5
19.944 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
19.944 * [taylor]: Taking taylor expansion of 1.0 in n
19.944 * [backup-simplify]: Simplify 1.0 into 1.0
19.944 * [taylor]: Taking taylor expansion of k in n
19.944 * [backup-simplify]: Simplify k into k
19.944 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
19.944 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
19.944 * [taylor]: Taking taylor expansion of 2.0 in n
19.944 * [backup-simplify]: Simplify 2.0 into 2.0
19.944 * [taylor]: Taking taylor expansion of (* n PI) in n
19.944 * [taylor]: Taking taylor expansion of n in n
19.944 * [backup-simplify]: Simplify 0 into 0
19.944 * [backup-simplify]: Simplify 1 into 1
19.944 * [taylor]: Taking taylor expansion of PI in n
19.944 * [backup-simplify]: Simplify PI into PI
19.945 * [backup-simplify]: Simplify (* 0 PI) into 0
19.945 * [backup-simplify]: Simplify (* 2.0 0) into 0
19.947 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.949 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
19.950 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.950 * [backup-simplify]: Simplify (- k) into (- k)
19.950 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
19.950 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
19.952 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
19.954 * [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))))
19.955 * [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)))))
19.956 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
19.956 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
19.956 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
19.956 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
19.956 * [taylor]: Taking taylor expansion of 0.5 in n
19.956 * [backup-simplify]: Simplify 0.5 into 0.5
19.956 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
19.956 * [taylor]: Taking taylor expansion of 1.0 in n
19.956 * [backup-simplify]: Simplify 1.0 into 1.0
19.956 * [taylor]: Taking taylor expansion of k in n
19.956 * [backup-simplify]: Simplify k into k
19.956 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
19.956 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
19.956 * [taylor]: Taking taylor expansion of 2.0 in n
19.956 * [backup-simplify]: Simplify 2.0 into 2.0
19.956 * [taylor]: Taking taylor expansion of (* n PI) in n
19.956 * [taylor]: Taking taylor expansion of n in n
19.956 * [backup-simplify]: Simplify 0 into 0
19.956 * [backup-simplify]: Simplify 1 into 1
19.956 * [taylor]: Taking taylor expansion of PI in n
19.956 * [backup-simplify]: Simplify PI into PI
19.957 * [backup-simplify]: Simplify (* 0 PI) into 0
19.957 * [backup-simplify]: Simplify (* 2.0 0) into 0
19.959 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.961 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
19.962 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.962 * [backup-simplify]: Simplify (- k) into (- k)
19.962 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
19.962 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
19.963 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
19.965 * [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))))
19.966 * [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)))))
19.966 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
19.966 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
19.966 * [taylor]: Taking taylor expansion of 0.5 in k
19.966 * [backup-simplify]: Simplify 0.5 into 0.5
19.966 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
19.966 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
19.966 * [taylor]: Taking taylor expansion of 1.0 in k
19.966 * [backup-simplify]: Simplify 1.0 into 1.0
19.966 * [taylor]: Taking taylor expansion of k in k
19.966 * [backup-simplify]: Simplify 0 into 0
19.966 * [backup-simplify]: Simplify 1 into 1
19.966 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
19.967 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
19.967 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
19.967 * [taylor]: Taking taylor expansion of 2.0 in k
19.967 * [backup-simplify]: Simplify 2.0 into 2.0
19.967 * [taylor]: Taking taylor expansion of PI in k
19.967 * [backup-simplify]: Simplify PI into PI
19.967 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
19.968 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.968 * [taylor]: Taking taylor expansion of (log n) in k
19.968 * [taylor]: Taking taylor expansion of n in k
19.968 * [backup-simplify]: Simplify n into n
19.968 * [backup-simplify]: Simplify (log n) into (log n)
19.969 * [backup-simplify]: Simplify (- 0) into 0
19.969 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
19.970 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
19.972 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
19.973 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
19.974 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
19.975 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
19.976 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
19.977 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
19.979 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
19.980 * [backup-simplify]: Simplify (- 0) into 0
19.980 * [backup-simplify]: Simplify (+ 0 0) into 0
19.981 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
19.982 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
19.983 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
19.985 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
19.985 * [taylor]: Taking taylor expansion of 0 in k
19.985 * [backup-simplify]: Simplify 0 into 0
19.985 * [backup-simplify]: Simplify 0 into 0
19.986 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
19.988 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
19.989 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
19.990 * [backup-simplify]: Simplify (+ 0 0) into 0
19.990 * [backup-simplify]: Simplify (- 1) into -1
19.990 * [backup-simplify]: Simplify (+ 0 -1) into -1
19.992 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
19.994 * [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))))
19.998 * [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))))))
20.001 * [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))))))
20.002 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
20.004 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
20.008 * [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
20.009 * [backup-simplify]: Simplify (- 0) into 0
20.009 * [backup-simplify]: Simplify (+ 0 0) into 0
20.010 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
20.011 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.013 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
20.016 * [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
20.016 * [taylor]: Taking taylor expansion of 0 in k
20.016 * [backup-simplify]: Simplify 0 into 0
20.016 * [backup-simplify]: Simplify 0 into 0
20.016 * [backup-simplify]: Simplify 0 into 0
20.017 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
20.021 * [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
20.023 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
20.023 * [backup-simplify]: Simplify (+ 0 0) into 0
20.024 * [backup-simplify]: Simplify (- 0) into 0
20.024 * [backup-simplify]: Simplify (+ 0 0) into 0
20.026 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
20.029 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
20.033 * [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))))))
20.039 * [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))))))
20.050 * [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))))))
20.052 * [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))))
20.052 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
20.052 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
20.052 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
20.052 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
20.052 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
20.052 * [taylor]: Taking taylor expansion of 0.5 in k
20.052 * [backup-simplify]: Simplify 0.5 into 0.5
20.052 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
20.052 * [taylor]: Taking taylor expansion of 1.0 in k
20.052 * [backup-simplify]: Simplify 1.0 into 1.0
20.052 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.052 * [taylor]: Taking taylor expansion of k in k
20.052 * [backup-simplify]: Simplify 0 into 0
20.052 * [backup-simplify]: Simplify 1 into 1
20.053 * [backup-simplify]: Simplify (/ 1 1) into 1
20.053 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
20.053 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
20.053 * [taylor]: Taking taylor expansion of 2.0 in k
20.053 * [backup-simplify]: Simplify 2.0 into 2.0
20.053 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.053 * [taylor]: Taking taylor expansion of PI in k
20.053 * [backup-simplify]: Simplify PI into PI
20.053 * [taylor]: Taking taylor expansion of n in k
20.053 * [backup-simplify]: Simplify n into n
20.053 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.053 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
20.053 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
20.054 * [backup-simplify]: Simplify (- 1) into -1
20.054 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.055 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
20.055 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
20.055 * [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)))))
20.055 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
20.055 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
20.055 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
20.055 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
20.055 * [taylor]: Taking taylor expansion of 0.5 in n
20.055 * [backup-simplify]: Simplify 0.5 into 0.5
20.055 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
20.055 * [taylor]: Taking taylor expansion of 1.0 in n
20.055 * [backup-simplify]: Simplify 1.0 into 1.0
20.055 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.055 * [taylor]: Taking taylor expansion of k in n
20.055 * [backup-simplify]: Simplify k into k
20.056 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.056 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
20.056 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.056 * [taylor]: Taking taylor expansion of 2.0 in n
20.056 * [backup-simplify]: Simplify 2.0 into 2.0
20.056 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.056 * [taylor]: Taking taylor expansion of PI in n
20.056 * [backup-simplify]: Simplify PI into PI
20.056 * [taylor]: Taking taylor expansion of n in n
20.056 * [backup-simplify]: Simplify 0 into 0
20.056 * [backup-simplify]: Simplify 1 into 1
20.057 * [backup-simplify]: Simplify (/ PI 1) into PI
20.057 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.058 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.059 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.059 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
20.059 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
20.060 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.062 * [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))))
20.063 * [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)))))
20.063 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
20.063 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
20.063 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
20.063 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
20.063 * [taylor]: Taking taylor expansion of 0.5 in n
20.063 * [backup-simplify]: Simplify 0.5 into 0.5
20.063 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
20.063 * [taylor]: Taking taylor expansion of 1.0 in n
20.063 * [backup-simplify]: Simplify 1.0 into 1.0
20.063 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.064 * [taylor]: Taking taylor expansion of k in n
20.064 * [backup-simplify]: Simplify k into k
20.064 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.064 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
20.064 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.064 * [taylor]: Taking taylor expansion of 2.0 in n
20.064 * [backup-simplify]: Simplify 2.0 into 2.0
20.064 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.064 * [taylor]: Taking taylor expansion of PI in n
20.064 * [backup-simplify]: Simplify PI into PI
20.064 * [taylor]: Taking taylor expansion of n in n
20.064 * [backup-simplify]: Simplify 0 into 0
20.064 * [backup-simplify]: Simplify 1 into 1
20.065 * [backup-simplify]: Simplify (/ PI 1) into PI
20.065 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.066 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.066 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.067 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
20.067 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
20.069 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.070 * [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))))
20.071 * [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)))))
20.071 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
20.071 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
20.071 * [taylor]: Taking taylor expansion of 0.5 in k
20.071 * [backup-simplify]: Simplify 0.5 into 0.5
20.071 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
20.071 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
20.071 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
20.071 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
20.071 * [taylor]: Taking taylor expansion of 2.0 in k
20.071 * [backup-simplify]: Simplify 2.0 into 2.0
20.071 * [taylor]: Taking taylor expansion of PI in k
20.071 * [backup-simplify]: Simplify PI into PI
20.073 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.073 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.073 * [taylor]: Taking taylor expansion of (log n) in k
20.073 * [taylor]: Taking taylor expansion of n in k
20.073 * [backup-simplify]: Simplify n into n
20.073 * [backup-simplify]: Simplify (log n) into (log n)
20.073 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
20.073 * [taylor]: Taking taylor expansion of 1.0 in k
20.073 * [backup-simplify]: Simplify 1.0 into 1.0
20.074 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.074 * [taylor]: Taking taylor expansion of k in k
20.074 * [backup-simplify]: Simplify 0 into 0
20.074 * [backup-simplify]: Simplify 1 into 1
20.074 * [backup-simplify]: Simplify (/ 1 1) into 1
20.074 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
20.075 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
20.075 * [backup-simplify]: Simplify (- 1) into -1
20.076 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.077 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
20.078 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
20.079 * [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)))))
20.081 * [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)))))
20.082 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.083 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
20.085 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
20.085 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.086 * [backup-simplify]: Simplify (- 0) into 0
20.086 * [backup-simplify]: Simplify (+ 0 0) into 0
20.087 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
20.088 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.089 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
20.091 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
20.092 * [taylor]: Taking taylor expansion of 0 in k
20.092 * [backup-simplify]: Simplify 0 into 0
20.092 * [backup-simplify]: Simplify 0 into 0
20.092 * [backup-simplify]: Simplify 0 into 0
20.093 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.094 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
20.104 * [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
20.105 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.105 * [backup-simplify]: Simplify (- 0) into 0
20.106 * [backup-simplify]: Simplify (+ 0 0) into 0
20.107 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
20.108 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.110 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
20.112 * [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
20.113 * [taylor]: Taking taylor expansion of 0 in k
20.113 * [backup-simplify]: Simplify 0 into 0
20.113 * [backup-simplify]: Simplify 0 into 0
20.113 * [backup-simplify]: Simplify 0 into 0
20.113 * [backup-simplify]: Simplify 0 into 0
20.114 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.115 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.121 * [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
20.122 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.122 * [backup-simplify]: Simplify (- 0) into 0
20.123 * [backup-simplify]: Simplify (+ 0 0) into 0
20.124 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
20.125 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.127 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
20.130 * [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
20.131 * [taylor]: Taking taylor expansion of 0 in k
20.131 * [backup-simplify]: Simplify 0 into 0
20.131 * [backup-simplify]: Simplify 0 into 0
20.132 * [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))))
20.134 * [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)))
20.134 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
20.134 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
20.134 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
20.134 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
20.134 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
20.134 * [taylor]: Taking taylor expansion of 0.5 in k
20.134 * [backup-simplify]: Simplify 0.5 into 0.5
20.134 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
20.134 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.134 * [taylor]: Taking taylor expansion of k in k
20.134 * [backup-simplify]: Simplify 0 into 0
20.134 * [backup-simplify]: Simplify 1 into 1
20.135 * [backup-simplify]: Simplify (/ 1 1) into 1
20.135 * [taylor]: Taking taylor expansion of 1.0 in k
20.135 * [backup-simplify]: Simplify 1.0 into 1.0
20.135 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
20.135 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
20.135 * [taylor]: Taking taylor expansion of -2.0 in k
20.135 * [backup-simplify]: Simplify -2.0 into -2.0
20.135 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.135 * [taylor]: Taking taylor expansion of PI in k
20.135 * [backup-simplify]: Simplify PI into PI
20.135 * [taylor]: Taking taylor expansion of n in k
20.135 * [backup-simplify]: Simplify n into n
20.135 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.135 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
20.135 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
20.136 * [backup-simplify]: Simplify (+ 1 0) into 1
20.136 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
20.137 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
20.137 * [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))))))
20.137 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
20.137 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
20.137 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
20.137 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
20.137 * [taylor]: Taking taylor expansion of 0.5 in n
20.137 * [backup-simplify]: Simplify 0.5 into 0.5
20.137 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
20.137 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.137 * [taylor]: Taking taylor expansion of k in n
20.137 * [backup-simplify]: Simplify k into k
20.137 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.137 * [taylor]: Taking taylor expansion of 1.0 in n
20.137 * [backup-simplify]: Simplify 1.0 into 1.0
20.137 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
20.137 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
20.137 * [taylor]: Taking taylor expansion of -2.0 in n
20.138 * [backup-simplify]: Simplify -2.0 into -2.0
20.138 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.138 * [taylor]: Taking taylor expansion of PI in n
20.138 * [backup-simplify]: Simplify PI into PI
20.138 * [taylor]: Taking taylor expansion of n in n
20.138 * [backup-simplify]: Simplify 0 into 0
20.138 * [backup-simplify]: Simplify 1 into 1
20.138 * [backup-simplify]: Simplify (/ PI 1) into PI
20.139 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
20.144 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
20.144 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
20.144 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
20.146 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
20.152 * [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))))
20.153 * [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)))))
20.153 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
20.153 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
20.154 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
20.154 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
20.154 * [taylor]: Taking taylor expansion of 0.5 in n
20.154 * [backup-simplify]: Simplify 0.5 into 0.5
20.154 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
20.154 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.154 * [taylor]: Taking taylor expansion of k in n
20.154 * [backup-simplify]: Simplify k into k
20.154 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.154 * [taylor]: Taking taylor expansion of 1.0 in n
20.154 * [backup-simplify]: Simplify 1.0 into 1.0
20.154 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
20.154 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
20.154 * [taylor]: Taking taylor expansion of -2.0 in n
20.154 * [backup-simplify]: Simplify -2.0 into -2.0
20.154 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.154 * [taylor]: Taking taylor expansion of PI in n
20.154 * [backup-simplify]: Simplify PI into PI
20.154 * [taylor]: Taking taylor expansion of n in n
20.154 * [backup-simplify]: Simplify 0 into 0
20.154 * [backup-simplify]: Simplify 1 into 1
20.155 * [backup-simplify]: Simplify (/ PI 1) into PI
20.162 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
20.164 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
20.164 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
20.165 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
20.167 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
20.176 * [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))))
20.177 * [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)))))
20.178 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
20.178 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
20.178 * [taylor]: Taking taylor expansion of 0.5 in k
20.178 * [backup-simplify]: Simplify 0.5 into 0.5
20.178 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
20.178 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
20.178 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.178 * [taylor]: Taking taylor expansion of k in k
20.178 * [backup-simplify]: Simplify 0 into 0
20.178 * [backup-simplify]: Simplify 1 into 1
20.179 * [backup-simplify]: Simplify (/ 1 1) into 1
20.179 * [taylor]: Taking taylor expansion of 1.0 in k
20.179 * [backup-simplify]: Simplify 1.0 into 1.0
20.179 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
20.179 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
20.179 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
20.179 * [taylor]: Taking taylor expansion of -2.0 in k
20.179 * [backup-simplify]: Simplify -2.0 into -2.0
20.179 * [taylor]: Taking taylor expansion of PI in k
20.179 * [backup-simplify]: Simplify PI into PI
20.179 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
20.181 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
20.181 * [taylor]: Taking taylor expansion of (log n) in k
20.181 * [taylor]: Taking taylor expansion of n in k
20.181 * [backup-simplify]: Simplify n into n
20.181 * [backup-simplify]: Simplify (log n) into (log n)
20.181 * [backup-simplify]: Simplify (+ 1 0) into 1
20.181 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
20.183 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
20.188 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
20.190 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
20.191 * [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)))))
20.197 * [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)))))
20.198 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.199 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
20.209 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
20.210 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.210 * [backup-simplify]: Simplify (+ 0 0) into 0
20.211 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
20.212 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
20.214 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
20.220 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
20.220 * [taylor]: Taking taylor expansion of 0 in k
20.220 * [backup-simplify]: Simplify 0 into 0
20.220 * [backup-simplify]: Simplify 0 into 0
20.220 * [backup-simplify]: Simplify 0 into 0
20.222 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.223 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
20.230 * [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
20.230 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.231 * [backup-simplify]: Simplify (+ 0 0) into 0
20.236 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
20.238 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
20.239 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
20.246 * [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
20.246 * [taylor]: Taking taylor expansion of 0 in k
20.246 * [backup-simplify]: Simplify 0 into 0
20.246 * [backup-simplify]: Simplify 0 into 0
20.246 * [backup-simplify]: Simplify 0 into 0
20.246 * [backup-simplify]: Simplify 0 into 0
20.248 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.253 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.263 * [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
20.263 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
20.268 * [backup-simplify]: Simplify (+ 0 0) into 0
20.269 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
20.271 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
20.287 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
20.290 * [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
20.290 * [taylor]: Taking taylor expansion of 0 in k
20.290 * [backup-simplify]: Simplify 0 into 0
20.290 * [backup-simplify]: Simplify 0 into 0
20.296 * [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))))))
20.296 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1)
20.297 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
20.297 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
20.297 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.297 * [taylor]: Taking taylor expansion of 2.0 in n
20.297 * [backup-simplify]: Simplify 2.0 into 2.0
20.297 * [taylor]: Taking taylor expansion of (* n PI) in n
20.297 * [taylor]: Taking taylor expansion of n in n
20.297 * [backup-simplify]: Simplify 0 into 0
20.297 * [backup-simplify]: Simplify 1 into 1
20.297 * [taylor]: Taking taylor expansion of PI in n
20.297 * [backup-simplify]: Simplify PI into PI
20.297 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.297 * [taylor]: Taking taylor expansion of 2.0 in n
20.297 * [backup-simplify]: Simplify 2.0 into 2.0
20.298 * [taylor]: Taking taylor expansion of (* n PI) in n
20.298 * [taylor]: Taking taylor expansion of n in n
20.298 * [backup-simplify]: Simplify 0 into 0
20.298 * [backup-simplify]: Simplify 1 into 1
20.298 * [taylor]: Taking taylor expansion of PI in n
20.298 * [backup-simplify]: Simplify PI into PI
20.298 * [backup-simplify]: Simplify (* 0 PI) into 0
20.299 * [backup-simplify]: Simplify (* 2.0 0) into 0
20.299 * [backup-simplify]: Simplify 0 into 0
20.303 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.304 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
20.305 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.306 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
20.307 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
20.307 * [backup-simplify]: Simplify 0 into 0
20.308 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
20.310 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
20.310 * [backup-simplify]: Simplify 0 into 0
20.311 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
20.313 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
20.313 * [backup-simplify]: Simplify 0 into 0
20.315 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
20.316 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
20.316 * [backup-simplify]: Simplify 0 into 0
20.318 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
20.320 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
20.320 * [backup-simplify]: Simplify 0 into 0
20.322 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
20.325 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
20.325 * [backup-simplify]: Simplify 0 into 0
20.325 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
20.326 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
20.326 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
20.326 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.326 * [taylor]: Taking taylor expansion of 2.0 in n
20.326 * [backup-simplify]: Simplify 2.0 into 2.0
20.326 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.326 * [taylor]: Taking taylor expansion of PI in n
20.326 * [backup-simplify]: Simplify PI into PI
20.326 * [taylor]: Taking taylor expansion of n in n
20.326 * [backup-simplify]: Simplify 0 into 0
20.326 * [backup-simplify]: Simplify 1 into 1
20.327 * [backup-simplify]: Simplify (/ PI 1) into PI
20.327 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.327 * [taylor]: Taking taylor expansion of 2.0 in n
20.327 * [backup-simplify]: Simplify 2.0 into 2.0
20.327 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.327 * [taylor]: Taking taylor expansion of PI in n
20.327 * [backup-simplify]: Simplify PI into PI
20.327 * [taylor]: Taking taylor expansion of n in n
20.327 * [backup-simplify]: Simplify 0 into 0
20.327 * [backup-simplify]: Simplify 1 into 1
20.327 * [backup-simplify]: Simplify (/ PI 1) into PI
20.328 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.328 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.329 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.330 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
20.330 * [backup-simplify]: Simplify 0 into 0
20.331 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.333 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
20.333 * [backup-simplify]: Simplify 0 into 0
20.334 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.335 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.335 * [backup-simplify]: Simplify 0 into 0
20.336 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.337 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
20.337 * [backup-simplify]: Simplify 0 into 0
20.338 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.340 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
20.340 * [backup-simplify]: Simplify 0 into 0
20.341 * [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
20.343 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
20.343 * [backup-simplify]: Simplify 0 into 0
20.344 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
20.345 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
20.345 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
20.345 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
20.345 * [taylor]: Taking taylor expansion of -2.0 in n
20.345 * [backup-simplify]: Simplify -2.0 into -2.0
20.345 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.345 * [taylor]: Taking taylor expansion of PI in n
20.345 * [backup-simplify]: Simplify PI into PI
20.345 * [taylor]: Taking taylor expansion of n in n
20.345 * [backup-simplify]: Simplify 0 into 0
20.345 * [backup-simplify]: Simplify 1 into 1
20.346 * [backup-simplify]: Simplify (/ PI 1) into PI
20.346 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
20.346 * [taylor]: Taking taylor expansion of -2.0 in n
20.346 * [backup-simplify]: Simplify -2.0 into -2.0
20.346 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.346 * [taylor]: Taking taylor expansion of PI in n
20.346 * [backup-simplify]: Simplify PI into PI
20.346 * [taylor]: Taking taylor expansion of n in n
20.346 * [backup-simplify]: Simplify 0 into 0
20.346 * [backup-simplify]: Simplify 1 into 1
20.347 * [backup-simplify]: Simplify (/ PI 1) into PI
20.347 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
20.347 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
20.348 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.349 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
20.349 * [backup-simplify]: Simplify 0 into 0
20.350 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.351 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
20.351 * [backup-simplify]: Simplify 0 into 0
20.352 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.353 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.353 * [backup-simplify]: Simplify 0 into 0
20.354 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.355 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
20.355 * [backup-simplify]: Simplify 0 into 0
