0.001 * [progress]: [Phase 1 of 3] Setting up.
0.001 * * * [progress]: [1/2] Preparing points
0.232 * * * [progress]: [2/2] Setting up program.
0.239 * [progress]: [Phase 2 of 3] Improving.
0.239 * * * * [progress]: [ 1 / 1 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
0.240 * [simplify]: Simplifying:
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.240 * * [simplify]: iteration 1: (13 enodes)
0.249 * * [simplify]: iteration 2: (56 enodes)
0.268 * * [simplify]: iteration 3: (99 enodes)
0.302 * * [simplify]: iteration 4: (183 enodes)
0.360 * * [simplify]: iteration 5: (374 enodes)
0.519 * * [simplify]: iteration 6: (880 enodes)
1.155 * * [simplify]: Extracting #0: cost 1 inf + 0
1.155 * * [simplify]: Extracting #1: cost 72 inf + 0
1.157 * * [simplify]: Extracting #2: cost 289 inf + 1
1.168 * * [simplify]: Extracting #3: cost 390 inf + 250
1.173 * * [simplify]: Extracting #4: cost 417 inf + 5173
1.193 * * [simplify]: Extracting #5: cost 252 inf + 78089
1.275 * * [simplify]: Extracting #6: cost 45 inf + 284924
1.344 * * [simplify]: Extracting #7: cost 0 inf + 292179
1.442 * * [simplify]: Extracting #8: cost 0 inf + 273136
1.539 * [simplify]: Simplified to:
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
1.546 * * [progress]: iteration 1 / 4
1.546 * * * [progress]: picking best candidate
1.553 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))>
1.553 * * * [progress]: localizing error
1.583 * * * [progress]: generating rewritten candidates
1.583 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
1.597 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1)
1.617 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
1.632 * * * [progress]: generating series expansions
1.632 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
1.632 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
1.633 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
1.633 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
1.633 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
1.633 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
1.633 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
1.633 * [taylor]: Taking taylor expansion of 1/2 in k
1.633 * [backup-simplify]: Simplify 1/2 into 1/2
1.633 * [taylor]: Taking taylor expansion of (- 1 k) in k
1.633 * [taylor]: Taking taylor expansion of 1 in k
1.633 * [backup-simplify]: Simplify 1 into 1
1.633 * [taylor]: Taking taylor expansion of k in k
1.633 * [backup-simplify]: Simplify 0 into 0
1.633 * [backup-simplify]: Simplify 1 into 1
1.633 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
1.633 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
1.633 * [taylor]: Taking taylor expansion of 2 in k
1.633 * [backup-simplify]: Simplify 2 into 2
1.633 * [taylor]: Taking taylor expansion of (* n PI) in k
1.633 * [taylor]: Taking taylor expansion of n in k
1.633 * [backup-simplify]: Simplify n into n
1.633 * [taylor]: Taking taylor expansion of PI in k
1.633 * [backup-simplify]: Simplify PI into PI
1.633 * [backup-simplify]: Simplify (* n PI) into (* n PI)
1.633 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
1.633 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
1.633 * [backup-simplify]: Simplify (- 0) into 0
1.633 * [backup-simplify]: Simplify (+ 1 0) into 1
1.634 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.634 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
1.634 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
1.634 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
1.634 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
1.634 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
1.634 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
1.634 * [taylor]: Taking taylor expansion of 1/2 in n
1.634 * [backup-simplify]: Simplify 1/2 into 1/2
1.634 * [taylor]: Taking taylor expansion of (- 1 k) in n
1.634 * [taylor]: Taking taylor expansion of 1 in n
1.634 * [backup-simplify]: Simplify 1 into 1
1.634 * [taylor]: Taking taylor expansion of k in n
1.634 * [backup-simplify]: Simplify k into k
1.634 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.634 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.634 * [taylor]: Taking taylor expansion of 2 in n
1.634 * [backup-simplify]: Simplify 2 into 2
1.634 * [taylor]: Taking taylor expansion of (* n PI) in n
1.634 * [taylor]: Taking taylor expansion of n in n
1.634 * [backup-simplify]: Simplify 0 into 0
1.634 * [backup-simplify]: Simplify 1 into 1
1.634 * [taylor]: Taking taylor expansion of PI in n
1.634 * [backup-simplify]: Simplify PI into PI
1.635 * [backup-simplify]: Simplify (* 0 PI) into 0
1.635 * [backup-simplify]: Simplify (* 2 0) into 0
1.636 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.637 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.637 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.637 * [backup-simplify]: Simplify (- k) into (- k)
1.637 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
1.637 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
1.638 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.639 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
1.640 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
1.640 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
1.640 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
1.640 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
1.640 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
1.640 * [taylor]: Taking taylor expansion of 1/2 in n
1.640 * [backup-simplify]: Simplify 1/2 into 1/2
1.640 * [taylor]: Taking taylor expansion of (- 1 k) in n
1.640 * [taylor]: Taking taylor expansion of 1 in n
1.640 * [backup-simplify]: Simplify 1 into 1
1.640 * [taylor]: Taking taylor expansion of k in n
1.640 * [backup-simplify]: Simplify k into k
1.640 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.640 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.640 * [taylor]: Taking taylor expansion of 2 in n
1.640 * [backup-simplify]: Simplify 2 into 2
1.640 * [taylor]: Taking taylor expansion of (* n PI) in n
1.640 * [taylor]: Taking taylor expansion of n in n
1.640 * [backup-simplify]: Simplify 0 into 0
1.640 * [backup-simplify]: Simplify 1 into 1
1.640 * [taylor]: Taking taylor expansion of PI in n
1.640 * [backup-simplify]: Simplify PI into PI
1.640 * [backup-simplify]: Simplify (* 0 PI) into 0
1.641 * [backup-simplify]: Simplify (* 2 0) into 0
1.641 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.642 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.643 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.643 * [backup-simplify]: Simplify (- k) into (- k)