20.357 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.359 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
20.359 * [backup-simplify]: Simplify 0 into 0
20.373 * [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
20.376 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
20.376 * [backup-simplify]: Simplify 0 into 0
20.377 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
20.377 * * * * [progress]: [ 3 / 4 ] generating series at (2 2)
20.378 * [backup-simplify]: Simplify (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))))
20.378 * [approximate]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0
20.378 * [taylor]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n
20.378 * [taylor]: Taking taylor expansion of (sqrt k) in n
20.378 * [taylor]: Taking taylor expansion of k in n
20.378 * [backup-simplify]: Simplify k into k
20.378 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
20.378 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
20.378 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n
20.378 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
20.378 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
20.378 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
20.378 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
20.378 * [taylor]: Taking taylor expansion of 0.5 in n
20.379 * [backup-simplify]: Simplify 0.5 into 0.5
20.379 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
20.379 * [taylor]: Taking taylor expansion of 1.0 in n
20.379 * [backup-simplify]: Simplify 1.0 into 1.0
20.379 * [taylor]: Taking taylor expansion of k in n
20.379 * [backup-simplify]: Simplify k into k
20.379 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
20.379 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.379 * [taylor]: Taking taylor expansion of 2.0 in n
20.379 * [backup-simplify]: Simplify 2.0 into 2.0
20.379 * [taylor]: Taking taylor expansion of (* n PI) in n
20.379 * [taylor]: Taking taylor expansion of n in n
20.379 * [backup-simplify]: Simplify 0 into 0
20.379 * [backup-simplify]: Simplify 1 into 1
20.379 * [taylor]: Taking taylor expansion of PI in n
20.379 * [backup-simplify]: Simplify PI into PI
20.380 * [backup-simplify]: Simplify (* 0 PI) into 0
20.380 * [backup-simplify]: Simplify (* 2.0 0) into 0
20.382 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.383 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
20.384 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.384 * [backup-simplify]: Simplify (- k) into (- k)
20.384 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
20.385 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
20.386 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.387 * [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))))
20.388 * [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)))))
20.390 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) into (/ 1 (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))
20.390 * [taylor]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
20.390 * [taylor]: Taking taylor expansion of (sqrt k) in k
20.390 * [taylor]: Taking taylor expansion of k in k
20.390 * [backup-simplify]: Simplify 0 into 0
20.390 * [backup-simplify]: Simplify 1 into 1
20.390 * [backup-simplify]: Simplify (sqrt 0) into 0
20.392 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.392 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
20.392 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
20.392 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
20.392 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
20.392 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
20.392 * [taylor]: Taking taylor expansion of 0.5 in k
20.392 * [backup-simplify]: Simplify 0.5 into 0.5
20.392 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
20.392 * [taylor]: Taking taylor expansion of 1.0 in k
20.392 * [backup-simplify]: Simplify 1.0 into 1.0
20.392 * [taylor]: Taking taylor expansion of k in k
20.392 * [backup-simplify]: Simplify 0 into 0
20.392 * [backup-simplify]: Simplify 1 into 1
20.392 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
20.392 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
20.392 * [taylor]: Taking taylor expansion of 2.0 in k
20.392 * [backup-simplify]: Simplify 2.0 into 2.0
20.392 * [taylor]: Taking taylor expansion of (* n PI) in k
20.392 * [taylor]: Taking taylor expansion of n in k
20.393 * [backup-simplify]: Simplify n into n
20.393 * [taylor]: Taking taylor expansion of PI in k
20.393 * [backup-simplify]: Simplify PI into PI
20.393 * [backup-simplify]: Simplify (* n PI) into (* n PI)
20.393 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
20.393 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
20.393 * [backup-simplify]: Simplify (- 0) into 0
20.394 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
20.394 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
20.394 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
20.394 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
20.395 * [backup-simplify]: Simplify (/ 1 (pow (* 2.0 (* n PI)) 0.5)) into (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)
20.395 * [taylor]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
20.395 * [taylor]: Taking taylor expansion of (sqrt k) in k
20.395 * [taylor]: Taking taylor expansion of k in k
20.395 * [backup-simplify]: Simplify 0 into 0
20.395 * [backup-simplify]: Simplify 1 into 1
20.395 * [backup-simplify]: Simplify (sqrt 0) into 0
20.397 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.397 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
20.397 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
20.397 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
20.397 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
20.397 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
20.397 * [taylor]: Taking taylor expansion of 0.5 in k
20.397 * [backup-simplify]: Simplify 0.5 into 0.5
20.397 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
20.397 * [taylor]: Taking taylor expansion of 1.0 in k
20.397 * [backup-simplify]: Simplify 1.0 into 1.0
20.397 * [taylor]: Taking taylor expansion of k in k
20.397 * [backup-simplify]: Simplify 0 into 0
20.397 * [backup-simplify]: Simplify 1 into 1
20.397 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
20.397 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
20.397 * [taylor]: Taking taylor expansion of 2.0 in k
20.397 * [backup-simplify]: Simplify 2.0 into 2.0
20.397 * [taylor]: Taking taylor expansion of (* n PI) in k
20.397 * [taylor]: Taking taylor expansion of n in k
20.398 * [backup-simplify]: Simplify n into n
20.398 * [taylor]: Taking taylor expansion of PI in k
20.398 * [backup-simplify]: Simplify PI into PI
20.398 * [backup-simplify]: Simplify (* n PI) into (* n PI)
20.398 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
20.398 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
20.399 * [backup-simplify]: Simplify (- 0) into 0
20.399 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
20.400 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
20.400 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
20.400 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
20.400 * [backup-simplify]: Simplify (/ 1 (pow (* 2.0 (* n PI)) 0.5)) into (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)
20.402 * [backup-simplify]: Simplify (* 0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) into 0
20.402 * [taylor]: Taking taylor expansion of 0 in n
20.402 * [backup-simplify]: Simplify 0 into 0
20.402 * [backup-simplify]: Simplify 0 into 0
20.403 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
20.403 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0
20.404 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0
20.404 * [backup-simplify]: Simplify (- 1) into -1
20.405 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.407 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5)
20.408 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI)))))
20.408 * [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)))
20.412 * [backup-simplify]: Simplify (- (+ (* (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) (/ (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (pow (* 2.0 (* n PI)) 0.5))))) into (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI)))))
20.415 * [backup-simplify]: Simplify (+ (* 0 (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI)))))) (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))
20.416 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) in n
20.416 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n
20.416 * [taylor]: Taking taylor expansion of +nan.0 in n
20.416 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.416 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n
20.416 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n
20.416 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
20.416 * [taylor]: Taking taylor expansion of 0.5 in n
20.416 * [backup-simplify]: Simplify 0.5 into 0.5
20.416 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
20.416 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
20.416 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
20.416 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.416 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.416 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.416 * [taylor]: Taking taylor expansion of 1.0 in n
20.416 * [backup-simplify]: Simplify 1.0 into 1.0
20.416 * [taylor]: Taking taylor expansion of (log PI) in n
20.416 * [taylor]: Taking taylor expansion of PI in n
20.416 * [backup-simplify]: Simplify PI into PI
20.417 * [backup-simplify]: Simplify (log PI) into (log PI)
20.418 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.420 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.420 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
20.420 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.420 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.420 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.420 * [taylor]: Taking taylor expansion of 1.0 in n
20.420 * [backup-simplify]: Simplify 1.0 into 1.0
20.420 * [taylor]: Taking taylor expansion of (log n) in n
20.420 * [taylor]: Taking taylor expansion of n in n
20.420 * [backup-simplify]: Simplify 0 into 0
20.420 * [backup-simplify]: Simplify 1 into 1
20.421 * [backup-simplify]: Simplify (log 1) into 0
20.421 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.421 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.422 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.422 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.422 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.422 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.422 * [taylor]: Taking taylor expansion of 1.0 in n
20.422 * [backup-simplify]: Simplify 1.0 into 1.0
20.422 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.422 * [taylor]: Taking taylor expansion of 2.0 in n
20.422 * [backup-simplify]: Simplify 2.0 into 2.0
20.422 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.423 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.425 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.426 * [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)
20.427 * [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)
20.428 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)
20.430 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))
20.431 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))
20.433 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.434 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))
20.436 * [backup-simplify]: Simplify (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))
20.438 * [backup-simplify]: Simplify (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))
20.438 * [backup-simplify]: Simplify 0 into 0
20.439 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
20.440 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
20.442 * [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
20.443 * [backup-simplify]: Simplify (- 0) into 0
20.443 * [backup-simplify]: Simplify (+ 0 0) into 0
20.444 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0
20.445 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0
20.446 * [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)))
20.454 * [backup-simplify]: Simplify (- (+ (* (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) (/ (* 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))) (pow (* 2.0 (* n PI)) 0.5))) (* (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI))))) (/ (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (pow (* 2.0 (* n PI)) 0.5))))) into (- (* 0.25 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 0.125 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))
20.458 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
20.466 * [backup-simplify]: Simplify (+ (* 0 (- (* 0.25 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 0.125 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) (+ (* +nan.0 (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI)))))) (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))) into (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))
20.466 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))) in n
20.466 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))) in n
20.466 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) in n
20.466 * [taylor]: Taking taylor expansion of +nan.0 in n
20.466 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.466 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5) in n
20.466 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))))) in n
20.466 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n
20.466 * [taylor]: Taking taylor expansion of 0.5 in n
20.466 * [backup-simplify]: Simplify 0.5 into 0.5
20.466 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n
20.466 * [taylor]: Taking taylor expansion of (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n
20.466 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n
20.466 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.466 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.466 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.466 * [taylor]: Taking taylor expansion of 1.0 in n
20.466 * [backup-simplify]: Simplify 1.0 into 1.0
20.467 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.467 * [taylor]: Taking taylor expansion of 2.0 in n
20.467 * [backup-simplify]: Simplify 2.0 into 2.0
20.467 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.468 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.470 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.470 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n
20.470 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.470 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.470 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.470 * [taylor]: Taking taylor expansion of 1.0 in n
20.470 * [backup-simplify]: Simplify 1.0 into 1.0
20.470 * [taylor]: Taking taylor expansion of (log n) in n
20.470 * [taylor]: Taking taylor expansion of n in n
20.470 * [backup-simplify]: Simplify 0 into 0
20.470 * [backup-simplify]: Simplify 1 into 1
20.471 * [backup-simplify]: Simplify (log 1) into 0
20.471 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.471 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.471 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.471 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.471 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.471 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.472 * [taylor]: Taking taylor expansion of 1.0 in n
20.472 * [backup-simplify]: Simplify 1.0 into 1.0
20.472 * [taylor]: Taking taylor expansion of (log PI) in n
20.472 * [taylor]: Taking taylor expansion of PI in n
20.472 * [backup-simplify]: Simplify PI into PI
20.472 * [backup-simplify]: Simplify (log PI) into (log PI)
20.473 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.475 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.476 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
20.477 * [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)
20.478 * [backup-simplify]: Simplify (/ 1 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0)
20.480 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0))
20.482 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0)))
20.484 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.484 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))) in n
20.484 * [taylor]: Taking taylor expansion of (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) in n
20.485 * [taylor]: Taking taylor expansion of +nan.0 in n
20.485 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.485 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n
20.485 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
20.485 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.485 * [taylor]: Taking taylor expansion of 2.0 in n
20.485 * [backup-simplify]: Simplify 2.0 into 2.0
20.485 * [taylor]: Taking taylor expansion of (* n PI) in n
20.485 * [taylor]: Taking taylor expansion of n in n
20.485 * [backup-simplify]: Simplify 0 into 0
20.485 * [backup-simplify]: Simplify 1 into 1
20.485 * [taylor]: Taking taylor expansion of PI in n
20.485 * [backup-simplify]: Simplify PI into PI
20.486 * [backup-simplify]: Simplify (* 0 PI) into 0
20.486 * [backup-simplify]: Simplify (* 2.0 0) into 0
20.488 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.490 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
20.491 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.491 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n
20.491 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n
20.491 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
20.491 * [taylor]: Taking taylor expansion of 0.5 in n
20.491 * [backup-simplify]: Simplify 0.5 into 0.5
20.491 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
20.491 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
20.491 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
20.491 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.491 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.491 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.491 * [taylor]: Taking taylor expansion of 1.0 in n
20.491 * [backup-simplify]: Simplify 1.0 into 1.0
20.491 * [taylor]: Taking taylor expansion of (log PI) in n
20.491 * [taylor]: Taking taylor expansion of PI in n
20.491 * [backup-simplify]: Simplify PI into PI
20.492 * [backup-simplify]: Simplify (log PI) into (log PI)
20.493 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.494 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.494 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
20.495 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.495 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.495 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.495 * [taylor]: Taking taylor expansion of 1.0 in n
20.495 * [backup-simplify]: Simplify 1.0 into 1.0
20.495 * [taylor]: Taking taylor expansion of (log n) in n
20.495 * [taylor]: Taking taylor expansion of n in n
20.495 * [backup-simplify]: Simplify 0 into 0
20.495 * [backup-simplify]: Simplify 1 into 1
20.495 * [backup-simplify]: Simplify (log 1) into 0
20.496 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.496 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.496 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.496 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.496 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.496 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.496 * [taylor]: Taking taylor expansion of 1.0 in n
20.496 * [backup-simplify]: Simplify 1.0 into 1.0
20.496 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.496 * [taylor]: Taking taylor expansion of 2.0 in n
20.496 * [backup-simplify]: Simplify 2.0 into 2.0
20.497 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.497 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.499 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.500 * [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)
20.502 * [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)
20.503 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)
20.505 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))
20.506 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))
20.508 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.510 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))
20.511 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.514 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))
20.518 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))
20.521 * [backup-simplify]: Simplify (- (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))
20.528 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))
20.535 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))
20.542 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))
20.550 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0
20.552 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0
20.554 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0
20.555 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
20.556 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.557 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0
20.557 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0
20.558 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0
20.561 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
20.562 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0
20.564 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
20.566 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0
20.568 * [backup-simplify]: Simplify (- (+ (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) (/ 0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0))))) into 0
20.571 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1)))) 1) into 0
20.573 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0)))) into 0
20.575 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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
20.577 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0
20.578 * [backup-simplify]: Simplify (- 0) into 0
20.578 * [backup-simplify]: Simplify 0 into 0
20.578 * [backup-simplify]: Simplify 0 into 0
20.579 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.581 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
20.584 * [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
20.584 * [backup-simplify]: Simplify (- 0) into 0
20.585 * [backup-simplify]: Simplify (+ 0 0) into 0
20.586 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0
20.588 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0
20.590 * [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)))
20.603 * [backup-simplify]: Simplify (- (+ (* (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) (/ (* -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))) (pow (* 2.0 (* n PI)) 0.5))) (* (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI))))) (/ (* 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))) (pow (* 2.0 (* n PI)) 0.5))) (* (- (* 0.25 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 0.125 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) (/ (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (pow (* 2.0 (* n PI)) 0.5))))) into (* 0.020833333333333332 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 3)))
20.607 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
20.617 * [backup-simplify]: Simplify (+ (* 0 (* 0.020833333333333332 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 3)))) (+ (* +nan.0 (- (* 0.25 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 0.125 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) (+ (* +nan.0 (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI)))))) (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))) into (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))
20.617 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))) in n
20.617 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))) in n
20.617 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n
20.617 * [taylor]: Taking taylor expansion of +nan.0 in n
20.617 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.617 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n
20.617 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n
20.618 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
20.618 * [taylor]: Taking taylor expansion of 0.5 in n
20.618 * [backup-simplify]: Simplify 0.5 into 0.5
20.618 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
20.618 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
20.618 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
20.618 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.618 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.618 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.618 * [taylor]: Taking taylor expansion of 1.0 in n
20.618 * [backup-simplify]: Simplify 1.0 into 1.0
20.618 * [taylor]: Taking taylor expansion of (log PI) in n
20.618 * [taylor]: Taking taylor expansion of PI in n
20.618 * [backup-simplify]: Simplify PI into PI
20.619 * [backup-simplify]: Simplify (log PI) into (log PI)
20.620 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.621 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.621 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
20.621 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.622 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.622 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.622 * [taylor]: Taking taylor expansion of 1.0 in n
20.622 * [backup-simplify]: Simplify 1.0 into 1.0
20.622 * [taylor]: Taking taylor expansion of (log n) in n
20.622 * [taylor]: Taking taylor expansion of n in n
20.622 * [backup-simplify]: Simplify 0 into 0
20.622 * [backup-simplify]: Simplify 1 into 1
20.622 * [backup-simplify]: Simplify (log 1) into 0
20.623 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.623 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.623 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.623 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.623 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.623 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.623 * [taylor]: Taking taylor expansion of 1.0 in n
20.623 * [backup-simplify]: Simplify 1.0 into 1.0
20.623 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.623 * [taylor]: Taking taylor expansion of 2.0 in n
20.623 * [backup-simplify]: Simplify 2.0 into 2.0
20.623 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.624 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.626 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.627 * [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)
20.628 * [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)
20.629 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)
20.631 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))
20.632 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))
20.634 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.634 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))) in n
20.634 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))) in n
20.634 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n
20.634 * [taylor]: Taking taylor expansion of +nan.0 in n
20.634 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.634 * [taylor]: Taking taylor expansion of (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n
20.634 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) in n
20.634 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))))) in n
20.634 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
20.635 * [taylor]: Taking taylor expansion of 0.5 in n
20.635 * [backup-simplify]: Simplify 0.5 into 0.5
20.635 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
20.635 * [taylor]: Taking taylor expansion of (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
20.635 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
20.635 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.635 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.635 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.635 * [taylor]: Taking taylor expansion of 1.0 in n
20.635 * [backup-simplify]: Simplify 1.0 into 1.0
20.635 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.635 * [taylor]: Taking taylor expansion of 2.0 in n
20.635 * [backup-simplify]: Simplify 2.0 into 2.0
20.636 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.637 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.638 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.638 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
20.638 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.638 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.638 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.638 * [taylor]: Taking taylor expansion of 1.0 in n
20.639 * [backup-simplify]: Simplify 1.0 into 1.0
20.639 * [taylor]: Taking taylor expansion of (log PI) in n
20.639 * [taylor]: Taking taylor expansion of PI in n
20.639 * [backup-simplify]: Simplify PI into PI
20.639 * [backup-simplify]: Simplify (log PI) into (log PI)
20.640 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.642 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.642 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.642 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.642 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.642 * [taylor]: Taking taylor expansion of 1.0 in n
20.642 * [backup-simplify]: Simplify 1.0 into 1.0
20.642 * [taylor]: Taking taylor expansion of (log n) in n
20.642 * [taylor]: Taking taylor expansion of n in n
20.642 * [backup-simplify]: Simplify 0 into 0
20.642 * [backup-simplify]: Simplify 1 into 1
20.643 * [backup-simplify]: Simplify (log 1) into 0
20.643 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.643 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.643 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.644 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
20.646 * [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)
20.647 * [backup-simplify]: Simplify (/ 1 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0)
20.649 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0))
20.650 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0)))
20.652 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.652 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n
20.652 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
20.652 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.652 * [taylor]: Taking taylor expansion of 2.0 in n
20.652 * [backup-simplify]: Simplify 2.0 into 2.0
20.652 * [taylor]: Taking taylor expansion of (* n PI) in n
20.652 * [taylor]: Taking taylor expansion of n in n
20.652 * [backup-simplify]: Simplify 0 into 0
20.652 * [backup-simplify]: Simplify 1 into 1
20.652 * [taylor]: Taking taylor expansion of PI in n
20.652 * [backup-simplify]: Simplify PI into PI
20.653 * [backup-simplify]: Simplify (* 0 PI) into 0
20.653 * [backup-simplify]: Simplify (* 2.0 0) into 0
20.655 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.657 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
20.658 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.659 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.659 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))) in n
20.660 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))) in n
20.660 * [taylor]: Taking taylor expansion of (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) in n
20.660 * [taylor]: Taking taylor expansion of +nan.0 in n
20.660 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.660 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n
20.660 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
20.660 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.660 * [taylor]: Taking taylor expansion of 2.0 in n
20.660 * [backup-simplify]: Simplify 2.0 into 2.0
20.660 * [taylor]: Taking taylor expansion of (* n PI) in n
20.660 * [taylor]: Taking taylor expansion of n in n
20.660 * [backup-simplify]: Simplify 0 into 0
20.660 * [backup-simplify]: Simplify 1 into 1
20.660 * [taylor]: Taking taylor expansion of PI in n
20.660 * [backup-simplify]: Simplify PI into PI
20.661 * [backup-simplify]: Simplify (* 0 PI) into 0
20.661 * [backup-simplify]: Simplify (* 2.0 0) into 0
20.663 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.665 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
20.666 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.666 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n
20.666 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n
20.666 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
20.666 * [taylor]: Taking taylor expansion of 0.5 in n
20.666 * [backup-simplify]: Simplify 0.5 into 0.5
20.666 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
20.666 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
20.666 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
20.666 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.666 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.666 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.666 * [taylor]: Taking taylor expansion of 1.0 in n
20.666 * [backup-simplify]: Simplify 1.0 into 1.0
20.666 * [taylor]: Taking taylor expansion of (log PI) in n
20.666 * [taylor]: Taking taylor expansion of PI in n
20.666 * [backup-simplify]: Simplify PI into PI
20.667 * [backup-simplify]: Simplify (log PI) into (log PI)
20.668 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.669 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.669 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
20.670 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.670 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.670 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.670 * [taylor]: Taking taylor expansion of 1.0 in n
20.670 * [backup-simplify]: Simplify 1.0 into 1.0
20.670 * [taylor]: Taking taylor expansion of (log n) in n
20.670 * [taylor]: Taking taylor expansion of n in n
20.670 * [backup-simplify]: Simplify 0 into 0
20.670 * [backup-simplify]: Simplify 1 into 1
20.670 * [backup-simplify]: Simplify (log 1) into 0
20.671 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.671 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.671 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.671 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.671 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.671 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.671 * [taylor]: Taking taylor expansion of 1.0 in n
20.671 * [backup-simplify]: Simplify 1.0 into 1.0
20.671 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.671 * [taylor]: Taking taylor expansion of 2.0 in n
20.671 * [backup-simplify]: Simplify 2.0 into 2.0
20.672 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.673 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.674 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.675 * [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)
20.677 * [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)
20.678 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)
20.679 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))
20.681 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))
20.683 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.683 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))) in n
20.683 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) in n
20.683 * [taylor]: Taking taylor expansion of +nan.0 in n
20.683 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.683 * [taylor]: Taking taylor expansion of (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n
20.683 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n
20.683 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
20.683 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.683 * [taylor]: Taking taylor expansion of 2.0 in n
20.683 * [backup-simplify]: Simplify 2.0 into 2.0
20.683 * [taylor]: Taking taylor expansion of (* n PI) in n
20.683 * [taylor]: Taking taylor expansion of n in n
20.683 * [backup-simplify]: Simplify 0 into 0
20.683 * [backup-simplify]: Simplify 1 into 1
20.683 * [taylor]: Taking taylor expansion of PI in n
20.683 * [backup-simplify]: Simplify PI into PI
20.684 * [backup-simplify]: Simplify (* 0 PI) into 0
20.684 * [backup-simplify]: Simplify (* 2.0 0) into 0
20.686 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.687 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
20.688 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.690 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.690 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n
20.690 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n
20.690 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
20.690 * [taylor]: Taking taylor expansion of 0.5 in n
20.690 * [backup-simplify]: Simplify 0.5 into 0.5
20.690 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
20.690 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
20.690 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
20.690 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.690 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.690 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.690 * [taylor]: Taking taylor expansion of 1.0 in n
20.690 * [backup-simplify]: Simplify 1.0 into 1.0
20.690 * [taylor]: Taking taylor expansion of (log PI) in n
20.690 * [taylor]: Taking taylor expansion of PI in n
20.691 * [backup-simplify]: Simplify PI into PI
20.691 * [backup-simplify]: Simplify (log PI) into (log PI)
20.692 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.694 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.694 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
20.694 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.694 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.694 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.694 * [taylor]: Taking taylor expansion of 1.0 in n
20.694 * [backup-simplify]: Simplify 1.0 into 1.0
20.694 * [taylor]: Taking taylor expansion of (log n) in n
20.694 * [taylor]: Taking taylor expansion of n in n
20.694 * [backup-simplify]: Simplify 0 into 0
20.694 * [backup-simplify]: Simplify 1 into 1
20.695 * [backup-simplify]: Simplify (log 1) into 0
20.695 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.695 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.695 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.695 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.695 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.695 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.695 * [taylor]: Taking taylor expansion of 1.0 in n
20.695 * [backup-simplify]: Simplify 1.0 into 1.0
20.695 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.695 * [taylor]: Taking taylor expansion of 2.0 in n
20.695 * [backup-simplify]: Simplify 2.0 into 2.0
20.696 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.697 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.698 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.699 * [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)
20.700 * [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)
20.702 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)
20.703 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))
20.704 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))
20.706 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.708 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))
20.709 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.711 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.713 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2)
20.723 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))
20.726 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (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 (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)))
20.728 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.731 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))
20.734 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))
20.735 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.737 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.739 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2)
20.742 * [backup-simplify]: Simplify (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))
20.745 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))
20.748 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))
20.761 * [backup-simplify]: Simplify (+ (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))
20.779 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))
20.800 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))
20.823 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))
20.849 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))))
20.875 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))))
20.903 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))))
20.939 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))))))))) (pow (* 1 k) 3)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 1 k)))) into (- (+ (* +nan.0 (* (pow k 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log (* 2.0 PI)) 2)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow k 3) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log (* 2.0 PI)) 2)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (log (* 2.0 PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* k (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (log n)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log n) 2)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (* (pow k 3) (* (log (* 2.0 PI)) (log n))) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))))))))))))))))))))))))
20.940 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))))
20.940 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0
20.940 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n
20.940 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
20.940 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.940 * [taylor]: Taking taylor expansion of k in n
20.940 * [backup-simplify]: Simplify k into k
20.941 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.941 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
20.941 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.941 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
20.941 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
20.941 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
20.941 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
20.941 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
20.941 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
20.941 * [taylor]: Taking taylor expansion of 0.5 in n
20.941 * [backup-simplify]: Simplify 0.5 into 0.5
20.941 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
20.941 * [taylor]: Taking taylor expansion of 1.0 in n
20.941 * [backup-simplify]: Simplify 1.0 into 1.0
20.941 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.941 * [taylor]: Taking taylor expansion of k in n
20.941 * [backup-simplify]: Simplify k into k
20.941 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.941 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
20.941 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.941 * [taylor]: Taking taylor expansion of 2.0 in n
20.942 * [backup-simplify]: Simplify 2.0 into 2.0
20.942 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.942 * [taylor]: Taking taylor expansion of PI in n
20.942 * [backup-simplify]: Simplify PI into PI
20.942 * [taylor]: Taking taylor expansion of n in n
20.942 * [backup-simplify]: Simplify 0 into 0
20.942 * [backup-simplify]: Simplify 1 into 1
20.942 * [backup-simplify]: Simplify (/ PI 1) into PI
20.943 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.944 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.944 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.944 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
20.944 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
20.946 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.947 * [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))))
20.948 * [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)))))
20.949 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
20.949 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
20.949 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
20.949 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.949 * [taylor]: Taking taylor expansion of k in k
20.949 * [backup-simplify]: Simplify 0 into 0
20.949 * [backup-simplify]: Simplify 1 into 1
20.950 * [backup-simplify]: Simplify (/ 1 1) into 1
20.950 * [backup-simplify]: Simplify (sqrt 0) into 0
20.951 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.952 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
20.952 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
20.952 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
20.952 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
20.952 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
20.952 * [taylor]: Taking taylor expansion of 0.5 in k
20.952 * [backup-simplify]: Simplify 0.5 into 0.5
20.952 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
20.952 * [taylor]: Taking taylor expansion of 1.0 in k
20.952 * [backup-simplify]: Simplify 1.0 into 1.0
20.952 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.952 * [taylor]: Taking taylor expansion of k in k
20.952 * [backup-simplify]: Simplify 0 into 0
20.952 * [backup-simplify]: Simplify 1 into 1
20.953 * [backup-simplify]: Simplify (/ 1 1) into 1
20.953 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
20.953 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
20.953 * [taylor]: Taking taylor expansion of 2.0 in k
20.953 * [backup-simplify]: Simplify 2.0 into 2.0
20.953 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.953 * [taylor]: Taking taylor expansion of PI in k
20.953 * [backup-simplify]: Simplify PI into PI
20.953 * [taylor]: Taking taylor expansion of n in k
20.953 * [backup-simplify]: Simplify n into n
20.953 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.953 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
20.953 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
20.953 * [backup-simplify]: Simplify (- 1) into -1
20.954 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.954 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
20.954 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
20.954 * [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)))))
20.955 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))
20.955 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
20.955 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
20.955 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.955 * [taylor]: Taking taylor expansion of k in k
20.955 * [backup-simplify]: Simplify 0 into 0
20.955 * [backup-simplify]: Simplify 1 into 1
20.955 * [backup-simplify]: Simplify (/ 1 1) into 1
20.956 * [backup-simplify]: Simplify (sqrt 0) into 0
20.957 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.957 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
20.957 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
20.957 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
20.957 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
20.957 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
20.957 * [taylor]: Taking taylor expansion of 0.5 in k
20.957 * [backup-simplify]: Simplify 0.5 into 0.5
20.957 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
20.957 * [taylor]: Taking taylor expansion of 1.0 in k
20.957 * [backup-simplify]: Simplify 1.0 into 1.0
20.957 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.957 * [taylor]: Taking taylor expansion of k in k
20.957 * [backup-simplify]: Simplify 0 into 0
20.957 * [backup-simplify]: Simplify 1 into 1
20.957 * [backup-simplify]: Simplify (/ 1 1) into 1
20.957 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
20.957 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
20.957 * [taylor]: Taking taylor expansion of 2.0 in k
20.957 * [backup-simplify]: Simplify 2.0 into 2.0
20.957 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.957 * [taylor]: Taking taylor expansion of PI in k
20.957 * [backup-simplify]: Simplify PI into PI
20.957 * [taylor]: Taking taylor expansion of n in k
20.957 * [backup-simplify]: Simplify n into n
20.958 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.958 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
20.958 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
20.958 * [backup-simplify]: Simplify (- 1) into -1
20.959 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.959 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
20.959 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
20.959 * [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)))))
20.960 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))
20.960 * [backup-simplify]: Simplify (* 0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) into 0
20.960 * [taylor]: Taking taylor expansion of 0 in n
20.960 * [backup-simplify]: Simplify 0 into 0
20.960 * [backup-simplify]: Simplify 0 into 0
20.961 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into 0
20.962 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))
20.962 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) in n
20.962 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
20.962 * [taylor]: Taking taylor expansion of +nan.0 in n
20.962 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.962 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
20.962 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
20.962 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
20.962 * [taylor]: Taking taylor expansion of 0.5 in n
20.962 * [backup-simplify]: Simplify 0.5 into 0.5
20.962 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
20.962 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
20.962 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.962 * [taylor]: Taking taylor expansion of 2.0 in n
20.962 * [backup-simplify]: Simplify 2.0 into 2.0
20.962 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.962 * [taylor]: Taking taylor expansion of PI in n
20.962 * [backup-simplify]: Simplify PI into PI
20.962 * [taylor]: Taking taylor expansion of n in n
20.962 * [backup-simplify]: Simplify 0 into 0
20.962 * [backup-simplify]: Simplify 1 into 1
20.963 * [backup-simplify]: Simplify (/ PI 1) into PI
20.963 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.964 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.964 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
20.964 * [taylor]: Taking taylor expansion of 1.0 in n
20.964 * [backup-simplify]: Simplify 1.0 into 1.0
20.964 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.964 * [taylor]: Taking taylor expansion of k in n
20.964 * [backup-simplify]: Simplify k into k
20.964 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.966 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.966 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.966 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
20.967 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
20.968 * [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))))
20.969 * [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)))))
20.971 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
20.972 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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))))))
20.973 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))
20.974 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))
20.975 * [backup-simplify]: Simplify 0 into 0
20.975 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) (* 0 (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into 0
20.976 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
20.979 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
20.980 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))
20.980 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) in n
20.980 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
20.980 * [taylor]: Taking taylor expansion of +nan.0 in n
20.980 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.980 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
20.980 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
20.980 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
20.980 * [taylor]: Taking taylor expansion of 0.5 in n
20.980 * [backup-simplify]: Simplify 0.5 into 0.5
20.980 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
20.980 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
20.980 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.980 * [taylor]: Taking taylor expansion of 2.0 in n
20.980 * [backup-simplify]: Simplify 2.0 into 2.0
20.980 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.980 * [taylor]: Taking taylor expansion of PI in n
20.980 * [backup-simplify]: Simplify PI into PI
20.980 * [taylor]: Taking taylor expansion of n in n
20.980 * [backup-simplify]: Simplify 0 into 0
20.980 * [backup-simplify]: Simplify 1 into 1
20.981 * [backup-simplify]: Simplify (/ PI 1) into PI
20.981 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.982 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.982 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
20.982 * [taylor]: Taking taylor expansion of 1.0 in n
20.982 * [backup-simplify]: Simplify 1.0 into 1.0
20.982 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.982 * [taylor]: Taking taylor expansion of k in n
20.982 * [backup-simplify]: Simplify k into k
20.982 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.983 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.984 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.984 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
20.985 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
20.986 * [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))))
20.987 * [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)))))
20.988 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
20.990 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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))))))
20.991 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))
20.993 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))
20.994 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.995 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.995 * [backup-simplify]: Simplify (- 0) into 0
20.995 * [backup-simplify]: Simplify (+ 0 0) into 0
20.996 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.997 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
20.999 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
21.000 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0
21.002 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0
21.004 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
21.008 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) (/ 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into 0
21.010 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0
21.010 * [backup-simplify]: Simplify (- 0) into 0
21.010 * [backup-simplify]: Simplify 0 into 0
21.010 * [backup-simplify]: Simplify 0 into 0
21.011 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) (* 0 (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) (* 0 (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into 0
21.012 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
21.015 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
21.017 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))
21.017 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) in n
21.017 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
21.017 * [taylor]: Taking taylor expansion of +nan.0 in n
21.017 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.017 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
21.017 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
21.017 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
21.017 * [taylor]: Taking taylor expansion of 0.5 in n
21.017 * [backup-simplify]: Simplify 0.5 into 0.5
21.017 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
21.017 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
21.017 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
21.017 * [taylor]: Taking taylor expansion of 2.0 in n
21.017 * [backup-simplify]: Simplify 2.0 into 2.0
21.017 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.017 * [taylor]: Taking taylor expansion of PI in n
21.017 * [backup-simplify]: Simplify PI into PI
21.017 * [taylor]: Taking taylor expansion of n in n
21.017 * [backup-simplify]: Simplify 0 into 0
21.017 * [backup-simplify]: Simplify 1 into 1
21.018 * [backup-simplify]: Simplify (/ PI 1) into PI
21.018 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
21.019 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.019 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
21.019 * [taylor]: Taking taylor expansion of 1.0 in n
21.019 * [backup-simplify]: Simplify 1.0 into 1.0
21.019 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.019 * [taylor]: Taking taylor expansion of k in n
21.019 * [backup-simplify]: Simplify k into k
21.019 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.021 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
21.021 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
21.021 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
21.023 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
21.025 * [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))))
21.026 * [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)))))
21.028 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
21.029 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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))))))
21.030 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))
21.039 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))
21.043 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k))))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k))))))))))) into (- (+ (* +nan.0 (/ 1 (* k (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))))) (- (+ (* +nan.0 (/ 1 (* (pow k 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))))) (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))))))))))
21.045 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))))
21.045 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in (k n) around 0
21.045 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in n
21.045 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
21.045 * [taylor]: Taking taylor expansion of (/ -1 k) in n
21.045 * [taylor]: Taking taylor expansion of -1 in n
21.045 * [backup-simplify]: Simplify -1 into -1
21.045 * [taylor]: Taking taylor expansion of k in n
21.045 * [backup-simplify]: Simplify k into k
21.045 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
21.045 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
21.045 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
21.045 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
21.045 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
21.045 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
21.045 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
21.046 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
21.046 * [taylor]: Taking taylor expansion of 0.5 in n
21.046 * [backup-simplify]: Simplify 0.5 into 0.5
21.046 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.046 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.046 * [taylor]: Taking taylor expansion of k in n
21.046 * [backup-simplify]: Simplify k into k
21.046 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.046 * [taylor]: Taking taylor expansion of 1.0 in n
21.046 * [backup-simplify]: Simplify 1.0 into 1.0
21.046 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.046 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.046 * [taylor]: Taking taylor expansion of -2.0 in n
21.046 * [backup-simplify]: Simplify -2.0 into -2.0
21.046 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.046 * [taylor]: Taking taylor expansion of PI in n
21.046 * [backup-simplify]: Simplify PI into PI
21.046 * [taylor]: Taking taylor expansion of n in n
21.046 * [backup-simplify]: Simplify 0 into 0
21.046 * [backup-simplify]: Simplify 1 into 1
21.047 * [backup-simplify]: Simplify (/ PI 1) into PI
21.047 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.048 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.048 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.048 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
21.050 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.051 * [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))))
21.052 * [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)))))
21.054 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (/ (sqrt (/ -1 k)) (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
21.054 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in k
21.054 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
21.054 * [taylor]: Taking taylor expansion of (/ -1 k) in k
21.054 * [taylor]: Taking taylor expansion of -1 in k
21.054 * [backup-simplify]: Simplify -1 into -1
21.054 * [taylor]: Taking taylor expansion of k in k
21.054 * [backup-simplify]: Simplify 0 into 0
21.054 * [backup-simplify]: Simplify 1 into 1
21.055 * [backup-simplify]: Simplify (/ -1 1) into -1
21.055 * [backup-simplify]: Simplify (sqrt 0) into 0
21.056 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
21.056 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
21.056 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
21.057 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
21.057 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
21.057 * [taylor]: Taking taylor expansion of 0.5 in k
21.057 * [backup-simplify]: Simplify 0.5 into 0.5
21.057 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
21.057 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.057 * [taylor]: Taking taylor expansion of k in k
21.057 * [backup-simplify]: Simplify 0 into 0
21.057 * [backup-simplify]: Simplify 1 into 1
21.057 * [backup-simplify]: Simplify (/ 1 1) into 1
21.057 * [taylor]: Taking taylor expansion of 1.0 in k
21.057 * [backup-simplify]: Simplify 1.0 into 1.0
21.057 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
21.057 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
21.057 * [taylor]: Taking taylor expansion of -2.0 in k
21.057 * [backup-simplify]: Simplify -2.0 into -2.0
21.057 * [taylor]: Taking taylor expansion of (/ PI n) in k
21.057 * [taylor]: Taking taylor expansion of PI in k
21.057 * [backup-simplify]: Simplify PI into PI
21.057 * [taylor]: Taking taylor expansion of n in k
21.057 * [backup-simplify]: Simplify n into n
21.057 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
21.058 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
21.058 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
21.058 * [backup-simplify]: Simplify (+ 1 0) into 1
21.059 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
21.059 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
21.059 * [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))))))
21.059 * [backup-simplify]: Simplify (/ +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)))))))
21.059 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in k
21.059 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
21.059 * [taylor]: Taking taylor expansion of (/ -1 k) in k
21.059 * [taylor]: Taking taylor expansion of -1 in k
21.059 * [backup-simplify]: Simplify -1 into -1
21.059 * [taylor]: Taking taylor expansion of k in k
21.059 * [backup-simplify]: Simplify 0 into 0
21.059 * [backup-simplify]: Simplify 1 into 1
21.063 * [backup-simplify]: Simplify (/ -1 1) into -1
21.063 * [backup-simplify]: Simplify (sqrt 0) into 0
21.064 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
21.064 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
21.064 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
21.064 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
21.065 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
21.065 * [taylor]: Taking taylor expansion of 0.5 in k
21.065 * [backup-simplify]: Simplify 0.5 into 0.5
21.065 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
21.065 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.065 * [taylor]: Taking taylor expansion of k in k
21.065 * [backup-simplify]: Simplify 0 into 0
21.065 * [backup-simplify]: Simplify 1 into 1
21.065 * [backup-simplify]: Simplify (/ 1 1) into 1
21.065 * [taylor]: Taking taylor expansion of 1.0 in k
21.065 * [backup-simplify]: Simplify 1.0 into 1.0
21.065 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
21.065 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
21.065 * [taylor]: Taking taylor expansion of -2.0 in k
21.065 * [backup-simplify]: Simplify -2.0 into -2.0
21.065 * [taylor]: Taking taylor expansion of (/ PI n) in k
21.065 * [taylor]: Taking taylor expansion of PI in k
21.065 * [backup-simplify]: Simplify PI into PI
21.065 * [taylor]: Taking taylor expansion of n in k
21.065 * [backup-simplify]: Simplify n into n
21.065 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
21.066 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
21.066 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
21.067 * [backup-simplify]: Simplify (+ 1 0) into 1
21.067 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
21.067 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
21.068 * [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))))))
21.068 * [backup-simplify]: Simplify (/ +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)))))))
21.068 * [taylor]: Taking taylor expansion of (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
21.068 * [taylor]: Taking taylor expansion of +nan.0 in n
21.068 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.068 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
21.068 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
21.068 * [taylor]: Taking taylor expansion of 0.5 in n
21.068 * [backup-simplify]: Simplify 0.5 into 0.5
21.068 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
21.068 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.068 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.068 * [taylor]: Taking taylor expansion of k in n
21.068 * [backup-simplify]: Simplify k into k
21.068 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.068 * [taylor]: Taking taylor expansion of 1.0 in n
21.068 * [backup-simplify]: Simplify 1.0 into 1.0
21.068 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.069 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.069 * [taylor]: Taking taylor expansion of -2.0 in n
21.069 * [backup-simplify]: Simplify -2.0 into -2.0
21.069 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.069 * [taylor]: Taking taylor expansion of PI in n
21.069 * [backup-simplify]: Simplify PI into PI