1.643 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
1.643 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
1.644 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.645 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
1.645 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
1.645 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
1.645 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
1.645 * [taylor]: Taking taylor expansion of 1/2 in k
1.645 * [backup-simplify]: Simplify 1/2 into 1/2
1.645 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
1.646 * [taylor]: Taking taylor expansion of (- 1 k) in k
1.646 * [taylor]: Taking taylor expansion of 1 in k
1.646 * [backup-simplify]: Simplify 1 into 1
1.646 * [taylor]: Taking taylor expansion of k in k
1.646 * [backup-simplify]: Simplify 0 into 0
1.646 * [backup-simplify]: Simplify 1 into 1
1.646 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
1.646 * [taylor]: Taking taylor expansion of (log n) in k
1.646 * [taylor]: Taking taylor expansion of n in k
1.646 * [backup-simplify]: Simplify n into n
1.646 * [backup-simplify]: Simplify (log n) into (log n)
1.646 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.646 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.646 * [taylor]: Taking taylor expansion of 2 in k
1.646 * [backup-simplify]: Simplify 2 into 2
1.646 * [taylor]: Taking taylor expansion of PI in k
1.646 * [backup-simplify]: Simplify PI into PI
1.646 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.647 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.647 * [backup-simplify]: Simplify (- 0) into 0
1.647 * [backup-simplify]: Simplify (+ 1 0) into 1
1.648 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.648 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
1.649 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
1.650 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.651 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.652 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
1.653 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
1.655 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.655 * [backup-simplify]: Simplify (- 0) into 0
1.656 * [backup-simplify]: Simplify (+ 0 0) into 0
1.656 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
1.657 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.659 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
1.660 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.660 * [taylor]: Taking taylor expansion of 0 in k
1.661 * [backup-simplify]: Simplify 0 into 0
1.661 * [backup-simplify]: Simplify 0 into 0
1.661 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
1.662 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.664 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.664 * [backup-simplify]: Simplify (+ 0 0) into 0
1.665 * [backup-simplify]: Simplify (- 1) into -1
1.665 * [backup-simplify]: Simplify (+ 0 -1) into -1
1.670 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
1.672 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
1.674 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
1.676 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
1.677 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
1.678 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
1.680 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
1.680 * [backup-simplify]: Simplify (- 0) into 0
1.681 * [backup-simplify]: Simplify (+ 0 0) into 0
1.681 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
1.682 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.683 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.684 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.684 * [taylor]: Taking taylor expansion of 0 in k
1.684 * [backup-simplify]: Simplify 0 into 0
1.684 * [backup-simplify]: Simplify 0 into 0
1.684 * [backup-simplify]: Simplify 0 into 0
1.685 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
1.686 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.688 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
1.688 * [backup-simplify]: Simplify (+ 0 0) into 0
1.688 * [backup-simplify]: Simplify (- 0) into 0
1.689 * [backup-simplify]: Simplify (+ 0 0) into 0
1.690 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.691 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.694 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
1.699 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
1.709 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
1.709 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
1.710 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
1.710 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
1.710 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
1.710 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
1.710 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
1.710 * [taylor]: Taking taylor expansion of 1/2 in k
1.710 * [backup-simplify]: Simplify 1/2 into 1/2
1.710 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
1.710 * [taylor]: Taking taylor expansion of 1 in k
1.710 * [backup-simplify]: Simplify 1 into 1
1.710 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.710 * [taylor]: Taking taylor expansion of k in k
1.710 * [backup-simplify]: Simplify 0 into 0
1.710 * [backup-simplify]: Simplify 1 into 1
1.710 * [backup-simplify]: Simplify (/ 1 1) into 1
1.710 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
1.710 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
1.710 * [taylor]: Taking taylor expansion of 2 in k
1.710 * [backup-simplify]: Simplify 2 into 2
1.710 * [taylor]: Taking taylor expansion of (/ PI n) in k
1.710 * [taylor]: Taking taylor expansion of PI in k
1.711 * [backup-simplify]: Simplify PI into PI
1.711 * [taylor]: Taking taylor expansion of n in k
1.711 * [backup-simplify]: Simplify n into n
1.711 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
1.711 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
1.711 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
1.711 * [backup-simplify]: Simplify (- 1) into -1
1.712 * [backup-simplify]: Simplify (+ 0 -1) into -1
1.712 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
1.712 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
1.712 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
1.713 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
1.713 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
1.713 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
1.713 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
1.713 * [taylor]: Taking taylor expansion of 1/2 in n