21.069 * [taylor]: Taking taylor expansion of n in n
21.069 * [backup-simplify]: Simplify 0 into 0
21.069 * [backup-simplify]: Simplify 1 into 1
21.069 * [backup-simplify]: Simplify (/ PI 1) into PI
21.070 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.071 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.071 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.072 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.073 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
21.074 * [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))))
21.076 * [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)))))
21.077 * [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))))))
21.078 * [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))))))
21.079 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
21.082 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
21.083 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (+ (* (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))
21.083 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) in n
21.083 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
21.083 * [taylor]: Taking taylor expansion of +nan.0 in n
21.083 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.083 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
21.083 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
21.083 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
21.083 * [taylor]: Taking taylor expansion of 0.5 in n
21.083 * [backup-simplify]: Simplify 0.5 into 0.5
21.083 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
21.083 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.083 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.083 * [taylor]: Taking taylor expansion of k in n
21.083 * [backup-simplify]: Simplify k into k
21.083 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.084 * [taylor]: Taking taylor expansion of 1.0 in n
21.084 * [backup-simplify]: Simplify 1.0 into 1.0
21.084 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.084 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.084 * [taylor]: Taking taylor expansion of -2.0 in n
21.084 * [backup-simplify]: Simplify -2.0 into -2.0
21.084 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.084 * [taylor]: Taking taylor expansion of PI in n
21.084 * [backup-simplify]: Simplify PI into PI
21.084 * [taylor]: Taking taylor expansion of n in n
21.084 * [backup-simplify]: Simplify 0 into 0
21.084 * [backup-simplify]: Simplify 1 into 1
21.085 * [backup-simplify]: Simplify (/ PI 1) into PI
21.086 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.087 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.087 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.088 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.090 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
21.091 * [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))))
21.093 * [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)))))
21.095 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
21.096 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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))))))
21.097 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))
21.099 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))
21.100 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
21.101 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
21.103 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
21.104 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
21.104 * [backup-simplify]: Simplify (+ 0 0) into 0
21.106 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.116 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
21.118 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0
21.120 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
21.125 * [backup-simplify]: Simplify (- (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) (+ (* (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))) into 0
21.126 * [backup-simplify]: Simplify 0 into 0
21.127 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
21.131 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
21.132 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (+ (* (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) (* (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))
21.132 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) in n
21.132 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
21.132 * [taylor]: Taking taylor expansion of +nan.0 in n
21.132 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.132 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
21.132 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
21.132 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
21.132 * [taylor]: Taking taylor expansion of 0.5 in n
21.132 * [backup-simplify]: Simplify 0.5 into 0.5
21.132 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
21.132 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.132 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.132 * [taylor]: Taking taylor expansion of k in n
21.132 * [backup-simplify]: Simplify k into k
21.132 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.133 * [taylor]: Taking taylor expansion of 1.0 in n
21.133 * [backup-simplify]: Simplify 1.0 into 1.0
21.133 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.133 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.133 * [taylor]: Taking taylor expansion of -2.0 in n
21.133 * [backup-simplify]: Simplify -2.0 into -2.0
21.133 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.133 * [taylor]: Taking taylor expansion of PI in n
21.133 * [backup-simplify]: Simplify PI into PI
21.133 * [taylor]: Taking taylor expansion of n in n
21.133 * [backup-simplify]: Simplify 0 into 0
21.133 * [backup-simplify]: Simplify 1 into 1
21.133 * [backup-simplify]: Simplify (/ PI 1) into PI
21.134 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.135 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.135 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.136 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.137 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
21.138 * [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))))
21.139 * [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)))))
21.140 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
21.141 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (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))))))
21.142 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))
21.143 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))
21.148 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (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 (/ 1 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ 1 (* k (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))) (- (* +nan.0 (/ 1 (* (pow k 2) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))))))))
21.148 * * * * [progress]: [ 4 / 4 ] generating series at (2)
21.150 * [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)))))
21.150 * [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
21.150 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n
21.150 * [taylor]: Taking taylor expansion of 1.0 in n
21.150 * [backup-simplify]: Simplify 1.0 into 1.0
21.150 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n
21.150 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
21.150 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.150 * [taylor]: Taking taylor expansion of k in n
21.150 * [backup-simplify]: Simplify k into k
21.150 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.150 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
21.150 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
21.150 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
21.150 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
21.150 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
21.150 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
21.150 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
21.150 * [taylor]: Taking taylor expansion of 0.5 in n
21.151 * [backup-simplify]: Simplify 0.5 into 0.5
21.151 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
21.151 * [taylor]: Taking taylor expansion of 1.0 in n
21.151 * [backup-simplify]: Simplify 1.0 into 1.0
21.151 * [taylor]: Taking taylor expansion of k in n
21.151 * [backup-simplify]: Simplify k into k
21.151 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
21.151 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
21.151 * [taylor]: Taking taylor expansion of 2.0 in n
21.151 * [backup-simplify]: Simplify 2.0 into 2.0
21.151 * [taylor]: Taking taylor expansion of (* n PI) in n
21.151 * [taylor]: Taking taylor expansion of n in n
21.151 * [backup-simplify]: Simplify 0 into 0
21.151 * [backup-simplify]: Simplify 1 into 1
21.151 * [taylor]: Taking taylor expansion of PI in n
21.151 * [backup-simplify]: Simplify PI into PI
21.152 * [backup-simplify]: Simplify (* 0 PI) into 0
21.153 * [backup-simplify]: Simplify (* 2.0 0) into 0
21.154 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
21.156 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
21.157 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.157 * [backup-simplify]: Simplify (- k) into (- k)
21.157 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
21.157 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
21.159 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
21.160 * [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))))
21.161 * [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)))))
21.161 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
21.161 * [taylor]: Taking taylor expansion of 1.0 in k
21.161 * [backup-simplify]: Simplify 1.0 into 1.0
21.161 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
21.161 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
21.161 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.161 * [taylor]: Taking taylor expansion of k in k
21.161 * [backup-simplify]: Simplify 0 into 0
21.161 * [backup-simplify]: Simplify 1 into 1
21.162 * [backup-simplify]: Simplify (/ 1 1) into 1
21.162 * [backup-simplify]: Simplify (sqrt 0) into 0
21.163 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
21.164 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
21.164 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
21.164 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
21.164 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
21.164 * [taylor]: Taking taylor expansion of 0.5 in k
21.164 * [backup-simplify]: Simplify 0.5 into 0.5
21.164 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
21.164 * [taylor]: Taking taylor expansion of 1.0 in k
21.164 * [backup-simplify]: Simplify 1.0 into 1.0
21.164 * [taylor]: Taking taylor expansion of k in k
21.164 * [backup-simplify]: Simplify 0 into 0
21.164 * [backup-simplify]: Simplify 1 into 1
21.164 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
21.164 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
21.164 * [taylor]: Taking taylor expansion of 2.0 in k
21.164 * [backup-simplify]: Simplify 2.0 into 2.0
21.164 * [taylor]: Taking taylor expansion of (* n PI) in k
21.164 * [taylor]: Taking taylor expansion of n in k
21.164 * [backup-simplify]: Simplify n into n
21.164 * [taylor]: Taking taylor expansion of PI in k
21.164 * [backup-simplify]: Simplify PI into PI
21.164 * [backup-simplify]: Simplify (* n PI) into (* n PI)
21.164 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
21.164 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
21.165 * [backup-simplify]: Simplify (- 0) into 0
21.165 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
21.166 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
21.166 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
21.166 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
21.166 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
21.166 * [taylor]: Taking taylor expansion of 1.0 in k
21.166 * [backup-simplify]: Simplify 1.0 into 1.0
21.166 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
21.166 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
21.166 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.166 * [taylor]: Taking taylor expansion of k in k
21.166 * [backup-simplify]: Simplify 0 into 0
21.166 * [backup-simplify]: Simplify 1 into 1
21.167 * [backup-simplify]: Simplify (/ 1 1) into 1
21.167 * [backup-simplify]: Simplify (sqrt 0) into 0
21.168 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
21.168 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
21.168 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
21.169 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
21.169 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
21.169 * [taylor]: Taking taylor expansion of 0.5 in k
21.169 * [backup-simplify]: Simplify 0.5 into 0.5
21.169 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
21.169 * [taylor]: Taking taylor expansion of 1.0 in k
21.169 * [backup-simplify]: Simplify 1.0 into 1.0
21.169 * [taylor]: Taking taylor expansion of k in k
21.169 * [backup-simplify]: Simplify 0 into 0
21.169 * [backup-simplify]: Simplify 1 into 1
21.169 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
21.169 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
21.169 * [taylor]: Taking taylor expansion of 2.0 in k
21.169 * [backup-simplify]: Simplify 2.0 into 2.0
21.169 * [taylor]: Taking taylor expansion of (* n PI) in k
21.169 * [taylor]: Taking taylor expansion of n in k
21.169 * [backup-simplify]: Simplify n into n
21.169 * [taylor]: Taking taylor expansion of PI in k
21.169 * [backup-simplify]: Simplify PI into PI
21.169 * [backup-simplify]: Simplify (* n PI) into (* n PI)
21.169 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
21.169 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
21.170 * [backup-simplify]: Simplify (- 0) into 0
21.170 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
21.171 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
21.171 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
21.171 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
21.171 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0
21.172 * [backup-simplify]: Simplify (* 1.0 0) into 0
21.172 * [taylor]: Taking taylor expansion of 0 in n
21.172 * [backup-simplify]: Simplify 0 into 0
21.172 * [backup-simplify]: Simplify 0 into 0
21.172 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
21.173 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0
21.174 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0
21.174 * [backup-simplify]: Simplify (- 1) into -1
21.175 * [backup-simplify]: Simplify (+ 0 -1) into -1
21.176 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5)
21.177 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI)))))
21.178 * [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)))
21.179 * [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)))
21.182 * [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)))
21.182 * [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
21.182 * [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
21.182 * [taylor]: Taking taylor expansion of +nan.0 in n
21.182 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.182 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
21.182 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
21.182 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
21.182 * [taylor]: Taking taylor expansion of 0.5 in n
21.182 * [backup-simplify]: Simplify 0.5 into 0.5
21.182 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
21.182 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
21.182 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
21.182 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
21.182 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
21.182 * [taylor]: Taking taylor expansion of 1.0 in n
21.182 * [backup-simplify]: Simplify 1.0 into 1.0
21.182 * [taylor]: Taking taylor expansion of (log PI) in n
21.182 * [taylor]: Taking taylor expansion of PI in n
21.182 * [backup-simplify]: Simplify PI into PI
21.183 * [backup-simplify]: Simplify (log PI) into (log PI)
21.184 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
21.186 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
21.186 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
21.186 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
21.186 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
21.186 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
21.186 * [taylor]: Taking taylor expansion of 1.0 in n
21.186 * [backup-simplify]: Simplify 1.0 into 1.0
21.186 * [taylor]: Taking taylor expansion of (log n) in n
21.186 * [taylor]: Taking taylor expansion of n in n
21.186 * [backup-simplify]: Simplify 0 into 0
21.186 * [backup-simplify]: Simplify 1 into 1
21.187 * [backup-simplify]: Simplify (log 1) into 0
21.187 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
21.187 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
21.187 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
21.187 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
21.187 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
21.187 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
21.187 * [taylor]: Taking taylor expansion of 1.0 in n
21.187 * [backup-simplify]: Simplify 1.0 into 1.0
21.187 * [taylor]: Taking taylor expansion of (log 2.0) in n
21.187 * [taylor]: Taking taylor expansion of 2.0 in n
21.188 * [backup-simplify]: Simplify 2.0 into 2.0
21.188 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
21.189 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
21.190 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
21.191 * [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)
21.193 * [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)
21.194 * [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))
21.196 * [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)))
21.198 * [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)
21.200 * [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))
21.201 * [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)))
21.203 * [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)))
21.203 * [backup-simplify]: Simplify 0 into 0
21.204 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
21.205 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
21.207 * [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
21.208 * [backup-simplify]: Simplify (- 0) into 0
21.208 * [backup-simplify]: Simplify (+ 0 0) into 0
21.209 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0
21.210 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0
21.218 * [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)))
21.219 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
21.223 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
21.227 * [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))))))))
21.232 * [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))))))))
21.232 * [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
21.232 * [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
21.232 * [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
21.232 * [taylor]: Taking taylor expansion of +nan.0 in n
21.232 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.232 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
21.232 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
21.232 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
21.233 * [taylor]: Taking taylor expansion of 0.5 in n
21.233 * [backup-simplify]: Simplify 0.5 into 0.5
21.233 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
21.233 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
21.233 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
21.233 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
21.233 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
21.233 * [taylor]: Taking taylor expansion of 1.0 in n
21.233 * [backup-simplify]: Simplify 1.0 into 1.0
21.233 * [taylor]: Taking taylor expansion of (log PI) in n
21.233 * [taylor]: Taking taylor expansion of PI in n
21.233 * [backup-simplify]: Simplify PI into PI
21.234 * [backup-simplify]: Simplify (log PI) into (log PI)
21.235 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
21.237 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
21.237 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
21.237 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
21.237 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
21.237 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
21.237 * [taylor]: Taking taylor expansion of 1.0 in n
21.237 * [backup-simplify]: Simplify 1.0 into 1.0
21.237 * [taylor]: Taking taylor expansion of (log n) in n
21.237 * [taylor]: Taking taylor expansion of n in n
21.237 * [backup-simplify]: Simplify 0 into 0
21.237 * [backup-simplify]: Simplify 1 into 1
21.237 * [backup-simplify]: Simplify (log 1) into 0
21.238 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
21.238 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
21.238 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
21.238 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
21.238 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
21.238 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
21.238 * [taylor]: Taking taylor expansion of 1.0 in n
21.238 * [backup-simplify]: Simplify 1.0 into 1.0
21.238 * [taylor]: Taking taylor expansion of (log 2.0) in n
21.238 * [taylor]: Taking taylor expansion of 2.0 in n
21.238 * [backup-simplify]: Simplify 2.0 into 2.0
21.239 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
21.240 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
21.241 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
21.242 * [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)
21.243 * [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)
21.245 * [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))
21.246 * [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)))
21.248 * [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)
21.248 * [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
21.248 * [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
21.248 * [taylor]: Taking taylor expansion of +nan.0 in n
21.248 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.248 * [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
21.248 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
21.248 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
21.248 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
21.248 * [taylor]: Taking taylor expansion of 0.5 in n
21.248 * [backup-simplify]: Simplify 0.5 into 0.5
21.248 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
21.248 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
21.248 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
21.248 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
21.248 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
21.248 * [taylor]: Taking taylor expansion of 1.0 in n
21.248 * [backup-simplify]: Simplify 1.0 into 1.0
21.248 * [taylor]: Taking taylor expansion of (log 2.0) in n
21.248 * [taylor]: Taking taylor expansion of 2.0 in n
21.248 * [backup-simplify]: Simplify 2.0 into 2.0
21.249 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
21.250 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
21.251 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
21.251 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
21.251 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
21.251 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
21.251 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
21.251 * [taylor]: Taking taylor expansion of 1.0 in n
21.251 * [backup-simplify]: Simplify 1.0 into 1.0
21.251 * [taylor]: Taking taylor expansion of (log PI) in n
21.252 * [taylor]: Taking taylor expansion of PI in n
21.252 * [backup-simplify]: Simplify PI into PI
21.252 * [backup-simplify]: Simplify (log PI) into (log PI)
21.253 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
21.255 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
21.255 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
21.255 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
21.255 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
21.255 * [taylor]: Taking taylor expansion of 1.0 in n
21.255 * [backup-simplify]: Simplify 1.0 into 1.0
21.255 * [taylor]: Taking taylor expansion of (log n) in n
21.255 * [taylor]: Taking taylor expansion of n in n
21.255 * [backup-simplify]: Simplify 0 into 0
21.255 * [backup-simplify]: Simplify 1 into 1
21.256 * [backup-simplify]: Simplify (log 1) into 0
21.256 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
21.256 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
21.257 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
21.257 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
21.259 * [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)
21.260 * [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))
21.262 * [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)))
21.264 * [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)
21.264 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
21.264 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
21.264 * [taylor]: Taking taylor expansion of 2.0 in n
21.264 * [backup-simplify]: Simplify 2.0 into 2.0
21.264 * [taylor]: Taking taylor expansion of (* n PI) in n
21.264 * [taylor]: Taking taylor expansion of n in n
21.264 * [backup-simplify]: Simplify 0 into 0
21.264 * [backup-simplify]: Simplify 1 into 1
21.264 * [taylor]: Taking taylor expansion of PI in n
21.264 * [backup-simplify]: Simplify PI into PI
21.265 * [backup-simplify]: Simplify (* 0 PI) into 0
21.266 * [backup-simplify]: Simplify (* 2.0 0) into 0
21.267 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
21.269 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
21.270 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.272 * [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))
21.273 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
21.276 * [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))
21.279 * [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)))
21.282 * [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))))))
21.289 * [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))))))))
21.296 * [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))))))))
21.303 * [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))))))))
21.305 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0
21.306 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0
21.308 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0
21.310 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
21.310 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
21.311 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0
21.312 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0
21.312 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0
21.314 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
21.315 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0
21.317 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
21.319 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0
21.321 * [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
21.323 * [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
21.326 * [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
21.329 * [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
21.329 * [backup-simplify]: Simplify (- 0) into 0
21.329 * [backup-simplify]: Simplify 0 into 0
21.329 * [backup-simplify]: Simplify 0 into 0
21.331 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
21.332 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
21.336 * [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
21.336 * [backup-simplify]: Simplify (- 0) into 0
21.337 * [backup-simplify]: Simplify (+ 0 0) into 0
21.338 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0
21.340 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0
21.342 * [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)))
21.343 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
21.348 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
21.355 * [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))))))))
21.367 * [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))))))))
21.367 * [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
21.368 * [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
21.368 * [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
21.368 * [taylor]: Taking taylor expansion of +nan.0 in n
21.368 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.368 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n
21.368 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n
21.368 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n
21.368 * [taylor]: Taking taylor expansion of 0.5 in n
21.368 * [backup-simplify]: Simplify 0.5 into 0.5
21.368 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n
21.368 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n
21.368 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
21.368 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
21.368 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
21.368 * [taylor]: Taking taylor expansion of 1.0 in n
21.368 * [backup-simplify]: Simplify 1.0 into 1.0
21.368 * [taylor]: Taking taylor expansion of (log 2.0) in n
21.368 * [taylor]: Taking taylor expansion of 2.0 in n
21.368 * [backup-simplify]: Simplify 2.0 into 2.0
21.369 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
21.370 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
21.371 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
21.371 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n
21.371 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
21.371 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
21.371 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
21.371 * [taylor]: Taking taylor expansion of 1.0 in n
21.371 * [backup-simplify]: Simplify 1.0 into 1.0
21.371 * [taylor]: Taking taylor expansion of (log n) in n
21.372 * [taylor]: Taking taylor expansion of n in n
21.372 * [backup-simplify]: Simplify 0 into 0
21.372 * [backup-simplify]: Simplify 1 into 1
21.372 * [backup-simplify]: Simplify (log 1) into 0
21.372 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
21.373 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
21.373 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
21.373 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
21.373 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
21.373 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
21.373 * [taylor]: Taking taylor expansion of 1.0 in n
21.373 * [backup-simplify]: Simplify 1.0 into 1.0
21.373 * [taylor]: Taking taylor expansion of (log PI) in n
21.373 * [taylor]: Taking taylor expansion of PI in n
21.373 * [backup-simplify]: Simplify PI into PI
21.373 * [backup-simplify]: Simplify (log PI) into (log PI)
21.375 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
21.377 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
21.378 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
21.379 * [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)
21.381 * [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))
21.384 * [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)))
21.386 * [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)
21.386 * [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
21.386 * [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
21.387 * [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
21.387 * [taylor]: Taking taylor expansion of +nan.0 in n
21.387 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.387 * [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
21.387 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
21.387 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
21.387 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
21.387 * [taylor]: Taking taylor expansion of 0.5 in n
21.387 * [backup-simplify]: Simplify 0.5 into 0.5
21.387 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
21.387 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
21.387 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
21.387 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
21.387 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
21.387 * [taylor]: Taking taylor expansion of 1.0 in n
21.387 * [backup-simplify]: Simplify 1.0 into 1.0
21.387 * [taylor]: Taking taylor expansion of (log 2.0) in n
21.387 * [taylor]: Taking taylor expansion of 2.0 in n
21.387 * [backup-simplify]: Simplify 2.0 into 2.0
21.388 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
21.389 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
21.390 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
21.391 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
21.391 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
21.391 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
21.391 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
21.391 * [taylor]: Taking taylor expansion of 1.0 in n
21.391 * [backup-simplify]: Simplify 1.0 into 1.0
21.391 * [taylor]: Taking taylor expansion of (log PI) in n
21.391 * [taylor]: Taking taylor expansion of PI in n
21.391 * [backup-simplify]: Simplify PI into PI
21.400 * [backup-simplify]: Simplify (log PI) into (log PI)
21.401 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
21.403 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