1.713 * [backup-simplify]: Simplify 1/2 into 1/2
1.713 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
1.713 * [taylor]: Taking taylor expansion of 1 in n
1.713 * [backup-simplify]: Simplify 1 into 1
1.713 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.713 * [taylor]: Taking taylor expansion of k in n
1.713 * [backup-simplify]: Simplify k into k
1.713 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.713 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
1.713 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.713 * [taylor]: Taking taylor expansion of 2 in n
1.713 * [backup-simplify]: Simplify 2 into 2
1.713 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.713 * [taylor]: Taking taylor expansion of PI in n
1.713 * [backup-simplify]: Simplify PI into PI
1.713 * [taylor]: Taking taylor expansion of n in n
1.713 * [backup-simplify]: Simplify 0 into 0
1.713 * [backup-simplify]: Simplify 1 into 1
1.714 * [backup-simplify]: Simplify (/ PI 1) into PI
1.714 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.715 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.715 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
1.716 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
1.716 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
1.717 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.718 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
1.720 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
1.720 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
1.720 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
1.720 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
1.720 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
1.720 * [taylor]: Taking taylor expansion of 1/2 in n
1.720 * [backup-simplify]: Simplify 1/2 into 1/2
1.720 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
1.720 * [taylor]: Taking taylor expansion of 1 in n
1.720 * [backup-simplify]: Simplify 1 into 1
1.720 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.720 * [taylor]: Taking taylor expansion of k in n
1.720 * [backup-simplify]: Simplify k into k
1.720 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.720 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
1.720 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.720 * [taylor]: Taking taylor expansion of 2 in n
1.720 * [backup-simplify]: Simplify 2 into 2
1.720 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.720 * [taylor]: Taking taylor expansion of PI in n
1.720 * [backup-simplify]: Simplify PI into PI
1.721 * [taylor]: Taking taylor expansion of n in n
1.721 * [backup-simplify]: Simplify 0 into 0
1.721 * [backup-simplify]: Simplify 1 into 1
1.721 * [backup-simplify]: Simplify (/ PI 1) into PI
1.722 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.723 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.723 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
1.723 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
1.723 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
1.724 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.725 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
1.727 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
1.727 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
1.727 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
1.727 * [taylor]: Taking taylor expansion of 1/2 in k
1.727 * [backup-simplify]: Simplify 1/2 into 1/2
1.727 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
1.727 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
1.727 * [taylor]: Taking taylor expansion of 1 in k
1.727 * [backup-simplify]: Simplify 1 into 1
1.727 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.727 * [taylor]: Taking taylor expansion of k in k
1.727 * [backup-simplify]: Simplify 0 into 0
1.727 * [backup-simplify]: Simplify 1 into 1
1.727 * [backup-simplify]: Simplify (/ 1 1) into 1
1.727 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
1.727 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.727 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.727 * [taylor]: Taking taylor expansion of 2 in k
1.728 * [backup-simplify]: Simplify 2 into 2
1.728 * [taylor]: Taking taylor expansion of PI in k
1.728 * [backup-simplify]: Simplify PI into PI
1.728 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.729 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.729 * [taylor]: Taking taylor expansion of (log n) in k
1.729 * [taylor]: Taking taylor expansion of n in k
1.729 * [backup-simplify]: Simplify n into n
1.729 * [backup-simplify]: Simplify (log n) into (log n)
1.730 * [backup-simplify]: Simplify (- 1) into -1
1.730 * [backup-simplify]: Simplify (+ 0 -1) into -1
1.730 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
1.731 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
1.732 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
1.733 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
1.734 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
1.736 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
1.737 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.737 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.739 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.739 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.740 * [backup-simplify]: Simplify (- 0) into 0
1.740 * [backup-simplify]: Simplify (+ 0 0) into 0
1.741 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
1.742 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.743 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
1.745 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.745 * [taylor]: Taking taylor expansion of 0 in k
1.745 * [backup-simplify]: Simplify 0 into 0
1.745 * [backup-simplify]: Simplify 0 into 0
1.745 * [backup-simplify]: Simplify 0 into 0
1.747 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.748 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.751 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
1.751 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.752 * [backup-simplify]: Simplify (- 0) into 0
1.752 * [backup-simplify]: Simplify (+ 0 0) into 0
1.753 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
1.755 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.756 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
1.759 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.759 * [taylor]: Taking taylor expansion of 0 in k
1.759 * [backup-simplify]: Simplify 0 into 0
1.759 * [backup-simplify]: Simplify 0 into 0
1.759 * [backup-simplify]: Simplify 0 into 0
1.759 * [backup-simplify]: Simplify 0 into 0
1.760 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.761 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.767 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
1.768 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.768 * [backup-simplify]: Simplify (- 0) into 0
1.769 * [backup-simplify]: Simplify (+ 0 0) into 0
1.770 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
1.772 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.774 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
1.776 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
1.776 * [taylor]: Taking taylor expansion of 0 in k
1.777 * [backup-simplify]: Simplify 0 into 0
1.777 * [backup-simplify]: Simplify 0 into 0
1.778 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
1.778 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
1.778 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
1.778 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
1.779 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
1.779 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
1.779 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
1.779 * [taylor]: Taking taylor expansion of 1/2 in k
1.779 * [backup-simplify]: Simplify 1/2 into 1/2
1.779 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
1.779 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.779 * [taylor]: Taking taylor expansion of k in k
1.779 * [backup-simplify]: Simplify 0 into 0
1.779 * [backup-simplify]: Simplify 1 into 1
1.779 * [backup-simplify]: Simplify (/ 1 1) into 1
1.779 * [taylor]: Taking taylor expansion of 1 in k
1.779 * [backup-simplify]: Simplify 1 into 1
1.779 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
1.779 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
1.779 * [taylor]: Taking taylor expansion of -2 in k
1.779 * [backup-simplify]: Simplify -2 into -2
1.779 * [taylor]: Taking taylor expansion of (/ PI n) in k
1.779 * [taylor]: Taking taylor expansion of PI in k
1.779 * [backup-simplify]: Simplify PI into PI
1.779 * [taylor]: Taking taylor expansion of n in k
1.779 * [backup-simplify]: Simplify n into n
1.779 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
1.780 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
1.780 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
1.780 * [backup-simplify]: Simplify (+ 1 0) into 1
1.781 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.781 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
1.781 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
1.781 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
1.781 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
1.781 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
1.781 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
1.781 * [taylor]: Taking taylor expansion of 1/2 in n
1.781 * [backup-simplify]: Simplify 1/2 into 1/2
1.781 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
1.781 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.781 * [taylor]: Taking taylor expansion of k in n
1.781 * [backup-simplify]: Simplify k into k
1.781 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.781 * [taylor]: Taking taylor expansion of 1 in n
1.781 * [backup-simplify]: Simplify 1 into 1
1.781 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
1.781 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.781 * [taylor]: Taking taylor expansion of -2 in n
1.781 * [backup-simplify]: Simplify -2 into -2
1.781 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.781 * [taylor]: Taking taylor expansion of PI in n
1.781 * [backup-simplify]: Simplify PI into PI
1.781 * [taylor]: Taking taylor expansion of n in n
1.781 * [backup-simplify]: Simplify 0 into 0
1.781 * [backup-simplify]: Simplify 1 into 1
1.782 * [backup-simplify]: Simplify (/ PI 1) into PI
1.782 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.783 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.783 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
1.784 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
1.785 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.786 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
1.787 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
1.787 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
1.787 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
1.787 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
1.787 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
1.787 * [taylor]: Taking taylor expansion of 1/2 in n
1.787 * [backup-simplify]: Simplify 1/2 into 1/2
1.787 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
1.787 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.787 * [taylor]: Taking taylor expansion of k in n
1.787 * [backup-simplify]: Simplify k into k
1.787 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.787 * [taylor]: Taking taylor expansion of 1 in n
1.787 * [backup-simplify]: Simplify 1 into 1
1.787 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
1.787 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.787 * [taylor]: Taking taylor expansion of -2 in n
1.787 * [backup-simplify]: Simplify -2 into -2
1.787 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.787 * [taylor]: Taking taylor expansion of PI in n
1.787 * [backup-simplify]: Simplify PI into PI
1.787 * [taylor]: Taking taylor expansion of n in n
1.787 * [backup-simplify]: Simplify 0 into 0
1.787 * [backup-simplify]: Simplify 1 into 1
1.787 * [backup-simplify]: Simplify (/ PI 1) into PI
1.788 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.788 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.788 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
1.788 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
1.789 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.790 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
1.791 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
1.791 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
1.791 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
1.791 * [taylor]: Taking taylor expansion of 1/2 in k
1.791 * [backup-simplify]: Simplify 1/2 into 1/2
1.791 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
1.791 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
1.791 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.791 * [taylor]: Taking taylor expansion of k in k
1.791 * [backup-simplify]: Simplify 0 into 0
1.791 * [backup-simplify]: Simplify 1 into 1
1.791 * [backup-simplify]: Simplify (/ 1 1) into 1
1.791 * [taylor]: Taking taylor expansion of 1 in k
1.791 * [backup-simplify]: Simplify 1 into 1
1.791 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