21.403 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
21.403 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
21.403 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
21.403 * [taylor]: Taking taylor expansion of 1.0 in n
21.403 * [backup-simplify]: Simplify 1.0 into 1.0
21.403 * [taylor]: Taking taylor expansion of (log n) in n
21.403 * [taylor]: Taking taylor expansion of n in n
21.403 * [backup-simplify]: Simplify 0 into 0
21.403 * [backup-simplify]: Simplify 1 into 1
21.404 * [backup-simplify]: Simplify (log 1) into 0
21.404 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
21.404 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
21.404 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
21.405 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
21.406 * [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)
21.408 * [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))
21.409 * [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)))
21.411 * [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)
21.411 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
21.411 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
21.411 * [taylor]: Taking taylor expansion of 2.0 in n
21.411 * [backup-simplify]: Simplify 2.0 into 2.0
21.411 * [taylor]: Taking taylor expansion of (* n PI) in n
21.411 * [taylor]: Taking taylor expansion of n in n
21.411 * [backup-simplify]: Simplify 0 into 0
21.411 * [backup-simplify]: Simplify 1 into 1
21.411 * [taylor]: Taking taylor expansion of PI in n
21.411 * [backup-simplify]: Simplify PI into PI
21.412 * [backup-simplify]: Simplify (* 0 PI) into 0
21.413 * [backup-simplify]: Simplify (* 2.0 0) into 0
21.414 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
21.416 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
21.417 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.417 * [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
21.417 * [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
21.418 * [taylor]: Taking taylor expansion of +nan.0 in n
21.418 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.418 * [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
21.418 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
21.418 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
21.418 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
21.418 * [taylor]: Taking taylor expansion of 0.5 in n
21.418 * [backup-simplify]: Simplify 0.5 into 0.5
21.418 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
21.418 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
21.418 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
21.418 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
21.418 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
21.418 * [taylor]: Taking taylor expansion of 1.0 in n
21.418 * [backup-simplify]: Simplify 1.0 into 1.0
21.418 * [taylor]: Taking taylor expansion of (log 2.0) in n
21.418 * [taylor]: Taking taylor expansion of 2.0 in n
21.418 * [backup-simplify]: Simplify 2.0 into 2.0
21.419 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
21.420 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
21.421 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
21.421 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
21.421 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
21.421 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
21.421 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
21.421 * [taylor]: Taking taylor expansion of 1.0 in n
21.421 * [backup-simplify]: Simplify 1.0 into 1.0
21.421 * [taylor]: Taking taylor expansion of (log PI) in n
21.421 * [taylor]: Taking taylor expansion of PI in n
21.421 * [backup-simplify]: Simplify PI into PI
21.422 * [backup-simplify]: Simplify (log PI) into (log PI)
21.423 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
21.426 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
21.426 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
21.426 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
21.426 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
21.426 * [taylor]: Taking taylor expansion of 1.0 in n
21.426 * [backup-simplify]: Simplify 1.0 into 1.0
21.426 * [taylor]: Taking taylor expansion of (log n) in n
21.426 * [taylor]: Taking taylor expansion of n in n
21.426 * [backup-simplify]: Simplify 0 into 0
21.426 * [backup-simplify]: Simplify 1 into 1
21.427 * [backup-simplify]: Simplify (log 1) into 0
21.427 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
21.427 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
21.427 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
21.428 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
21.430 * [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)
21.431 * [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))
21.432 * [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)))
21.434 * [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)
21.434 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n
21.434 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
21.434 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
21.434 * [taylor]: Taking taylor expansion of 2.0 in n
21.434 * [backup-simplify]: Simplify 2.0 into 2.0
21.434 * [taylor]: Taking taylor expansion of (* n PI) in n
21.434 * [taylor]: Taking taylor expansion of n in n
21.434 * [backup-simplify]: Simplify 0 into 0
21.434 * [backup-simplify]: Simplify 1 into 1
21.434 * [taylor]: Taking taylor expansion of PI in n
21.434 * [backup-simplify]: Simplify PI into PI
21.435 * [backup-simplify]: Simplify (* 0 PI) into 0
21.435 * [backup-simplify]: Simplify (* 2.0 0) into 0
21.438 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
21.439 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
21.442 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.443 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
21.445 * [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))
21.446 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
21.449 * [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))
21.457 * [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)))
21.459 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
21.460 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
21.463 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2)
21.466 * [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))
21.469 * [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)))
21.473 * [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))))))))
21.485 * [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))))))))))))
21.501 * [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))))))))))))
21.518 * [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))))))))))))))
21.536 * [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))))))))))))))
21.554 * [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))))))))))))))
21.606 * [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))))))))))))))))))))))
21.607 * [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))))))
21.607 * [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
21.607 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n
21.607 * [taylor]: Taking taylor expansion of 1.0 in n
21.607 * [backup-simplify]: Simplify 1.0 into 1.0
21.607 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
21.607 * [taylor]: Taking taylor expansion of (sqrt k) in n
21.607 * [taylor]: Taking taylor expansion of k in n
21.607 * [backup-simplify]: Simplify k into k
21.607 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
21.607 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
21.607 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
21.607 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
21.607 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
21.607 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
21.607 * [taylor]: Taking taylor expansion of 0.5 in n
21.607 * [backup-simplify]: Simplify 0.5 into 0.5
21.607 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
21.607 * [taylor]: Taking taylor expansion of 1.0 in n
21.607 * [backup-simplify]: Simplify 1.0 into 1.0
21.607 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.607 * [taylor]: Taking taylor expansion of k in n
21.608 * [backup-simplify]: Simplify k into k
21.608 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.608 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
21.608 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
21.608 * [taylor]: Taking taylor expansion of 2.0 in n
21.608 * [backup-simplify]: Simplify 2.0 into 2.0
21.608 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.608 * [taylor]: Taking taylor expansion of PI in n
21.608 * [backup-simplify]: Simplify PI into PI
21.608 * [taylor]: Taking taylor expansion of n in n
21.608 * [backup-simplify]: Simplify 0 into 0
21.608 * [backup-simplify]: Simplify 1 into 1
21.608 * [backup-simplify]: Simplify (/ PI 1) into PI
21.608 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
21.609 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.609 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
21.609 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
21.609 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
21.610 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
21.611 * [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))))
21.612 * [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)))))
21.612 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
21.612 * [taylor]: Taking taylor expansion of 1.0 in k
21.612 * [backup-simplify]: Simplify 1.0 into 1.0
21.612 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
21.612 * [taylor]: Taking taylor expansion of (sqrt k) in k
21.612 * [taylor]: Taking taylor expansion of k in k
21.612 * [backup-simplify]: Simplify 0 into 0
21.612 * [backup-simplify]: Simplify 1 into 1
21.612 * [backup-simplify]: Simplify (sqrt 0) into 0
21.613 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
21.613 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
21.613 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
21.613 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
21.613 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
21.613 * [taylor]: Taking taylor expansion of 0.5 in k
21.613 * [backup-simplify]: Simplify 0.5 into 0.5
21.613 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
21.613 * [taylor]: Taking taylor expansion of 1.0 in k
21.613 * [backup-simplify]: Simplify 1.0 into 1.0
21.613 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.613 * [taylor]: Taking taylor expansion of k in k
21.613 * [backup-simplify]: Simplify 0 into 0
21.613 * [backup-simplify]: Simplify 1 into 1
21.614 * [backup-simplify]: Simplify (/ 1 1) into 1
21.614 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
21.614 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
21.614 * [taylor]: Taking taylor expansion of 2.0 in k
21.614 * [backup-simplify]: Simplify 2.0 into 2.0
21.614 * [taylor]: Taking taylor expansion of (/ PI n) in k
21.614 * [taylor]: Taking taylor expansion of PI in k
21.614 * [backup-simplify]: Simplify PI into PI
21.614 * [taylor]: Taking taylor expansion of n in k
21.614 * [backup-simplify]: Simplify n into n
21.614 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
21.614 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
21.614 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
21.614 * [backup-simplify]: Simplify (- 1) into -1
21.615 * [backup-simplify]: Simplify (+ 0 -1) into -1
21.615 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
21.615 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
21.615 * [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)))))
21.615 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
21.615 * [taylor]: Taking taylor expansion of 1.0 in k
21.615 * [backup-simplify]: Simplify 1.0 into 1.0
21.615 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
21.615 * [taylor]: Taking taylor expansion of (sqrt k) in k
21.615 * [taylor]: Taking taylor expansion of k in k
21.615 * [backup-simplify]: Simplify 0 into 0
21.615 * [backup-simplify]: Simplify 1 into 1
21.616 * [backup-simplify]: Simplify (sqrt 0) into 0
21.617 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
21.617 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
21.617 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
21.617 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
21.617 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
21.617 * [taylor]: Taking taylor expansion of 0.5 in k
21.617 * [backup-simplify]: Simplify 0.5 into 0.5
21.617 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
21.617 * [taylor]: Taking taylor expansion of 1.0 in k
21.617 * [backup-simplify]: Simplify 1.0 into 1.0
21.617 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.617 * [taylor]: Taking taylor expansion of k in k
21.617 * [backup-simplify]: Simplify 0 into 0
21.617 * [backup-simplify]: Simplify 1 into 1
21.618 * [backup-simplify]: Simplify (/ 1 1) into 1
21.618 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
21.618 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
21.618 * [taylor]: Taking taylor expansion of 2.0 in k
21.618 * [backup-simplify]: Simplify 2.0 into 2.0
21.618 * [taylor]: Taking taylor expansion of (/ PI n) in k
21.618 * [taylor]: Taking taylor expansion of PI in k
21.618 * [backup-simplify]: Simplify PI into PI
21.618 * [taylor]: Taking taylor expansion of n in k
21.618 * [backup-simplify]: Simplify n into n
21.618 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
21.618 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
21.618 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
21.619 * [backup-simplify]: Simplify (- 1) into -1
21.619 * [backup-simplify]: Simplify (+ 0 -1) into -1
21.619 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
21.620 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
21.620 * [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)))))
21.620 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0
21.621 * [backup-simplify]: Simplify (* 1.0 0) into 0
21.621 * [taylor]: Taking taylor expansion of 0 in n
21.621 * [backup-simplify]: Simplify 0 into 0
21.621 * [backup-simplify]: Simplify 0 into 0
21.622 * [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)))))))
21.622 * [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)))))))
21.622 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
21.622 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
21.622 * [taylor]: Taking taylor expansion of +nan.0 in n
21.622 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.622 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
21.622 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
21.623 * [taylor]: Taking taylor expansion of 0.5 in n
21.623 * [backup-simplify]: Simplify 0.5 into 0.5
21.623 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
21.623 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
21.623 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
21.623 * [taylor]: Taking taylor expansion of 2.0 in n
21.623 * [backup-simplify]: Simplify 2.0 into 2.0
21.623 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.623 * [taylor]: Taking taylor expansion of PI in n
21.623 * [backup-simplify]: Simplify PI into PI
21.623 * [taylor]: Taking taylor expansion of n in n
21.623 * [backup-simplify]: Simplify 0 into 0
21.623 * [backup-simplify]: Simplify 1 into 1
21.624 * [backup-simplify]: Simplify (/ PI 1) into PI
21.625 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
21.626 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.626 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
21.626 * [taylor]: Taking taylor expansion of 1.0 in n
21.626 * [backup-simplify]: Simplify 1.0 into 1.0
21.627 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.627 * [taylor]: Taking taylor expansion of k in n
21.627 * [backup-simplify]: Simplify k into k
21.627 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.629 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
21.629 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
21.629 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
21.630 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
21.632 * [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))))
21.633 * [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)))))
21.634 * [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))))))
21.636 * [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)))))))
21.637 * [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)))))))
21.637 * [backup-simplify]: Simplify 0 into 0
21.640 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
21.641 * [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)))))))
21.642 * [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)))))))
21.642 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
21.643 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
21.643 * [taylor]: Taking taylor expansion of +nan.0 in n
21.643 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.643 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
21.643 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
21.643 * [taylor]: Taking taylor expansion of 0.5 in n
21.643 * [backup-simplify]: Simplify 0.5 into 0.5
21.643 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
21.643 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
21.643 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
21.643 * [taylor]: Taking taylor expansion of 2.0 in n
21.643 * [backup-simplify]: Simplify 2.0 into 2.0
21.643 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.643 * [taylor]: Taking taylor expansion of PI in n
21.643 * [backup-simplify]: Simplify PI into PI
21.643 * [taylor]: Taking taylor expansion of n in n
21.643 * [backup-simplify]: Simplify 0 into 0
21.643 * [backup-simplify]: Simplify 1 into 1
21.644 * [backup-simplify]: Simplify (/ PI 1) into PI
21.644 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
21.645 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.646 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
21.646 * [taylor]: Taking taylor expansion of 1.0 in n
21.646 * [backup-simplify]: Simplify 1.0 into 1.0
21.646 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.646 * [taylor]: Taking taylor expansion of k in n
21.646 * [backup-simplify]: Simplify k into k
21.646 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.648 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
21.648 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
21.648 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
21.650 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
21.652 * [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))))
21.654 * [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)))))
21.655 * [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))))))
21.656 * [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)))))))
21.658 * [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)))))))
21.660 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
21.660 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
21.660 * [backup-simplify]: Simplify (- 0) into 0
21.660 * [backup-simplify]: Simplify (+ 0 0) into 0
21.661 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
21.661 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
21.662 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
21.663 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0
21.665 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0
21.666 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
21.667 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0
21.668 * [backup-simplify]: Simplify (- 0) into 0
21.668 * [backup-simplify]: Simplify 0 into 0
21.668 * [backup-simplify]: Simplify 0 into 0
21.671 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
21.672 * [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)))))))
21.673 * [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)))))))
21.674 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
21.674 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
21.674 * [taylor]: Taking taylor expansion of +nan.0 in n
21.674 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.674 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
21.674 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
21.674 * [taylor]: Taking taylor expansion of 0.5 in n
21.674 * [backup-simplify]: Simplify 0.5 into 0.5
21.674 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
21.674 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
21.674 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
21.674 * [taylor]: Taking taylor expansion of 2.0 in n
21.674 * [backup-simplify]: Simplify 2.0 into 2.0
21.674 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.674 * [taylor]: Taking taylor expansion of PI in n
21.674 * [backup-simplify]: Simplify PI into PI
21.674 * [taylor]: Taking taylor expansion of n in n
21.674 * [backup-simplify]: Simplify 0 into 0
21.674 * [backup-simplify]: Simplify 1 into 1
21.674 * [backup-simplify]: Simplify (/ PI 1) into PI
21.675 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
21.676 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.676 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
21.676 * [taylor]: Taking taylor expansion of 1.0 in n
21.676 * [backup-simplify]: Simplify 1.0 into 1.0
21.676 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.676 * [taylor]: Taking taylor expansion of k in n
21.676 * [backup-simplify]: Simplify k into k
21.676 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.677 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
21.677 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
21.677 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
21.678 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
21.678 * [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))))
21.679 * [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)))))
21.681 * [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))))))
21.683 * [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)))))))
21.684 * [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)))))))
21.689 * [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))))))))
21.691 * [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))))
21.691 * [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
21.691 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
21.691 * [taylor]: Taking taylor expansion of 1.0 in n
21.691 * [backup-simplify]: Simplify 1.0 into 1.0
21.691 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
21.691 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
21.691 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
21.691 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
21.691 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
21.691 * [taylor]: Taking taylor expansion of 0.5 in n
21.691 * [backup-simplify]: Simplify 0.5 into 0.5
21.691 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.691 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.691 * [taylor]: Taking taylor expansion of k in n
21.691 * [backup-simplify]: Simplify k into k
21.691 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.691 * [taylor]: Taking taylor expansion of 1.0 in n
21.691 * [backup-simplify]: Simplify 1.0 into 1.0
21.691 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.691 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.691 * [taylor]: Taking taylor expansion of -2.0 in n
21.692 * [backup-simplify]: Simplify -2.0 into -2.0
21.692 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.692 * [taylor]: Taking taylor expansion of PI in n
21.692 * [backup-simplify]: Simplify PI into PI
21.692 * [taylor]: Taking taylor expansion of n in n
21.692 * [backup-simplify]: Simplify 0 into 0
21.692 * [backup-simplify]: Simplify 1 into 1
21.692 * [backup-simplify]: Simplify (/ PI 1) into PI
21.693 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.694 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.694 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.694 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
21.696 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.697 * [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))))
21.698 * [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)))))
21.698 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
21.698 * [taylor]: Taking taylor expansion of (/ -1 k) in n
21.698 * [taylor]: Taking taylor expansion of -1 in n
21.698 * [backup-simplify]: Simplify -1 into -1
21.698 * [taylor]: Taking taylor expansion of k in n
21.698 * [backup-simplify]: Simplify k into k
21.699 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
21.699 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
21.699 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
21.699 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
21.700 * [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)))
21.701 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
21.701 * [taylor]: Taking taylor expansion of 1.0 in k
21.701 * [backup-simplify]: Simplify 1.0 into 1.0
21.701 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
21.701 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
21.701 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
21.701 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
21.701 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
21.701 * [taylor]: Taking taylor expansion of 0.5 in k
21.701 * [backup-simplify]: Simplify 0.5 into 0.5
21.701 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
21.701 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.701 * [taylor]: Taking taylor expansion of k in k
21.701 * [backup-simplify]: Simplify 0 into 0
21.701 * [backup-simplify]: Simplify 1 into 1
21.701 * [backup-simplify]: Simplify (/ 1 1) into 1
21.701 * [taylor]: Taking taylor expansion of 1.0 in k
21.701 * [backup-simplify]: Simplify 1.0 into 1.0
21.701 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
21.701 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
21.702 * [taylor]: Taking taylor expansion of -2.0 in k
21.702 * [backup-simplify]: Simplify -2.0 into -2.0
21.702 * [taylor]: Taking taylor expansion of (/ PI n) in k
21.702 * [taylor]: Taking taylor expansion of PI in k
21.702 * [backup-simplify]: Simplify PI into PI
21.702 * [taylor]: Taking taylor expansion of n in k
21.702 * [backup-simplify]: Simplify n into n
21.702 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
21.702 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
21.702 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
21.702 * [backup-simplify]: Simplify (+ 1 0) into 1
21.703 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
21.703 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
21.703 * [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))))))
21.703 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
21.703 * [taylor]: Taking taylor expansion of (/ -1 k) in k
21.703 * [taylor]: Taking taylor expansion of -1 in k
21.703 * [backup-simplify]: Simplify -1 into -1
21.703 * [taylor]: Taking taylor expansion of k in k
21.703 * [backup-simplify]: Simplify 0 into 0
21.703 * [backup-simplify]: Simplify 1 into 1
21.704 * [backup-simplify]: Simplify (/ -1 1) into -1
21.704 * [backup-simplify]: Simplify (sqrt 0) into 0
21.706 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
21.706 * [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)))))))
21.706 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
21.706 * [taylor]: Taking taylor expansion of 1.0 in k
21.706 * [backup-simplify]: Simplify 1.0 into 1.0
21.706 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
21.706 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
21.706 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
21.706 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
21.706 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
21.706 * [taylor]: Taking taylor expansion of 0.5 in k
21.706 * [backup-simplify]: Simplify 0.5 into 0.5
21.706 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
21.706 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.706 * [taylor]: Taking taylor expansion of k in k
21.707 * [backup-simplify]: Simplify 0 into 0
21.707 * [backup-simplify]: Simplify 1 into 1
21.707 * [backup-simplify]: Simplify (/ 1 1) into 1
21.707 * [taylor]: Taking taylor expansion of 1.0 in k
21.707 * [backup-simplify]: Simplify 1.0 into 1.0
21.707 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
21.707 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
21.707 * [taylor]: Taking taylor expansion of -2.0 in k
21.707 * [backup-simplify]: Simplify -2.0 into -2.0
21.707 * [taylor]: Taking taylor expansion of (/ PI n) in k
21.707 * [taylor]: Taking taylor expansion of PI in k
21.707 * [backup-simplify]: Simplify PI into PI
21.707 * [taylor]: Taking taylor expansion of n in k
21.707 * [backup-simplify]: Simplify n into n
21.707 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
21.707 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
21.708 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
21.708 * [backup-simplify]: Simplify (+ 1 0) into 1
21.709 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
21.709 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
21.709 * [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))))))
21.709 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
21.709 * [taylor]: Taking taylor expansion of (/ -1 k) in k
21.709 * [taylor]: Taking taylor expansion of -1 in k
21.709 * [backup-simplify]: Simplify -1 into -1
21.709 * [taylor]: Taking taylor expansion of k in k
21.709 * [backup-simplify]: Simplify 0 into 0
21.709 * [backup-simplify]: Simplify 1 into 1
21.710 * [backup-simplify]: Simplify (/ -1 1) into -1
21.710 * [backup-simplify]: Simplify (sqrt 0) into 0
21.711 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
21.712 * [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)))))))
21.712 * [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)))))))
21.712 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
21.712 * [taylor]: Taking taylor expansion of +nan.0 in n
21.712 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.712 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
21.712 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
21.712 * [taylor]: Taking taylor expansion of 0.5 in n
21.712 * [backup-simplify]: Simplify 0.5 into 0.5
21.712 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
21.712 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.712 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.712 * [taylor]: Taking taylor expansion of k in n
21.713 * [backup-simplify]: Simplify k into k
21.713 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.713 * [taylor]: Taking taylor expansion of 1.0 in n
21.713 * [backup-simplify]: Simplify 1.0 into 1.0
21.713 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.713 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.713 * [taylor]: Taking taylor expansion of -2.0 in n
21.713 * [backup-simplify]: Simplify -2.0 into -2.0
21.713 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.713 * [taylor]: Taking taylor expansion of PI in n
21.713 * [backup-simplify]: Simplify PI into PI
21.713 * [taylor]: Taking taylor expansion of n in n
21.713 * [backup-simplify]: Simplify 0 into 0
21.713 * [backup-simplify]: Simplify 1 into 1
21.713 * [backup-simplify]: Simplify (/ PI 1) into PI
21.714 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.715 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.715 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.717 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.718 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
21.720 * [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))))
21.721 * [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)))))
21.722 * [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))))))
21.724 * [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))))))
21.725 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
21.728 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
21.729 * [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))))))))
21.730 * [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))))))))
21.730 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
21.730 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
21.730 * [taylor]: Taking taylor expansion of +nan.0 in n
21.730 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.730 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
21.730 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
21.730 * [taylor]: Taking taylor expansion of 0.5 in n
21.730 * [backup-simplify]: Simplify 0.5 into 0.5
21.730 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
21.731 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.731 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.731 * [taylor]: Taking taylor expansion of k in n
21.731 * [backup-simplify]: Simplify k into k
21.731 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.731 * [taylor]: Taking taylor expansion of 1.0 in n
21.731 * [backup-simplify]: Simplify 1.0 into 1.0
21.731 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.731 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.731 * [taylor]: Taking taylor expansion of -2.0 in n
21.731 * [backup-simplify]: Simplify -2.0 into -2.0
21.731 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.731 * [taylor]: Taking taylor expansion of PI in n