1.791 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
1.791 * [taylor]: Taking taylor expansion of (* -2 PI) in k
1.791 * [taylor]: Taking taylor expansion of -2 in k
1.791 * [backup-simplify]: Simplify -2 into -2
1.791 * [taylor]: Taking taylor expansion of PI in k
1.791 * [backup-simplify]: Simplify PI into PI
1.792 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.792 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.792 * [taylor]: Taking taylor expansion of (log n) in k
1.792 * [taylor]: Taking taylor expansion of n in k
1.792 * [backup-simplify]: Simplify n into n
1.792 * [backup-simplify]: Simplify (log n) into (log n)
1.793 * [backup-simplify]: Simplify (+ 1 0) into 1
1.793 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
1.793 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
1.794 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
1.799 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
1.800 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
1.801 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
1.801 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.802 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
1.803 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
1.803 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.803 * [backup-simplify]: Simplify (+ 0 0) into 0
1.804 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
1.804 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.805 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
1.806 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.806 * [taylor]: Taking taylor expansion of 0 in k
1.806 * [backup-simplify]: Simplify 0 into 0
1.806 * [backup-simplify]: Simplify 0 into 0
1.806 * [backup-simplify]: Simplify 0 into 0
1.807 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.808 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
1.810 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
1.810 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.810 * [backup-simplify]: Simplify (+ 0 0) into 0
1.811 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
1.812 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.812 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
1.814 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.814 * [taylor]: Taking taylor expansion of 0 in k
1.814 * [backup-simplify]: Simplify 0 into 0
1.814 * [backup-simplify]: Simplify 0 into 0
1.814 * [backup-simplify]: Simplify 0 into 0
1.814 * [backup-simplify]: Simplify 0 into 0
1.815 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.817 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.823 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
1.823 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.824 * [backup-simplify]: Simplify (+ 0 0) into 0
1.825 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
1.827 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.829 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
1.832 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
1.832 * [taylor]: Taking taylor expansion of 0 in k
1.832 * [backup-simplify]: Simplify 0 into 0
1.832 * [backup-simplify]: Simplify 0 into 0
1.833 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
1.833 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1)
1.834 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
1.834 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
1.834 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.834 * [taylor]: Taking taylor expansion of 2 in n
1.834 * [backup-simplify]: Simplify 2 into 2
1.834 * [taylor]: Taking taylor expansion of (* n PI) in n
1.834 * [taylor]: Taking taylor expansion of n in n
1.834 * [backup-simplify]: Simplify 0 into 0
1.834 * [backup-simplify]: Simplify 1 into 1
1.834 * [taylor]: Taking taylor expansion of PI in n
1.834 * [backup-simplify]: Simplify PI into PI
1.834 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.834 * [taylor]: Taking taylor expansion of 2 in n
1.834 * [backup-simplify]: Simplify 2 into 2
1.834 * [taylor]: Taking taylor expansion of (* n PI) in n
1.834 * [taylor]: Taking taylor expansion of n in n
1.834 * [backup-simplify]: Simplify 0 into 0
1.834 * [backup-simplify]: Simplify 1 into 1
1.834 * [taylor]: Taking taylor expansion of PI in n
1.834 * [backup-simplify]: Simplify PI into PI
1.835 * [backup-simplify]: Simplify (* 0 PI) into 0
1.835 * [backup-simplify]: Simplify (* 2 0) into 0
1.835 * [backup-simplify]: Simplify 0 into 0
1.837 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.838 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.839 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.840 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
1.841 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
1.841 * [backup-simplify]: Simplify 0 into 0
1.843 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
1.844 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
1.844 * [backup-simplify]: Simplify 0 into 0
1.845 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
1.847 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
1.847 * [backup-simplify]: Simplify 0 into 0
1.848 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
1.850 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
1.850 * [backup-simplify]: Simplify 0 into 0
1.852 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
1.854 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
1.854 * [backup-simplify]: Simplify 0 into 0
1.856 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
1.858 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
1.859 * [backup-simplify]: Simplify 0 into 0
1.859 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
1.860 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
1.860 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
1.860 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.860 * [taylor]: Taking taylor expansion of 2 in n
1.860 * [backup-simplify]: Simplify 2 into 2
1.860 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.860 * [taylor]: Taking taylor expansion of PI in n
1.860 * [backup-simplify]: Simplify PI into PI
1.860 * [taylor]: Taking taylor expansion of n in n
1.860 * [backup-simplify]: Simplify 0 into 0
1.860 * [backup-simplify]: Simplify 1 into 1
1.860 * [backup-simplify]: Simplify (/ PI 1) into PI
1.860 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.860 * [taylor]: Taking taylor expansion of 2 in n
1.860 * [backup-simplify]: Simplify 2 into 2
1.860 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.861 * [taylor]: Taking taylor expansion of PI in n
1.861 * [backup-simplify]: Simplify PI into PI