21.731 * [backup-simplify]: Simplify PI into PI
21.731 * [taylor]: Taking taylor expansion of n in n
21.731 * [backup-simplify]: Simplify 0 into 0
21.731 * [backup-simplify]: Simplify 1 into 1
21.732 * [backup-simplify]: Simplify (/ PI 1) into PI
21.732 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.733 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.734 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.735 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.736 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
21.746 * [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))))
21.747 * [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)))))
21.753 * [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))))))
21.755 * [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)))))))
21.761 * [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)))))))
21.763 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
21.764 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
21.766 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
21.766 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
21.767 * [backup-simplify]: Simplify (+ 0 0) into 0
21.776 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.777 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
21.779 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0
21.781 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
21.783 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0
21.783 * [backup-simplify]: Simplify 0 into 0
21.784 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
21.788 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
21.790 * [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))))))))
21.791 * [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))))))))
21.791 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
21.791 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
21.791 * [taylor]: Taking taylor expansion of +nan.0 in n
21.791 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.791 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
21.791 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
21.791 * [taylor]: Taking taylor expansion of 0.5 in n
21.792 * [backup-simplify]: Simplify 0.5 into 0.5
21.792 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
21.792 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.792 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.792 * [taylor]: Taking taylor expansion of k in n
21.792 * [backup-simplify]: Simplify k into k
21.792 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.792 * [taylor]: Taking taylor expansion of 1.0 in n
21.792 * [backup-simplify]: Simplify 1.0 into 1.0
21.792 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.792 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.792 * [taylor]: Taking taylor expansion of -2.0 in n
21.792 * [backup-simplify]: Simplify -2.0 into -2.0
21.792 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.792 * [taylor]: Taking taylor expansion of PI in n
21.792 * [backup-simplify]: Simplify PI into PI
21.792 * [taylor]: Taking taylor expansion of n in n
21.792 * [backup-simplify]: Simplify 0 into 0
21.792 * [backup-simplify]: Simplify 1 into 1
21.793 * [backup-simplify]: Simplify (/ PI 1) into PI
21.794 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.795 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.795 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.797 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.798 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
21.800 * [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))))
21.801 * [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)))))
21.803 * [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))))))
21.804 * [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)))))))
21.806 * [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)))))))
21.811 * [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))))))))))))
21.811 * * * [progress]: simplifying candidates
21.829 * [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 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (log1p (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- (log (sqrt k)) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (- (log (sqrt k)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (- (log (sqrt k)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (- (log (sqrt k)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (- (log (sqrt k)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (log (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (exp (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (* (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))))
  (* (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (cbrt (/ (sqrt k) (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) (/ (- 1.0 k) 2.0)))) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
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  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (cbrt (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)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) 1))
  (/ (sqrt 1.0) (/ (sqrt (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) 2))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ (sqrt 1.0) (/ (sqrt 1) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ (sqrt k) (pow n (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ (sqrt 1) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ (sqrt 1.0) (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ (sqrt 1) (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 1) 1))
  (/ (sqrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ (sqrt 1) (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)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (cbrt (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)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) 1))
  (/ (sqrt 1.0) (/ (sqrt (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) 2))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ (sqrt 1.0) (/ 1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ (sqrt k) (pow n (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ 1 (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ (sqrt 1.0) (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ 1 (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) (/ 1 1))
  (/ (sqrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ 1 (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) 1)
  (/ (sqrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (/ 1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
  (/ (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (/ 1 (* (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (/ (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 (sqrt (/ (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 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (cbrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (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 (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (cbrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1))
  (/ 1.0 (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (cbrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt 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 (cbrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1))
  (/ 1.0 (/ (sqrt (cbrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt (cbrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt (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 (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1 (/ (sqrt 1) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt k) (pow n (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt 1) (* (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) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt 1) (sqrt (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 (/ (sqrt 1) 1))
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt 1) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt (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 (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1 (/ 1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt k) (pow n (/ (- 1.0 k) 2.0))))
  (/ 1 (/ 1 (* (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) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ 1 (sqrt (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 (/ 1 1))
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ 1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1 1)
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (sqrt k))
  (/ 1.0 (/ 1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
  (/ 1.0 (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (/ 1 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1.0)
  (/ 1.0 (* (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (/ (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 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (* (cbrt (sqrt k)) (cbrt (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 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1))
  (/ 1.0 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (* (cbrt k) (cbrt 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 (* (cbrt k) (cbrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (* (cbrt k) (cbrt k))) 1))
  (/ 1.0 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (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 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (sqrt k)) 1))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt 1) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt 1) (* (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 1) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt 1) 1))
  (/ 1.0 (/ (sqrt 1) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (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 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (sqrt k)) 1))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ 1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ 1 (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ 1 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ 1 1))
  (/ 1.0 (/ 1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 1)
  (/ 1.0 (sqrt k))
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
  (/ (/ (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))) (sqrt 1.0))
  (/ (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1.0)
  (/ 1.0 (sqrt k))
  (- (+ (* 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) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log (* 2.0 PI)) 2)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow k 3) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log (* 2.0 PI)) 2)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (log (* 2.0 PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* k (pow (/ 1 (* (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 (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (log n)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log n) 2)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (* (pow k 3) (* (log (* 2.0 PI)) (log n))) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))))))))))))))))))))))))
  (- (+ (* +nan.0 (/ 1 (* k (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))))) (- (+ (* +nan.0 (/ 1 (* (pow k 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))))) (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))))))))))
  (- (+ (* +nan.0 (/ 1 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ 1 (* k (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))) (- (* +nan.0 (/ 1 (* (pow k 2) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))))))))
  (- (+ (* +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))))))))))))
21.853 * * [simplify]: iteration 0: 610 enodes
22.323 * * [simplify]: iteration 1: 1732 enodes
23.689 * * [simplify]: iteration complete: 5000 enodes
23.690 * * [simplify]: Extracting #0: cost 283 inf + 0
23.694 * * [simplify]: Extracting #1: cost 982 inf + 2
23.710 * * [simplify]: Extracting #2: cost 1343 inf + 10203
23.747 * * [simplify]: Extracting #3: cost 1177 inf + 116116
23.825 * * [simplify]: Extracting #4: cost 769 inf + 360437
23.964 * * [simplify]: Extracting #5: cost 533 inf + 537043
24.123 * * [simplify]: Extracting #6: cost 491 inf + 624286
24.333 * * [simplify]: Extracting #7: cost 330 inf + 828927
24.534 * * [simplify]: Extracting #8: cost 131 inf + 1045318
24.813 * * [simplify]: Extracting #9: cost 25 inf + 1164798
25.132 * * [simplify]: Extracting #10: cost 6 inf + 1208109
25.468 * * [simplify]: Extracting #11: cost 0 inf + 1222817
25.816 * * [simplify]: Extracting #12: cost 0 inf + 1222572
26.147 * * [simplify]: Extracting #13: cost 0 inf + 1222522
26.462 * [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)))
  (* (/ (- 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) (log (* (* 2.0 PI) n)))
  (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))
  (/ (- 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 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (cbrt (- 1.0 k)) (/ (sqrt 2.0) (cbrt (- 1.0 k)))))
  (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 k) (sqrt 1.0)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (+ (sqrt k) (sqrt 1.0)))
  (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))
  (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n)))
  (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 PI) n))
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 (* (* 2.0 PI) (* 2.0 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)))
  (* (sqrt n) (* 2.0 PI))
  (* 2.0 PI)
  (* n PI)
  (expm1 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (log1p (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- (log (sqrt k)) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (- (log (sqrt k)) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (- (log (sqrt k)) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (- (log (sqrt k)) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (- (log (sqrt k)) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (- (log (sqrt k)) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (exp (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (/ (* (sqrt k) 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 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (cbrt (/ (sqrt k) (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) (/ (- 1.0 k) 2.0)))) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- (sqrt k))
  (- (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (cbrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (cbrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (cbrt (sqrt k)) (cbrt (sqrt k)))
  (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (fabs (cbrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt (cbrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (/ (/ (fabs (cbrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (cbrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (fabs (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (fabs (cbrt k))
  (/ (sqrt (cbrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (fabs (cbrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt (cbrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (sqrt k))
  (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ 1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt k) (pow n (/ (- 1.0 k) 2.0)))
  (/ (/ 1 (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt k) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  1
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ 1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (sqrt k))
  (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ 1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt k) (pow n (/ (- 1.0 k) 2.0)))
  (/ (/ 1 (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt k) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  1
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ 1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ 1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ (sqrt k) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt k) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt k)
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
  (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))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (+ (log (/ 1.0 (sqrt k))) (* (/ (- 1.0 k) 2.0) (log (* (* 2.0 PI) n))))
  (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (/ (/ (* (sqrt k) 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 1.0)))
  (* (* (/ 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)))))
  (* (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)
  (- (/ (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) (cbrt (/ (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) (cbrt 1.0)) (sqrt (/ (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) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ (cbrt 1.0) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ (cbrt 1.0) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt 1.0) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (sqrt k)))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k))))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (fabs (cbrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (* (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (cbrt 1.0) (/ (sqrt (cbrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (* (* (cbrt 1.0) (cbrt 1.0)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (fabs (cbrt k)))
  (/ (cbrt 1.0) (/ (sqrt (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k)))
  (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (fabs (cbrt k)))
  (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (* (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (* (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (cbrt 1.0) (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (* (cbrt 1.0) (cbrt 1.0)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (cbrt 1.0) (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (cbrt 1.0) (cbrt 1.0))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (cbrt 1.0) (cbrt 1.0)) (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) 2)))
  (/ (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (* (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (cbrt 1.0) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (* (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (cbrt 1.0) (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (* (cbrt 1.0) (cbrt 1.0)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (cbrt 1.0) (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (cbrt 1.0) (cbrt 1.0))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (cbrt 1.0) (cbrt 1.0)) (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) 2)))
  (* (cbrt 1.0) (cbrt 1.0))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (cbrt 1.0) (/ (sqrt k) (cbrt 1.0)))
  (* (cbrt 1.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
  (/ (cbrt 1.0) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (/ (/ (sqrt 1.0) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (/ (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 (/ (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) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1.0) (/ (cbrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (/ (/ (sqrt 1.0) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (cbrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (sqrt k)))
  (* (/ (sqrt 1.0) (fabs (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (* (/ (sqrt 1.0) (fabs (cbrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (sqrt 1.0) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (cbrt k)))
  (* (/ (sqrt 1.0) (fabs (cbrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ (sqrt (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (fabs (cbrt k)))
  (/ (sqrt 1.0) (/ (sqrt (cbrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (fabs (cbrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (* (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (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))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (* (/ (sqrt 1.0) (sqrt (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) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (sqrt 1.0) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (* (sqrt 1.0) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt 1.0) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (sqrt 1.0) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt k))
  (sqrt 1.0)
  (/ (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
  (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (* (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (cbrt (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))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (* (/ (sqrt 1.0) (sqrt (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) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (sqrt 1.0) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (* (sqrt 1.0) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt 1.0) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (sqrt 1.0) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt k))
  (sqrt 1.0)
  (/ (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
  (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (sqrt 1.0)
  (/ (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
  (/ (sqrt 1.0) (sqrt k))
  (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
  (/ (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (/ 1 (* (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (/ (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 (sqrt (/ (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 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (* (/ 1.0 (cbrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (/ (/ 1 (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ 1.0 (cbrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* 1 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (* (/ 1.0 (cbrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (sqrt k)))
  (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (sqrt k)))
  (* (/ 1 (fabs (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (cbrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (/ 1 (fabs (cbrt 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 (cbrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (fabs (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ 1.0 (sqrt (cbrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (fabs (cbrt k)))
  (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1 (fabs (cbrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (/ 1 (sqrt (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 (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ 1.0 (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (sqrt (sqrt k)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* 1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (sqrt k)))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (/ (* 1.0 (pow n (/ (- 1.0 k) 2.0))) (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) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (sqrt (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
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (/ 1 (sqrt (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 (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ 1.0 (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (sqrt (sqrt k)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* 1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (sqrt k)))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (/ (* 1.0 (pow n (/ (- 1.0 k) 2.0))) (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) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (sqrt (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
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  1
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ 1 (sqrt k))
  (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ 1 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
  (/ 1.0 (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (/ (sqrt k) 1.0) (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)))) (cbrt (/ (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 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (/ 1.0 (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (* (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ 1.0 (fabs (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (* (/ 1.0 (fabs (cbrt 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 (fabs (cbrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (fabs (cbrt k)))
  (/ 1.0 (/ (fabs (cbrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (* (* (/ 1.0 (sqrt (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 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (sqrt k)))
  (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* 1.0 (* (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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  1.0
  (* 1.0 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (* (* (/ 1.0 (sqrt (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 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (sqrt k)))
  (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* 1.0 (* (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 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  1.0
  (* 1.0 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  1.0
  (/ 1.0 (sqrt k))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (sqrt k))
  (/ (/ (sqrt k) (cbrt 1.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (/ (sqrt k) (sqrt 1.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (/ (sqrt k) 1.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ 1.0 (sqrt k))
  (+ (* (* 0.125 (* k k)) (+ (* (* (exp (* 0.5 (log (* (* 2.0 PI) n)))) (log (* 2.0 PI))) (log (* 2.0 PI))) (* (* (log n) (log n)) (exp (* 0.5 (log (* (* 2.0 PI) n))))))) (- (fma (* 0.25 (* k k)) (* (log n) (* (exp (* 0.5 (log (* (* 2.0 PI) n)))) (log (* 2.0 PI)))) (exp (* 0.5 (log (* (* 2.0 PI) n))))) (* 0.5 (* k (+ (* (exp (* 0.5 (log (* (* 2.0 PI) n)))) (log (* 2.0 PI))) (* (exp (* 0.5 (log (* (* 2.0 PI) n)))) (log n)))))))
  (exp (* (* 0.5 (- 1.0 k)) (log (* (* 2.0 PI) n))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n))))))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (- (fma +nan.0 (* (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5) (* k k)) (+ (* (- (* (* +nan.0 (* (log (* 2.0 PI)) (log (* 2.0 PI)))) (* k (* k k)))) (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5)) (fma (* +nan.0 (* k (* k k))) (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5) (+ (* (- (* (* +nan.0 (* (log (* 2.0 PI)) (log (* 2.0 PI)))) (* k (* k k)))) (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5)) (fma (* +nan.0 (* k (* (log (* 2.0 PI)) (* k k)))) (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5) (+ (* (* +nan.0 k) (- (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (+ (- (* (* +nan.0 (* (log (* 2.0 PI)) (* k k))) (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5)) (* (* +nan.0 (* (log n) (* k (* k k)))) (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (* (* +nan.0 (* k (* k k))) (* (* (log n) (log n)) (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (* +nan.0 (+ (* (log n) (* (* k k) (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (* (* (* k (* (log (* 2.0 PI)) (* k k))) (log n)) (- (pow (/ (/ 1 (pow 2.0 1.0)) (* (pow PI 1.0) (pow n 1.0))) 0.5))))))))))))))
  (+ (- (/ (/ +nan.0 k) (exp (* (* 0.5 (- 1.0 k)) (log (* (* 2.0 PI) n)))))) (- (/ (/ +nan.0 (* k k)) (exp (* (* 0.5 (- 1.0 k)) (log (* (* 2.0 PI) n))))) (/ +nan.0 (exp (* (* 0.5 (- 1.0 k)) (log (* (* 2.0 PI) n)))))))
  (+ (- (/ +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))))))) (- (/ (/ +nan.0 k) (exp (* 0.5 (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n))))))) (/ (/ +nan.0 (* k k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))))))))
  (+ (* (- (* (* +nan.0 (* k k)) (* (log (* 2.0 PI)) (log (* 2.0 PI))))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (+ (- (* +nan.0 (* (* (log (* 2.0 PI)) (* k k)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (* +nan.0 (* (* (* (log (* 2.0 PI)) (* k k)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (log n)))) (+ (- (* (* (* +nan.0 (log n)) (* k k)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (* (* +nan.0 (* k (log (* 2.0 PI)))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (+ (- (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (* (* (log n) (log n)) (* k k)) +nan.0)) (* (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (* k (log n)))) (+ (- (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) +nan.0) (* (* +nan.0 (* k k)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (* k (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) +nan.0)))))))
  (+ (* (- +nan.0) (/ (exp (* (* 0.5 (- 1.0 k)) (log (* (* 2.0 PI) n)))) (* k (* k k)))) (* +nan.0 (- (/ (exp (* (* 0.5 (- 1.0 k)) (log (* (* 2.0 PI) n)))) k) (/ (exp (* (* 0.5 (- 1.0 k)) (log (* (* 2.0 PI) n)))) (* k k)))))
  (+ (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))))) k))) (* +nan.0 (- (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))))) (* k k)) (exp (* 0.5 (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))))))))
26.519 * * * [progress]: adding candidates to table
28.857 * * [progress]: iteration 4 / 4
28.857 * * * [progress]: picking best candidate
29.012 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))>
29.012 * * * [progress]: localizing error
29.117 * * * [progress]: generating rewritten candidates
29.117 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2)
29.161 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1)
29.218 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1)
29.249 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1)
29.340 * * * [progress]: generating series expansions
29.340 * * * * [progress]: [ 1 / 4 ] generating series at (2 2)
29.341 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
29.341 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
29.342 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
29.342 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
29.342 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
29.342 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
29.342 * [taylor]: Taking taylor expansion of 0.5 in k
29.342 * [backup-simplify]: Simplify 0.5 into 0.5
29.342 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
29.342 * [taylor]: Taking taylor expansion of 1.0 in k
29.342 * [backup-simplify]: Simplify 1.0 into 1.0
29.342 * [taylor]: Taking taylor expansion of k in k
29.342 * [backup-simplify]: Simplify 0 into 0
29.342 * [backup-simplify]: Simplify 1 into 1
29.342 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
29.342 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
29.342 * [taylor]: Taking taylor expansion of 2.0 in k
29.342 * [backup-simplify]: Simplify 2.0 into 2.0
29.342 * [taylor]: Taking taylor expansion of (* n PI) in k
29.342 * [taylor]: Taking taylor expansion of n in k
29.342 * [backup-simplify]: Simplify n into n
29.342 * [taylor]: Taking taylor expansion of PI in k
29.342 * [backup-simplify]: Simplify PI into PI
29.342 * [backup-simplify]: Simplify (* n PI) into (* n PI)
29.342 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
29.342 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
29.343 * [backup-simplify]: Simplify (- 0) into 0
29.343 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
29.344 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
29.344 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
29.344 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
29.344 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
29.344 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
29.344 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
29.344 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
29.344 * [taylor]: Taking taylor expansion of 0.5 in n
29.344 * [backup-simplify]: Simplify 0.5 into 0.5
29.345 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
29.345 * [taylor]: Taking taylor expansion of 1.0 in n
29.345 * [backup-simplify]: Simplify 1.0 into 1.0
29.345 * [taylor]: Taking taylor expansion of k in n
29.345 * [backup-simplify]: Simplify k into k
29.345 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
29.345 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
29.345 * [taylor]: Taking taylor expansion of 2.0 in n
29.345 * [backup-simplify]: Simplify 2.0 into 2.0
29.345 * [taylor]: Taking taylor expansion of (* n PI) in n
29.345 * [taylor]: Taking taylor expansion of n in n
29.345 * [backup-simplify]: Simplify 0 into 0
29.345 * [backup-simplify]: Simplify 1 into 1
29.345 * [taylor]: Taking taylor expansion of PI in n
29.345 * [backup-simplify]: Simplify PI into PI
29.346 * [backup-simplify]: Simplify (* 0 PI) into 0
29.346 * [backup-simplify]: Simplify (* 2.0 0) into 0
29.348 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
29.350 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
29.351 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
29.351 * [backup-simplify]: Simplify (- k) into (- k)
29.351 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
29.352 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
29.353 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