1.861 * [taylor]: Taking taylor expansion of n in n
1.861 * [backup-simplify]: Simplify 0 into 0
1.861 * [backup-simplify]: Simplify 1 into 1
1.861 * [backup-simplify]: Simplify (/ PI 1) into PI
1.862 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.862 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.863 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.864 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.864 * [backup-simplify]: Simplify 0 into 0
1.865 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.866 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.866 * [backup-simplify]: Simplify 0 into 0
1.867 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.868 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.868 * [backup-simplify]: Simplify 0 into 0
1.869 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.871 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
1.871 * [backup-simplify]: Simplify 0 into 0
1.872 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.874 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
1.874 * [backup-simplify]: Simplify 0 into 0
1.875 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.877 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
1.877 * [backup-simplify]: Simplify 0 into 0
1.877 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
1.878 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
1.878 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
1.878 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.878 * [taylor]: Taking taylor expansion of -2 in n
1.878 * [backup-simplify]: Simplify -2 into -2
1.878 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.878 * [taylor]: Taking taylor expansion of PI in n
1.878 * [backup-simplify]: Simplify PI into PI
1.878 * [taylor]: Taking taylor expansion of n in n
1.878 * [backup-simplify]: Simplify 0 into 0
1.878 * [backup-simplify]: Simplify 1 into 1
1.879 * [backup-simplify]: Simplify (/ PI 1) into PI
1.879 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.879 * [taylor]: Taking taylor expansion of -2 in n
1.879 * [backup-simplify]: Simplify -2 into -2
1.879 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.879 * [taylor]: Taking taylor expansion of PI in n
1.879 * [backup-simplify]: Simplify PI into PI
1.879 * [taylor]: Taking taylor expansion of n in n
1.879 * [backup-simplify]: Simplify 0 into 0
1.879 * [backup-simplify]: Simplify 1 into 1
1.879 * [backup-simplify]: Simplify (/ PI 1) into PI
1.880 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.880 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.881 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.882 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
1.882 * [backup-simplify]: Simplify 0 into 0
1.883 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.884 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
1.884 * [backup-simplify]: Simplify 0 into 0
1.885 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.887 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.887 * [backup-simplify]: Simplify 0 into 0
1.888 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.889 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
1.889 * [backup-simplify]: Simplify 0 into 0
1.890 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.892 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
1.892 * [backup-simplify]: Simplify 0 into 0
1.893 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.895 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
1.895 * [backup-simplify]: Simplify 0 into 0
1.896 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
1.896 * * * * [progress]: [ 3 / 3 ] generating series at (2)
1.896 * [backup-simplify]: Simplify (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
1.897 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (n k) around 0
1.897 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
1.897 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
1.897 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
1.897 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
1.897 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
1.897 * [taylor]: Taking taylor expansion of 1/2 in k
1.897 * [backup-simplify]: Simplify 1/2 into 1/2
1.897 * [taylor]: Taking taylor expansion of (- 1 k) in k
1.897 * [taylor]: Taking taylor expansion of 1 in k
1.897 * [backup-simplify]: Simplify 1 into 1
1.897 * [taylor]: Taking taylor expansion of k in k
1.897 * [backup-simplify]: Simplify 0 into 0
1.897 * [backup-simplify]: Simplify 1 into 1
1.897 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
1.897 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
1.897 * [taylor]: Taking taylor expansion of 2 in k
1.897 * [backup-simplify]: Simplify 2 into 2
1.897 * [taylor]: Taking taylor expansion of (* n PI) in k
1.897 * [taylor]: Taking taylor expansion of n in k
1.897 * [backup-simplify]: Simplify n into n
1.897 * [taylor]: Taking taylor expansion of PI in k
1.897 * [backup-simplify]: Simplify PI into PI
1.897 * [backup-simplify]: Simplify (* n PI) into (* n PI)
1.897 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
1.897 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
1.898 * [backup-simplify]: Simplify (- 0) into 0
1.898 * [backup-simplify]: Simplify (+ 1 0) into 1
1.899 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.899 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
1.899 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
1.899 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
1.899 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.899 * [taylor]: Taking taylor expansion of k in k
1.899 * [backup-simplify]: Simplify 0 into 0
1.899 * [backup-simplify]: Simplify 1 into 1
1.899 * [backup-simplify]: Simplify (/ 1 1) into 1
1.900 * [backup-simplify]: Simplify (sqrt 0) into 0
1.901 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
1.901 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
1.901 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
1.902 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
1.902 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
1.902 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
1.902 * [taylor]: Taking taylor expansion of 1/2 in n
1.902 * [backup-simplify]: Simplify 1/2 into 1/2
1.902 * [taylor]: Taking taylor expansion of (- 1 k) in n
1.902 * [taylor]: Taking taylor expansion of 1 in n
1.902 * [backup-simplify]: Simplify 1 into 1
1.902 * [taylor]: Taking taylor expansion of k in n
1.902 * [backup-simplify]: Simplify k into k