29.355 * [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))))
29.357 * [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)))))
29.357 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
29.357 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
29.357 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
29.357 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
29.357 * [taylor]: Taking taylor expansion of 0.5 in n
29.357 * [backup-simplify]: Simplify 0.5 into 0.5
29.357 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
29.357 * [taylor]: Taking taylor expansion of 1.0 in n
29.357 * [backup-simplify]: Simplify 1.0 into 1.0
29.357 * [taylor]: Taking taylor expansion of k in n
29.357 * [backup-simplify]: Simplify k into k
29.357 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
29.357 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
29.357 * [taylor]: Taking taylor expansion of 2.0 in n
29.357 * [backup-simplify]: Simplify 2.0 into 2.0
29.357 * [taylor]: Taking taylor expansion of (* n PI) in n
29.357 * [taylor]: Taking taylor expansion of n in n
29.357 * [backup-simplify]: Simplify 0 into 0
29.357 * [backup-simplify]: Simplify 1 into 1
29.357 * [taylor]: Taking taylor expansion of PI in n
29.357 * [backup-simplify]: Simplify PI into PI
29.358 * [backup-simplify]: Simplify (* 0 PI) into 0
29.359 * [backup-simplify]: Simplify (* 2.0 0) into 0
29.360 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
29.362 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
29.363 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
29.363 * [backup-simplify]: Simplify (- k) into (- k)
29.363 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
29.363 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
29.365 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
29.366 * [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))))
29.367 * [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)))))
29.368 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
29.368 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
29.368 * [taylor]: Taking taylor expansion of 0.5 in k
29.368 * [backup-simplify]: Simplify 0.5 into 0.5
29.368 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
29.368 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
29.368 * [taylor]: Taking taylor expansion of 1.0 in k
29.368 * [backup-simplify]: Simplify 1.0 into 1.0
29.368 * [taylor]: Taking taylor expansion of k in k
29.368 * [backup-simplify]: Simplify 0 into 0
29.368 * [backup-simplify]: Simplify 1 into 1
29.368 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
29.368 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
29.368 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
29.368 * [taylor]: Taking taylor expansion of 2.0 in k
29.368 * [backup-simplify]: Simplify 2.0 into 2.0
29.368 * [taylor]: Taking taylor expansion of PI in k
29.368 * [backup-simplify]: Simplify PI into PI
29.369 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
29.370 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
29.370 * [taylor]: Taking taylor expansion of (log n) in k
29.370 * [taylor]: Taking taylor expansion of n in k
29.370 * [backup-simplify]: Simplify n into n
29.370 * [backup-simplify]: Simplify (log n) into (log n)
29.371 * [backup-simplify]: Simplify (- 0) into 0
29.371 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
29.372 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
29.373 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
29.375 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
29.376 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
29.377 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
29.379 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
29.380 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
29.382 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
29.382 * [backup-simplify]: Simplify (- 0) into 0
29.383 * [backup-simplify]: Simplify (+ 0 0) into 0
29.383 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
29.385 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
29.386 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
29.388 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
29.388 * [taylor]: Taking taylor expansion of 0 in k
29.388 * [backup-simplify]: Simplify 0 into 0
29.388 * [backup-simplify]: Simplify 0 into 0
29.389 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
29.391 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
29.393 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
29.393 * [backup-simplify]: Simplify (+ 0 0) into 0
29.393 * [backup-simplify]: Simplify (- 1) into -1
29.394 * [backup-simplify]: Simplify (+ 0 -1) into -1
29.395 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
29.398 * [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))))
29.402 * [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))))))
29.407 * [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))))))
29.409 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
29.410 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
29.414 * [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
29.414 * [backup-simplify]: Simplify (- 0) into 0
29.415 * [backup-simplify]: Simplify (+ 0 0) into 0
29.416 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
29.417 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
29.419 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
29.422 * [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
29.422 * [taylor]: Taking taylor expansion of 0 in k
29.422 * [backup-simplify]: Simplify 0 into 0
29.422 * [backup-simplify]: Simplify 0 into 0
29.422 * [backup-simplify]: Simplify 0 into 0
29.423 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
29.427 * [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
29.429 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
29.430 * [backup-simplify]: Simplify (+ 0 0) into 0
29.430 * [backup-simplify]: Simplify (- 0) into 0
29.430 * [backup-simplify]: Simplify (+ 0 0) into 0
29.433 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
29.435 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
29.440 * [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))))))
29.447 * [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))))))
29.464 * [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))))))
29.465 * [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))))
29.465 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
29.465 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
29.465 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
29.465 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
29.465 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
29.465 * [taylor]: Taking taylor expansion of 0.5 in k
29.465 * [backup-simplify]: Simplify 0.5 into 0.5
29.465 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
29.466 * [taylor]: Taking taylor expansion of 1.0 in k
29.466 * [backup-simplify]: Simplify 1.0 into 1.0
29.466 * [taylor]: Taking taylor expansion of (/ 1 k) in k
29.466 * [taylor]: Taking taylor expansion of k in k
29.466 * [backup-simplify]: Simplify 0 into 0
29.466 * [backup-simplify]: Simplify 1 into 1
29.466 * [backup-simplify]: Simplify (/ 1 1) into 1
29.466 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
29.466 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
29.466 * [taylor]: Taking taylor expansion of 2.0 in k
29.466 * [backup-simplify]: Simplify 2.0 into 2.0
29.466 * [taylor]: Taking taylor expansion of (/ PI n) in k
29.466 * [taylor]: Taking taylor expansion of PI in k
29.466 * [backup-simplify]: Simplify PI into PI
29.466 * [taylor]: Taking taylor expansion of n in k
29.466 * [backup-simplify]: Simplify n into n
29.466 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
29.466 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
29.467 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
29.467 * [backup-simplify]: Simplify (- 1) into -1
29.467 * [backup-simplify]: Simplify (+ 0 -1) into -1
29.468 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
29.468 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
29.468 * [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)))))
29.468 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
29.468 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
29.468 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
29.468 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
29.468 * [taylor]: Taking taylor expansion of 0.5 in n
29.468 * [backup-simplify]: Simplify 0.5 into 0.5
29.468 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
29.468 * [taylor]: Taking taylor expansion of 1.0 in n
29.469 * [backup-simplify]: Simplify 1.0 into 1.0
29.469 * [taylor]: Taking taylor expansion of (/ 1 k) in n
29.469 * [taylor]: Taking taylor expansion of k in n
29.469 * [backup-simplify]: Simplify k into k
29.469 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
29.469 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
29.469 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
29.469 * [taylor]: Taking taylor expansion of 2.0 in n
29.469 * [backup-simplify]: Simplify 2.0 into 2.0
29.469 * [taylor]: Taking taylor expansion of (/ PI n) in n
29.469 * [taylor]: Taking taylor expansion of PI in n
29.469 * [backup-simplify]: Simplify PI into PI
29.469 * [taylor]: Taking taylor expansion of n in n
29.469 * [backup-simplify]: Simplify 0 into 0
29.469 * [backup-simplify]: Simplify 1 into 1
29.470 * [backup-simplify]: Simplify (/ PI 1) into PI
29.470 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
29.471 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
29.471 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
29.471 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
29.471 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
29.473 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
29.474 * [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))))
29.475 * [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)))))
29.476 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
29.476 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
29.476 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
29.476 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
29.476 * [taylor]: Taking taylor expansion of 0.5 in n
29.476 * [backup-simplify]: Simplify 0.5 into 0.5
29.476 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
29.476 * [taylor]: Taking taylor expansion of 1.0 in n
29.476 * [backup-simplify]: Simplify 1.0 into 1.0
29.476 * [taylor]: Taking taylor expansion of (/ 1 k) in n
29.476 * [taylor]: Taking taylor expansion of k in n
29.476 * [backup-simplify]: Simplify k into k
29.476 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
29.476 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
29.476 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
29.476 * [taylor]: Taking taylor expansion of 2.0 in n
29.476 * [backup-simplify]: Simplify 2.0 into 2.0
29.476 * [taylor]: Taking taylor expansion of (/ PI n) in n
29.476 * [taylor]: Taking taylor expansion of PI in n
29.476 * [backup-simplify]: Simplify PI into PI
29.476 * [taylor]: Taking taylor expansion of n in n
29.476 * [backup-simplify]: Simplify 0 into 0
29.476 * [backup-simplify]: Simplify 1 into 1
29.477 * [backup-simplify]: Simplify (/ PI 1) into PI
29.477 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
29.478 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
29.479 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
29.479 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
29.479 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
29.480 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
29.482 * [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))))
29.483 * [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)))))
29.483 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
29.483 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
29.483 * [taylor]: Taking taylor expansion of 0.5 in k
29.483 * [backup-simplify]: Simplify 0.5 into 0.5
29.483 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
29.483 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
29.483 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
29.483 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
29.483 * [taylor]: Taking taylor expansion of 2.0 in k
29.483 * [backup-simplify]: Simplify 2.0 into 2.0
29.483 * [taylor]: Taking taylor expansion of PI in k
29.483 * [backup-simplify]: Simplify PI into PI
29.484 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
29.485 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
29.485 * [taylor]: Taking taylor expansion of (log n) in k
29.485 * [taylor]: Taking taylor expansion of n in k
29.485 * [backup-simplify]: Simplify n into n
29.485 * [backup-simplify]: Simplify (log n) into (log n)
29.485 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
29.485 * [taylor]: Taking taylor expansion of 1.0 in k
29.485 * [backup-simplify]: Simplify 1.0 into 1.0
29.485 * [taylor]: Taking taylor expansion of (/ 1 k) in k
29.485 * [taylor]: Taking taylor expansion of k in k
29.485 * [backup-simplify]: Simplify 0 into 0
29.485 * [backup-simplify]: Simplify 1 into 1
29.486 * [backup-simplify]: Simplify (/ 1 1) into 1
29.486 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
29.487 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
29.487 * [backup-simplify]: Simplify (- 1) into -1
29.488 * [backup-simplify]: Simplify (+ 0 -1) into -1
29.489 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
29.490 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
29.491 * [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)))))
29.493 * [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)))))
29.494 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
29.494 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
29.496 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
29.497 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
29.497 * [backup-simplify]: Simplify (- 0) into 0
29.497 * [backup-simplify]: Simplify (+ 0 0) into 0
29.498 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
29.499 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
29.501 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
29.509 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
29.510 * [taylor]: Taking taylor expansion of 0 in k
29.510 * [backup-simplify]: Simplify 0 into 0
29.510 * [backup-simplify]: Simplify 0 into 0
29.510 * [backup-simplify]: Simplify 0 into 0
29.511 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.512 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
29.514 * [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
29.514 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
29.515 * [backup-simplify]: Simplify (- 0) into 0
29.515 * [backup-simplify]: Simplify (+ 0 0) into 0
29.516 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
29.517 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
29.519 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
29.521 * [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
29.521 * [taylor]: Taking taylor expansion of 0 in k
29.522 * [backup-simplify]: Simplify 0 into 0
29.522 * [backup-simplify]: Simplify 0 into 0
29.522 * [backup-simplify]: Simplify 0 into 0
29.522 * [backup-simplify]: Simplify 0 into 0
29.523 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.524 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
29.530 * [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
29.530 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
29.530 * [backup-simplify]: Simplify (- 0) into 0
29.531 * [backup-simplify]: Simplify (+ 0 0) into 0
29.532 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
29.533 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
29.535 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
29.538 * [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
29.538 * [taylor]: Taking taylor expansion of 0 in k
29.538 * [backup-simplify]: Simplify 0 into 0
29.538 * [backup-simplify]: Simplify 0 into 0
29.539 * [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))))
29.540 * [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)))
29.540 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
29.540 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
29.541 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
29.541 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
29.541 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
29.541 * [taylor]: Taking taylor expansion of 0.5 in k
29.541 * [backup-simplify]: Simplify 0.5 into 0.5
29.541 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
29.541 * [taylor]: Taking taylor expansion of (/ 1 k) in k
29.541 * [taylor]: Taking taylor expansion of k in k
29.541 * [backup-simplify]: Simplify 0 into 0
29.541 * [backup-simplify]: Simplify 1 into 1
29.541 * [backup-simplify]: Simplify (/ 1 1) into 1
29.541 * [taylor]: Taking taylor expansion of 1.0 in k
29.541 * [backup-simplify]: Simplify 1.0 into 1.0
29.541 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
29.541 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
29.541 * [taylor]: Taking taylor expansion of -2.0 in k
29.541 * [backup-simplify]: Simplify -2.0 into -2.0
29.541 * [taylor]: Taking taylor expansion of (/ PI n) in k
29.541 * [taylor]: Taking taylor expansion of PI in k
29.541 * [backup-simplify]: Simplify PI into PI
29.542 * [taylor]: Taking taylor expansion of n in k
29.542 * [backup-simplify]: Simplify n into n
29.542 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
29.542 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
29.542 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
29.542 * [backup-simplify]: Simplify (+ 1 0) into 1
29.543 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
29.543 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
29.543 * [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))))))
29.543 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
29.543 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
29.543 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
29.543 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
29.543 * [taylor]: Taking taylor expansion of 0.5 in n
29.543 * [backup-simplify]: Simplify 0.5 into 0.5
29.543 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
29.543 * [taylor]: Taking taylor expansion of (/ 1 k) in n
29.543 * [taylor]: Taking taylor expansion of k in n
29.543 * [backup-simplify]: Simplify k into k
29.543 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
29.544 * [taylor]: Taking taylor expansion of 1.0 in n
29.544 * [backup-simplify]: Simplify 1.0 into 1.0
29.544 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
29.544 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
29.544 * [taylor]: Taking taylor expansion of -2.0 in n
29.544 * [backup-simplify]: Simplify -2.0 into -2.0
29.544 * [taylor]: Taking taylor expansion of (/ PI n) in n
29.544 * [taylor]: Taking taylor expansion of PI in n
29.544 * [backup-simplify]: Simplify PI into PI
29.544 * [taylor]: Taking taylor expansion of n in n
29.544 * [backup-simplify]: Simplify 0 into 0
29.544 * [backup-simplify]: Simplify 1 into 1
29.544 * [backup-simplify]: Simplify (/ PI 1) into PI
29.545 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
29.546 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
29.546 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
29.546 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
29.548 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
29.549 * [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))))
29.550 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
29.550 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
29.550 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
29.550 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
29.550 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
29.550 * [taylor]: Taking taylor expansion of 0.5 in n
29.550 * [backup-simplify]: Simplify 0.5 into 0.5
29.550 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
29.550 * [taylor]: Taking taylor expansion of (/ 1 k) in n
29.550 * [taylor]: Taking taylor expansion of k in n
29.550 * [backup-simplify]: Simplify k into k
29.550 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
29.550 * [taylor]: Taking taylor expansion of 1.0 in n
29.551 * [backup-simplify]: Simplify 1.0 into 1.0
29.551 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
29.551 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
29.551 * [taylor]: Taking taylor expansion of -2.0 in n
29.551 * [backup-simplify]: Simplify -2.0 into -2.0
29.551 * [taylor]: Taking taylor expansion of (/ PI n) in n
29.551 * [taylor]: Taking taylor expansion of PI in n
29.551 * [backup-simplify]: Simplify PI into PI
29.551 * [taylor]: Taking taylor expansion of n in n
29.551 * [backup-simplify]: Simplify 0 into 0
29.551 * [backup-simplify]: Simplify 1 into 1
29.552 * [backup-simplify]: Simplify (/ PI 1) into PI
29.552 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
29.553 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
29.553 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
29.553 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
29.555 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
29.556 * [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))))
29.557 * [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)))))
29.558 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
29.558 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
29.558 * [taylor]: Taking taylor expansion of 0.5 in k
29.558 * [backup-simplify]: Simplify 0.5 into 0.5
29.558 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
29.558 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
29.558 * [taylor]: Taking taylor expansion of (/ 1 k) in k
29.558 * [taylor]: Taking taylor expansion of k in k
29.558 * [backup-simplify]: Simplify 0 into 0
29.558 * [backup-simplify]: Simplify 1 into 1
29.558 * [backup-simplify]: Simplify (/ 1 1) into 1
29.558 * [taylor]: Taking taylor expansion of 1.0 in k
29.558 * [backup-simplify]: Simplify 1.0 into 1.0
29.558 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
29.558 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
29.558 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
29.558 * [taylor]: Taking taylor expansion of -2.0 in k
29.559 * [backup-simplify]: Simplify -2.0 into -2.0
29.559 * [taylor]: Taking taylor expansion of PI in k
29.559 * [backup-simplify]: Simplify PI into PI
29.559 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
29.560 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
29.560 * [taylor]: Taking taylor expansion of (log n) in k
29.560 * [taylor]: Taking taylor expansion of n in k
29.560 * [backup-simplify]: Simplify n into n
29.560 * [backup-simplify]: Simplify (log n) into (log n)
29.561 * [backup-simplify]: Simplify (+ 1 0) into 1
29.561 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
29.562 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
29.564 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
29.566 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
29.567 * [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)))))
29.569 * [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)))))
29.570 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
29.571 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
29.573 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
29.574 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
29.574 * [backup-simplify]: Simplify (+ 0 0) into 0
29.575 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
29.577 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
29.579 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
29.580 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
29.580 * [taylor]: Taking taylor expansion of 0 in k
29.580 * [backup-simplify]: Simplify 0 into 0
29.580 * [backup-simplify]: Simplify 0 into 0
29.581 * [backup-simplify]: Simplify 0 into 0
29.581 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.582 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
29.584 * [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
29.584 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
29.584 * [backup-simplify]: Simplify (+ 0 0) into 0
29.585 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
29.586 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
29.588 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
29.591 * [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
29.592 * [taylor]: Taking taylor expansion of 0 in k
29.592 * [backup-simplify]: Simplify 0 into 0
29.592 * [backup-simplify]: Simplify 0 into 0
29.592 * [backup-simplify]: Simplify 0 into 0
29.592 * [backup-simplify]: Simplify 0 into 0
29.593 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.594 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
29.599 * [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
29.599 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
29.600 * [backup-simplify]: Simplify (+ 0 0) into 0
29.601 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
29.602 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
29.604 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
29.606 * [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
29.606 * [taylor]: Taking taylor expansion of 0 in k
29.607 * [backup-simplify]: Simplify 0 into 0
29.607 * [backup-simplify]: Simplify 0 into 0
29.608 * [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))))))
29.608 * * * * [progress]: [ 2 / 4 ] generating series at (2 1)
29.608 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) into (* 1.0 (sqrt (/ 1 k)))
29.608 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0
29.608 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
29.608 * [taylor]: Taking taylor expansion of 1.0 in k
29.608 * [backup-simplify]: Simplify 1.0 into 1.0
29.609 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
29.609 * [taylor]: Taking taylor expansion of (/ 1 k) in k
29.609 * [taylor]: Taking taylor expansion of k in k
29.609 * [backup-simplify]: Simplify 0 into 0
29.609 * [backup-simplify]: Simplify 1 into 1
29.609 * [backup-simplify]: Simplify (/ 1 1) into 1
29.609 * [backup-simplify]: Simplify (sqrt 0) into 0
29.611 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
29.611 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
29.611 * [taylor]: Taking taylor expansion of 1.0 in k
29.611 * [backup-simplify]: Simplify 1.0 into 1.0
29.611 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
29.611 * [taylor]: Taking taylor expansion of (/ 1 k) in k
29.611 * [taylor]: Taking taylor expansion of k in k
29.611 * [backup-simplify]: Simplify 0 into 0
29.611 * [backup-simplify]: Simplify 1 into 1
29.611 * [backup-simplify]: Simplify (/ 1 1) into 1
29.612 * [backup-simplify]: Simplify (sqrt 0) into 0
29.613 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
29.614 * [backup-simplify]: Simplify (* 1.0 0) into 0
29.614 * [backup-simplify]: Simplify 0 into 0
29.615 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
29.616 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
29.617 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
29.620 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
29.622 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
29.622 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
29.623 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.626 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
29.628 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
29.629 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
29.631 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0)))))
29.631 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))) into (* 1.0 (sqrt k))
29.632 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0
29.632 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
29.632 * [taylor]: Taking taylor expansion of 1.0 in k
29.632 * [backup-simplify]: Simplify 1.0 into 1.0
29.632 * [taylor]: Taking taylor expansion of (sqrt k) in k
29.632 * [taylor]: Taking taylor expansion of k in k
29.632 * [backup-simplify]: Simplify 0 into 0
29.632 * [backup-simplify]: Simplify 1 into 1
29.632 * [backup-simplify]: Simplify (sqrt 0) into 0
29.634 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
29.634 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
29.634 * [taylor]: Taking taylor expansion of 1.0 in k
29.634 * [backup-simplify]: Simplify 1.0 into 1.0
29.634 * [taylor]: Taking taylor expansion of (sqrt k) in k
29.634 * [taylor]: Taking taylor expansion of k in k
29.634 * [backup-simplify]: Simplify 0 into 0
29.634 * [backup-simplify]: Simplify 1 into 1
29.634 * [backup-simplify]: Simplify (sqrt 0) into 0
29.635 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
29.636 * [backup-simplify]: Simplify (* 1.0 0) into 0
29.636 * [backup-simplify]: Simplify 0 into 0
29.637 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
29.638 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
29.641 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
29.644 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
29.645 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
29.649 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
29.651 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
29.652 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
29.653 * [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))))))))
29.654 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))) into (/ 1.0 (sqrt (/ -1 k)))
29.654 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0
29.654 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
29.654 * [taylor]: Taking taylor expansion of 1.0 in k
29.654 * [backup-simplify]: Simplify 1.0 into 1.0
29.654 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
29.654 * [taylor]: Taking taylor expansion of (/ -1 k) in k
29.654 * [taylor]: Taking taylor expansion of -1 in k
29.654 * [backup-simplify]: Simplify -1 into -1
29.654 * [taylor]: Taking taylor expansion of k in k
29.654 * [backup-simplify]: Simplify 0 into 0
29.654 * [backup-simplify]: Simplify 1 into 1
29.654 * [backup-simplify]: Simplify (/ -1 1) into -1
29.655 * [backup-simplify]: Simplify (sqrt 0) into 0
29.656 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
29.665 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
29.665 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
29.665 * [taylor]: Taking taylor expansion of 1.0 in k
29.665 * [backup-simplify]: Simplify 1.0 into 1.0
29.666 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
29.666 * [taylor]: Taking taylor expansion of (/ -1 k) in k
29.666 * [taylor]: Taking taylor expansion of -1 in k
29.666 * [backup-simplify]: Simplify -1 into -1
29.666 * [taylor]: Taking taylor expansion of k in k
29.666 * [backup-simplify]: Simplify 0 into 0
29.666 * [backup-simplify]: Simplify 1 into 1
29.666 * [backup-simplify]: Simplify (/ -1 1) into -1
29.667 * [backup-simplify]: Simplify (sqrt 0) into 0
29.668 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
29.668 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
29.668 * [backup-simplify]: Simplify +nan.0 into +nan.0
29.669 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
29.672 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
29.675 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
29.676 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
29.676 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.679 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
29.682 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
29.682 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
29.683 * [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)))))
29.683 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1)
29.683 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
29.683 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
29.683 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
29.683 * [taylor]: Taking taylor expansion of 2.0 in n
29.683 * [backup-simplify]: Simplify 2.0 into 2.0
29.683 * [taylor]: Taking taylor expansion of (* n PI) in n
29.683 * [taylor]: Taking taylor expansion of n in n
29.683 * [backup-simplify]: Simplify 0 into 0
29.683 * [backup-simplify]: Simplify 1 into 1
29.683 * [taylor]: Taking taylor expansion of PI in n
29.683 * [backup-simplify]: Simplify PI into PI
29.683 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
29.683 * [taylor]: Taking taylor expansion of 2.0 in n
29.683 * [backup-simplify]: Simplify 2.0 into 2.0
29.683 * [taylor]: Taking taylor expansion of (* n PI) in n
29.683 * [taylor]: Taking taylor expansion of n in n
29.683 * [backup-simplify]: Simplify 0 into 0
29.684 * [backup-simplify]: Simplify 1 into 1
29.684 * [taylor]: Taking taylor expansion of PI in n
29.684 * [backup-simplify]: Simplify PI into PI
29.684 * [backup-simplify]: Simplify (* 0 PI) into 0
29.685 * [backup-simplify]: Simplify (* 2.0 0) into 0
29.685 * [backup-simplify]: Simplify 0 into 0
29.686 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
29.688 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
29.688 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
29.689 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
29.690 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
29.690 * [backup-simplify]: Simplify 0 into 0
29.692 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
29.693 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
29.693 * [backup-simplify]: Simplify 0 into 0