1.902 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.902 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.902 * [taylor]: Taking taylor expansion of 2 in n
1.902 * [backup-simplify]: Simplify 2 into 2
1.902 * [taylor]: Taking taylor expansion of (* n PI) in n
1.902 * [taylor]: Taking taylor expansion of n in n
1.902 * [backup-simplify]: Simplify 0 into 0
1.902 * [backup-simplify]: Simplify 1 into 1
1.902 * [taylor]: Taking taylor expansion of PI in n
1.902 * [backup-simplify]: Simplify PI into PI
1.902 * [backup-simplify]: Simplify (* 0 PI) into 0
1.903 * [backup-simplify]: Simplify (* 2 0) into 0
1.904 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.906 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.907 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.907 * [backup-simplify]: Simplify (- k) into (- k)
1.907 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
1.907 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
1.909 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.910 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
1.911 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
1.911 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
1.911 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.911 * [taylor]: Taking taylor expansion of k in n
1.911 * [backup-simplify]: Simplify k into k
1.911 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.911 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
1.911 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.912 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
1.912 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
1.912 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
1.912 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
1.912 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
1.912 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
1.912 * [taylor]: Taking taylor expansion of 1/2 in n
1.912 * [backup-simplify]: Simplify 1/2 into 1/2
1.912 * [taylor]: Taking taylor expansion of (- 1 k) in n
1.912 * [taylor]: Taking taylor expansion of 1 in n
1.912 * [backup-simplify]: Simplify 1 into 1
1.912 * [taylor]: Taking taylor expansion of k in n
1.912 * [backup-simplify]: Simplify k into k
1.912 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.912 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.912 * [taylor]: Taking taylor expansion of 2 in n
1.912 * [backup-simplify]: Simplify 2 into 2
1.912 * [taylor]: Taking taylor expansion of (* n PI) in n
1.912 * [taylor]: Taking taylor expansion of n in n
1.912 * [backup-simplify]: Simplify 0 into 0
1.912 * [backup-simplify]: Simplify 1 into 1
1.912 * [taylor]: Taking taylor expansion of PI in n
1.912 * [backup-simplify]: Simplify PI into PI
1.913 * [backup-simplify]: Simplify (* 0 PI) into 0
1.913 * [backup-simplify]: Simplify (* 2 0) into 0
1.914 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.916 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.917 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.917 * [backup-simplify]: Simplify (- k) into (- k)
1.917 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
1.917 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
1.918 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.920 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
1.921 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
1.921 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
1.921 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.921 * [taylor]: Taking taylor expansion of k in n
1.921 * [backup-simplify]: Simplify k into k
1.921 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.921 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
1.921 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.921 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
1.922 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k)))
1.922 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) in k
1.922 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
1.922 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
1.922 * [taylor]: Taking taylor expansion of 1/2 in k
1.922 * [backup-simplify]: Simplify 1/2 into 1/2
1.922 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
1.923 * [taylor]: Taking taylor expansion of (- 1 k) in k
1.923 * [taylor]: Taking taylor expansion of 1 in k
1.923 * [backup-simplify]: Simplify 1 into 1
1.923 * [taylor]: Taking taylor expansion of k in k
1.923 * [backup-simplify]: Simplify 0 into 0
1.923 * [backup-simplify]: Simplify 1 into 1
1.923 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
1.923 * [taylor]: Taking taylor expansion of (log n) in k
1.923 * [taylor]: Taking taylor expansion of n in k
1.923 * [backup-simplify]: Simplify n into n
1.923 * [backup-simplify]: Simplify (log n) into (log n)
1.923 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.923 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.923 * [taylor]: Taking taylor expansion of 2 in k
1.923 * [backup-simplify]: Simplify 2 into 2
1.923 * [taylor]: Taking taylor expansion of PI in k
1.923 * [backup-simplify]: Simplify PI into PI
1.923 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.924 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.925 * [backup-simplify]: Simplify (- 0) into 0
1.925 * [backup-simplify]: Simplify (+ 1 0) into 1
1.926 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.927 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
1.929 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
1.930 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.930 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
1.930 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.930 * [taylor]: Taking taylor expansion of k in k
1.930 * [backup-simplify]: Simplify 0 into 0
1.930 * [backup-simplify]: Simplify 1 into 1
1.930 * [backup-simplify]: Simplify (/ 1 1) into 1
1.931 * [backup-simplify]: Simplify (sqrt 0) into 0
1.932 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
1.933 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
1.933 * [backup-simplify]: Simplify 0 into 0
1.934 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
1.935 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
1.937 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.937 * [backup-simplify]: Simplify (- 0) into 0
1.944 * [backup-simplify]: Simplify (+ 0 0) into 0
1.945 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
1.946 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.947 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
1.949 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.951 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