29.694 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
29.696 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
29.696 * [backup-simplify]: Simplify 0 into 0
29.697 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
29.699 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
29.699 * [backup-simplify]: Simplify 0 into 0
29.700 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
29.702 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
29.702 * [backup-simplify]: Simplify 0 into 0
29.704 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
29.706 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
29.707 * [backup-simplify]: Simplify 0 into 0
29.707 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
29.708 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
29.708 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
29.708 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
29.708 * [taylor]: Taking taylor expansion of 2.0 in n
29.708 * [backup-simplify]: Simplify 2.0 into 2.0
29.708 * [taylor]: Taking taylor expansion of (/ PI n) in n
29.708 * [taylor]: Taking taylor expansion of PI in n
29.709 * [backup-simplify]: Simplify PI into PI
29.709 * [taylor]: Taking taylor expansion of n in n
29.709 * [backup-simplify]: Simplify 0 into 0
29.709 * [backup-simplify]: Simplify 1 into 1
29.709 * [backup-simplify]: Simplify (/ PI 1) into PI
29.709 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
29.709 * [taylor]: Taking taylor expansion of 2.0 in n
29.709 * [backup-simplify]: Simplify 2.0 into 2.0
29.709 * [taylor]: Taking taylor expansion of (/ PI n) in n
29.709 * [taylor]: Taking taylor expansion of PI in n
29.709 * [backup-simplify]: Simplify PI into PI
29.709 * [taylor]: Taking taylor expansion of n in n
29.709 * [backup-simplify]: Simplify 0 into 0
29.709 * [backup-simplify]: Simplify 1 into 1
29.710 * [backup-simplify]: Simplify (/ PI 1) into PI
29.710 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
29.711 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
29.712 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
29.712 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
29.712 * [backup-simplify]: Simplify 0 into 0
29.713 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.714 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
29.714 * [backup-simplify]: Simplify 0 into 0
29.715 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.716 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
29.716 * [backup-simplify]: Simplify 0 into 0
29.717 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.719 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
29.719 * [backup-simplify]: Simplify 0 into 0
29.721 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.723 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
29.724 * [backup-simplify]: Simplify 0 into 0
29.726 * [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
29.728 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
29.729 * [backup-simplify]: Simplify 0 into 0
29.729 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
29.730 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
29.730 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
29.730 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
29.731 * [taylor]: Taking taylor expansion of -2.0 in n
29.731 * [backup-simplify]: Simplify -2.0 into -2.0
29.731 * [taylor]: Taking taylor expansion of (/ PI n) in n
29.731 * [taylor]: Taking taylor expansion of PI in n
29.731 * [backup-simplify]: Simplify PI into PI
29.731 * [taylor]: Taking taylor expansion of n in n
29.731 * [backup-simplify]: Simplify 0 into 0
29.731 * [backup-simplify]: Simplify 1 into 1
29.732 * [backup-simplify]: Simplify (/ PI 1) into PI
29.732 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
29.732 * [taylor]: Taking taylor expansion of -2.0 in n
29.732 * [backup-simplify]: Simplify -2.0 into -2.0
29.732 * [taylor]: Taking taylor expansion of (/ PI n) in n
29.732 * [taylor]: Taking taylor expansion of PI in n
29.732 * [backup-simplify]: Simplify PI into PI
29.732 * [taylor]: Taking taylor expansion of n in n
29.732 * [backup-simplify]: Simplify 0 into 0
29.732 * [backup-simplify]: Simplify 1 into 1
29.732 * [backup-simplify]: Simplify (/ PI 1) into PI
29.733 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
29.734 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
29.735 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
29.736 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
29.736 * [backup-simplify]: Simplify 0 into 0
29.737 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.738 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
29.738 * [backup-simplify]: Simplify 0 into 0
29.740 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.741 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
29.741 * [backup-simplify]: Simplify 0 into 0
29.743 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.744 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
29.744 * [backup-simplify]: Simplify 0 into 0
29.745 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.747 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
29.747 * [backup-simplify]: Simplify 0 into 0
29.748 * [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
29.750 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
29.750 * [backup-simplify]: Simplify 0 into 0
29.751 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
29.751 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1)
29.751 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt k))) into (* 1.0 (pow (/ 1 k) 1/4))
29.751 * [approximate]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in (k) around 0
29.751 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k
29.751 * [taylor]: Taking taylor expansion of 1.0 in k
29.751 * [backup-simplify]: Simplify 1.0 into 1.0
29.751 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
29.751 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
29.751 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
29.751 * [taylor]: Taking taylor expansion of 1/4 in k
29.751 * [backup-simplify]: Simplify 1/4 into 1/4
29.751 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
29.751 * [taylor]: Taking taylor expansion of (/ 1 k) in k
29.751 * [taylor]: Taking taylor expansion of k in k
29.751 * [backup-simplify]: Simplify 0 into 0
29.751 * [backup-simplify]: Simplify 1 into 1
29.752 * [backup-simplify]: Simplify (/ 1 1) into 1
29.752 * [backup-simplify]: Simplify (log 1) into 0
29.753 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
29.753 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
29.753 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
29.753 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k
29.753 * [taylor]: Taking taylor expansion of 1.0 in k
29.753 * [backup-simplify]: Simplify 1.0 into 1.0
29.753 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
29.753 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
29.753 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
29.753 * [taylor]: Taking taylor expansion of 1/4 in k
29.753 * [backup-simplify]: Simplify 1/4 into 1/4
29.753 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
29.753 * [taylor]: Taking taylor expansion of (/ 1 k) in k
29.753 * [taylor]: Taking taylor expansion of k in k
29.753 * [backup-simplify]: Simplify 0 into 0
29.753 * [backup-simplify]: Simplify 1 into 1
29.754 * [backup-simplify]: Simplify (/ 1 1) into 1
29.754 * [backup-simplify]: Simplify (log 1) into 0
29.755 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
29.755 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
29.755 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
29.755 * [backup-simplify]: Simplify (* 1.0 (pow k -1/4)) into (* 1.0 (pow (/ 1 k) 1/4))
29.755 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4))
29.756 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
29.758 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
29.758 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
29.759 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0
29.760 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
29.760 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k -1/4))) into 0
29.760 * [backup-simplify]: Simplify 0 into 0
29.761 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.765 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
29.765 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
29.766 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0
29.768 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
29.769 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k -1/4)))) into 0
29.769 * [backup-simplify]: Simplify 0 into 0
29.770 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.775 * [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
29.775 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
29.777 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0
29.779 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
29.780 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))) into 0
29.780 * [backup-simplify]: Simplify 0 into 0
29.781 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.792 * [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
29.792 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
29.794 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0
29.797 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (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
29.798 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))) into 0
29.798 * [backup-simplify]: Simplify 0 into 0
29.800 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.817 * [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
29.817 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
29.827 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0
29.829 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (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
29.831 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))))) into 0
29.831 * [backup-simplify]: Simplify 0 into 0
29.832 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.858 * [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
29.858 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
29.860 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0
29.863 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (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
29.865 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))))) into 0
29.866 * [backup-simplify]: Simplify 0 into 0
29.866 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4))
29.866 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 k)))) into (* 1.0 (pow k 1/4))
29.866 * [approximate]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in (k) around 0
29.866 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k
29.866 * [taylor]: Taking taylor expansion of 1.0 in k
29.866 * [backup-simplify]: Simplify 1.0 into 1.0
29.866 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
29.866 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
29.866 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
29.866 * [taylor]: Taking taylor expansion of 1/4 in k
29.866 * [backup-simplify]: Simplify 1/4 into 1/4
29.866 * [taylor]: Taking taylor expansion of (log k) in k
29.866 * [taylor]: Taking taylor expansion of k in k
29.866 * [backup-simplify]: Simplify 0 into 0
29.866 * [backup-simplify]: Simplify 1 into 1
29.867 * [backup-simplify]: Simplify (log 1) into 0
29.867 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
29.867 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
29.867 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
29.868 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k
29.868 * [taylor]: Taking taylor expansion of 1.0 in k
29.868 * [backup-simplify]: Simplify 1.0 into 1.0
29.868 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
29.868 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
29.868 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
29.868 * [taylor]: Taking taylor expansion of 1/4 in k
29.868 * [backup-simplify]: Simplify 1/4 into 1/4
29.868 * [taylor]: Taking taylor expansion of (log k) in k
29.868 * [taylor]: Taking taylor expansion of k in k
29.868 * [backup-simplify]: Simplify 0 into 0
29.868 * [backup-simplify]: Simplify 1 into 1
29.868 * [backup-simplify]: Simplify (log 1) into 0
29.869 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
29.869 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
29.869 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
29.869 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4))
29.869 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4))
29.871 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
29.871 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
29.872 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0
29.873 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
29.873 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k 1/4))) into 0
29.873 * [backup-simplify]: Simplify 0 into 0
29.876 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
29.877 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
29.878 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0
29.879 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
29.880 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0
29.880 * [backup-simplify]: Simplify 0 into 0
29.886 * [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
29.887 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
29.888 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0
29.890 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
29.891 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))) into 0
29.891 * [backup-simplify]: Simplify 0 into 0
29.902 * [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
29.903 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
29.904 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0
29.907 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (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
29.909 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))) into 0
29.909 * [backup-simplify]: Simplify 0 into 0
29.927 * [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
29.927 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
29.929 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0
29.933 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (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
29.935 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))))) into 0
29.935 * [backup-simplify]: Simplify 0 into 0
29.978 * [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
29.979 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
29.981 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0
29.987 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (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
29.990 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))))) into 0
29.991 * [backup-simplify]: Simplify 0 into 0
29.991 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4))
29.991 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) into (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k)))))
29.991 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in (k) around 0
29.991 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k
29.991 * [taylor]: Taking taylor expansion of 1.0 in k
29.991 * [backup-simplify]: Simplify 1.0 into 1.0
29.991 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k
29.991 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
29.991 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
29.991 * [taylor]: Taking taylor expansion of (/ -1 k) in k
29.991 * [taylor]: Taking taylor expansion of -1 in k
29.991 * [backup-simplify]: Simplify -1 into -1
29.991 * [taylor]: Taking taylor expansion of k in k
29.991 * [backup-simplify]: Simplify 0 into 0
29.991 * [backup-simplify]: Simplify 1 into 1
29.992 * [backup-simplify]: Simplify (/ -1 1) into -1
29.993 * [backup-simplify]: Simplify (sqrt 0) into 0
29.994 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
29.995 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
29.995 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
29.996 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
30.003 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
30.006 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
30.008 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
30.008 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k
30.008 * [taylor]: Taking taylor expansion of 1.0 in k
30.008 * [backup-simplify]: Simplify 1.0 into 1.0
30.008 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k
30.008 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
30.008 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
30.008 * [taylor]: Taking taylor expansion of (/ -1 k) in k
30.008 * [taylor]: Taking taylor expansion of -1 in k
30.008 * [backup-simplify]: Simplify -1 into -1
30.008 * [taylor]: Taking taylor expansion of k in k
30.008 * [backup-simplify]: Simplify 0 into 0
30.008 * [backup-simplify]: Simplify 1 into 1
30.009 * [backup-simplify]: Simplify (/ -1 1) into -1
30.009 * [backup-simplify]: Simplify (sqrt 0) into 0
30.011 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
30.011 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
30.012 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
30.013 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
30.017 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
30.019 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
30.021 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
30.022 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0))
30.022 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0))
30.025 * [backup-simplify]: Simplify (+ (* 1.0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0))) into (- (* +nan.0 (/ 1 (sqrt +nan.0))))
30.027 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (sqrt +nan.0)))) into (- (* +nan.0 (/ 1 (sqrt +nan.0))))
30.028 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
30.031 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
30.034 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
30.043 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
30.054 * [backup-simplify]: Simplify (+ (* 1.0 (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))) (+ (* 0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0)))) into (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))))
30.062 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) into (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))))
30.074 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ 1 (sqrt +nan.0)))) (/ 1 (- k))) (* 1.0 (sqrt +nan.0)))) into (- (* 1.0 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))))))))
30.074 * * * [progress]: simplifying candidates
30.090 * [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 (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (log1p (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (- (- (log 1.0) (log (sqrt (sqrt k)))) (log (sqrt (sqrt k))))
  (- (log (/ 1.0 (sqrt (sqrt k)))) (log (sqrt (sqrt k))))
  (log (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (exp (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (/ (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))
  (/ (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k)))) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))
  (* (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))))
  (cbrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (* (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (sqrt (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))))
  (- (/ 1.0 (sqrt (sqrt k))))
  (- (sqrt (sqrt k)))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt 1)))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt 1))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) 1)
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt 1)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt 1))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) 1)
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt 1)))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt 1))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1)
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt 1)))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt 1))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1)
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt 1)))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt 1))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) 1)
  (/ (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1)))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt 1))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) 1)
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt 1)))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt 1))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1))) 1)
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1)))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt 1))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) 1)
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (sqrt (sqrt 1)))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (sqrt 1))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1)) 1)
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (sqrt k)))
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  (/ (/ 1 (sqrt (sqrt 1))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt 1))) (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt 1))) 1)
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) 1)
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt 1)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt 1)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ (/ 1 (sqrt 1)) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (/ 1 (sqrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt 1)) (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt 1)) (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt 1)) 1)
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) 1)
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ 1 1) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (/ 1 1) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ (/ 1 1) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (/ 1 1) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 1) (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 1) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 1) (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 1) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 1) 1)
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1 1)
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt 1)))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt 1))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1.0 1)
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) 1)
  (/ (sqrt (sqrt k)) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1.0 (cbrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (cbrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (cbrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1 (sqrt (sqrt k))))
  (* (sqrt (sqrt k)) (sqrt (sqrt k)))
  (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 (sqrt k))))
  (log1p (/ 1.0 (sqrt (sqrt k))))
  (- (log 1.0) (log (sqrt (sqrt k))))
  (log (/ 1.0 (sqrt (sqrt k))))
  (exp (/ 1.0 (sqrt (sqrt k))))
  (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))
  (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (cbrt (/ 1.0 (sqrt (sqrt k))))
  (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (- 1.0)
  (- (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (cbrt 1.0) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (cbrt 1.0) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (cbrt 1.0) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) 1)
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt 1.0) (cbrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (sqrt 1.0) (sqrt (cbrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (sqrt 1.0) (sqrt (sqrt (cbrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt 1)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt 1))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) 1)
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1.0 (cbrt (sqrt (sqrt k))))
  (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1.0 (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1.0 (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt 1)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt 1))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1 1)
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (sqrt (sqrt k)) 1.0)
  (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt 1)))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt 1))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1.0 1)
  (/ (sqrt (sqrt k)) (cbrt 1.0))
  (/ (sqrt (sqrt k)) (sqrt 1.0))
  (/ (sqrt (sqrt k)) 1.0)
  (- (+ (* 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))))))
  (- (+ (* +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)))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 1.0 (pow (/ 1 k) 1/4))
  (* 1.0 (pow (/ 1 k) 1/4))
  (- (* 1.0 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))))))))
30.120 * * [simplify]: iteration 0: 566 enodes
30.514 * * [simplify]: iteration 1: 1372 enodes
31.418 * * [simplify]: iteration 2: 3578 enodes
33.252 * * [simplify]: iteration complete: 5023 enodes
33.253 * * [simplify]: Extracting #0: cost 252 inf + 0
33.258 * * [simplify]: Extracting #1: cost 1163 inf + 2
33.271 * * [simplify]: Extracting #2: cost 1692 inf + 4697
33.304 * * [simplify]: Extracting #3: cost 1338 inf + 96806
33.407 * * [simplify]: Extracting #4: cost 393 inf + 352603
33.564 * * [simplify]: Extracting #5: cost 56 inf + 475820
33.737 * * [simplify]: Extracting #6: cost 12 inf + 489658
33.906 * * [simplify]: Extracting #7: cost 0 inf + 493293
34.099 * * [simplify]: Extracting #8: cost 0 inf + 493238
34.281 * [simplify]: Simplified to:
  (expm1 (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (* (/ (- 1.0 k) 2.0) (log (* PI (* n 2.0))))
  (* (/ (- 1.0 k) 2.0) (log (* PI (* n 2.0))))
  (* (/ (- 1.0 k) 2.0) (log (* PI (* n 2.0))))
  (* (/ (- 1.0 k) 2.0) (log (* PI (* n 2.0))))
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (pow (* PI (* n 2.0)) (/ 1.0 2.0))
  (pow (* PI (* n 2.0)) (/ k 2.0))
  (pow (* PI (* n 2.0)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* PI (* n 2.0)) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* PI (* n 2.0)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0))))
  (pow (* PI (* n 2.0)) (/ (cbrt (- 1.0 k)) (/ (sqrt 2.0) (cbrt (- 1.0 k)))))
  (pow (* PI (* n 2.0)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* PI (* n 2.0)) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* PI (* n 2.0)) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* PI (* n 2.0)) (sqrt (- 1.0 k)))
  (pow (* PI (* n 2.0)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0)))
  (pow (* PI (* n 2.0)) (/ 1 (sqrt 2.0)))
  (* PI (* n 2.0))
  (pow (* PI (* n 2.0)) (/ (+ (sqrt k) (sqrt 1.0)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* PI (* n 2.0)) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0)))
  (pow (* PI (* n 2.0)) (+ (sqrt k) (sqrt 1.0)))
  (pow (* PI (* n 2.0)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0)))
  (pow (* PI (* n 2.0)) (/ 1 (sqrt 2.0)))
  (* PI (* n 2.0))
  (* PI (* n 2.0))
  (pow (* PI (* n 2.0)) (- 1.0 k))
  (pow (* PI 2.0) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (* (/ (- 1.0 k) 2.0) (log (* PI (* n 2.0))))
  (exp (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0))) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
  (pow (* PI (* n 2.0)) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* PI (* n 2.0)) (/ (/ (- 1.0 k) 2.0) 2))
  (expm1 (/ 1.0 (sqrt k)))
  (log1p (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k)))
  (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (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 (sqrt k))))
  (- (sqrt (sqrt k)))
  (* (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (* (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (fabs (cbrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (fabs (cbrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
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  (/ (sqrt (sqrt k)) (sqrt 1.0))
  (/ (sqrt (sqrt k)) 1.0)
  (fma (* 0.125 (* k k)) (fma (* (log (* PI 2.0)) (exp (* 0.5 (log (* PI (* n 2.0)))))) (log (* PI 2.0)) (* (* (log n) (log n)) (exp (* 0.5 (log (* PI (* n 2.0))))))) (- (fma (* (* (* (* k k) (log (* PI 2.0))) (exp (* 0.5 (log (* PI (* n 2.0)))))) (log n)) 0.25 (exp (* 0.5 (log (* PI (* n 2.0)))))) (* (* k 0.5) (fma (log (* PI 2.0)) (exp (* 0.5 (log (* PI (* n 2.0))))) (* (exp (* 0.5 (log (* PI (* n 2.0))))) (log n))))))
  (exp (* (* 0.5 (log (* PI (* n 2.0)))) (- 1.0 k)))
  (exp (* (* (- 1.0 k) 0.5) (- (log (* PI -2.0)) (log (/ -1 n)))))
  (- (- (fma +nan.0 k +nan.0) (* +nan.0 (* k k))))
  (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ +nan.0 (* (* k k) k))))
  (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) +nan.0))
  (* PI (* n 2.0))
  (* PI (* n 2.0))
  (* PI (* n 2.0))
  (* (pow (/ 1 k) 1/4) 1.0)
  (* (pow (/ 1 k) 1/4) 1.0)
  (- (* 1.0 (sqrt +nan.0)) (+ (- (/ (/ +nan.0 (sqrt +nan.0)) (* k k)) (/ (/ +nan.0 k) (sqrt +nan.0))) (/ +nan.0 (* (* +nan.0 (* k k)) (sqrt +nan.0)))))
34.396 * * * [progress]: adding candidates to table
37.193 * [progress]: [Phase 3 of 3] Extracting.
37.193 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (* (* (/ (/ 1 (sqrt (fabs (cbrt k)))) (fabs (cbrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k))))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)))))> #<alt (λ (k n) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))> #<alt (λ (k n) (/ (* 1.0 (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt k)))> #<alt (λ (k n) (/ 1.0 (/ (sqrt (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))))))> #<alt (λ (k n) (* (* (/ (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))))))> #<alt (λ (k n) (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ 1.0 (* (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))))>)
37.205 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k)
37.205 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (#<alt (λ (k n) (* (* (/ (/ 1 (sqrt (fabs (cbrt k)))) (fabs (cbrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k))))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)))))> #<alt (λ (k n) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))> #<alt (λ (k n) (/ (* 1.0 (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt k)))> #<alt (λ (k n) (/ 1.0 (/ (sqrt (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))))))> #<alt (λ (k n) (* (* (/ (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))))))> #<alt (λ (k n) (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ 1.0 (* (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))))>)
37.360 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (* (* (/ (/ 1 (sqrt (fabs (cbrt k)))) (fabs (cbrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k))))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)))))> #<alt (λ (k n) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))> #<alt (λ (k n) (/ (* 1.0 (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt k)))> #<alt (λ (k n) (/ 1.0 (/ (sqrt (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))))))> #<alt (λ (k n) (* (* (/ (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))))))> #<alt (λ (k n) (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ 1.0 (* (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))))>)
37.516 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (* (* (/ (/ 1 (sqrt (fabs (cbrt k)))) (fabs (cbrt (sqrt k)))) (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k))))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)))))> #<alt (λ (k n) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))> #<alt (λ (k n) (/ (* 1.0 (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt k)))> #<alt (λ (k n) (/ 1.0 (/ (sqrt (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))))))> #<alt (λ (k n) (* (* (/ (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))))))> #<alt (λ (k n) (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ 1.0 (* (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))))>)
37.687 * * * [regime]: Found split indices: #<option (#s(si 3 255))>
37.688 * [simplify]: Simplifying:
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
37.688 * * [simplify]: iteration 0: 13 enodes
37.690 * * [simplify]: iteration 1: 15 enodes
37.692 * * [simplify]: iteration complete: 15 enodes
37.693 * * [simplify]: Extracting #0: cost 1 inf + 0
37.693 * * [simplify]: Extracting #1: cost 3 inf + 0
37.693 * * [simplify]: Extracting #2: cost 4 inf + 1
37.693 * * [simplify]: Extracting #3: cost 7 inf + 1
37.693 * * [simplify]: Extracting #4: cost 9 inf + 43
37.693 * * [simplify]: Extracting #5: cost 6 inf + 170
37.693 * * [simplify]: Extracting #6: cost 3 inf + 296
37.693 * * [simplify]: Extracting #7: cost 1 inf + 1126
37.694 * * [simplify]: Extracting #8: cost 0 inf + 1621
37.694 * [simplify]: Simplified to:
  (/ 1.0 (/ (sqrt k) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))))
48.221 * [regime-testing]: Baseline error score: 0.36206858809282094
48.238 * [regime-testing]: Oracle error score: 0.03604698712375105
48.273 * [regime-testing]: End program error score: 0.36206858809282094