1.951 * [taylor]: Taking taylor expansion of 0 in k
1.951 * [backup-simplify]: Simplify 0 into 0
1.952 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
1.952 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.954 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.955 * [backup-simplify]: Simplify (+ 0 0) into 0
1.955 * [backup-simplify]: Simplify (- 1) into -1
1.955 * [backup-simplify]: Simplify (+ 0 -1) into -1
1.957 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
1.959 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
1.962 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
1.966 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
1.968 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
1.968 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.969 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
1.970 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
1.971 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
1.975 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
1.975 * [backup-simplify]: Simplify (- 0) into 0
1.976 * [backup-simplify]: Simplify (+ 0 0) into 0
1.977 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
1.978 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.980 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.982 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.984 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
1.984 * [taylor]: Taking taylor expansion of 0 in k
1.984 * [backup-simplify]: Simplify 0 into 0
1.984 * [backup-simplify]: Simplify 0 into 0
1.985 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
1.988 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
1.990 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
1.991 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.995 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
1.995 * [backup-simplify]: Simplify (+ 0 0) into 0
1.996 * [backup-simplify]: Simplify (- 0) into 0
1.996 * [backup-simplify]: Simplify (+ 0 0) into 0
1.998 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.001 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.005 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
2.014 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
2.019 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
2.019 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.020 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
2.021 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.023 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
2.029 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
2.030 * [backup-simplify]: Simplify (- 0) into 0
2.030 * [backup-simplify]: Simplify (+ 0 0) into 0
2.032 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 k))))) into 0
2.033 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.035 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.038 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.040 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
2.040 * [taylor]: Taking taylor expansion of 0 in k
2.040 * [backup-simplify]: Simplify 0 into 0
2.040 * [backup-simplify]: Simplify 0 into 0
2.040 * [backup-simplify]: Simplify 0 into 0
2.041 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.045 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.048 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
2.049 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.056 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
2.057 * [backup-simplify]: Simplify (+ 0 0) into 0
2.057 * [backup-simplify]: Simplify (- 0) into 0
2.057 * [backup-simplify]: Simplify (+ 0 0) into 0
2.059 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.061 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.065 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.075 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
2.088 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
2.107 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
2.108 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) (* 2 PI)) (/ (- 1 (/ 1 k)) 2)) (sqrt (/ 1 k))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
2.108 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (n k) around 0
2.108 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
2.108 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
2.109 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
2.109 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
2.109 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
2.109 * [taylor]: Taking taylor expansion of 1/2 in k
2.109 * [backup-simplify]: Simplify 1/2 into 1/2
2.109 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
2.109 * [taylor]: Taking taylor expansion of 1 in k
2.109 * [backup-simplify]: Simplify 1 into 1
2.109 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.109 * [taylor]: Taking taylor expansion of k in k
2.109 * [backup-simplify]: Simplify 0 into 0
2.109 * [backup-simplify]: Simplify 1 into 1
2.109 * [backup-simplify]: Simplify (/ 1 1) into 1
2.109 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
2.109 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
2.109 * [taylor]: Taking taylor expansion of 2 in k
2.109 * [backup-simplify]: Simplify 2 into 2
2.109 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.109 * [taylor]: Taking taylor expansion of PI in k
2.109 * [backup-simplify]: Simplify PI into PI
2.109 * [taylor]: Taking taylor expansion of n in k
2.109 * [backup-simplify]: Simplify n into n
2.109 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.109 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
2.110 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
2.110 * [backup-simplify]: Simplify (- 1) into -1
2.110 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.111 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
2.111 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
2.111 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
2.111 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.111 * [taylor]: Taking taylor expansion of k in k
2.111 * [backup-simplify]: Simplify 0 into 0
2.111 * [backup-simplify]: Simplify 1 into 1
2.112 * [backup-simplify]: Simplify (sqrt 0) into 0
2.113 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.113 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
2.114 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
2.114 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.114 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.114 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
2.114 * [taylor]: Taking taylor expansion of 1/2 in n
2.114 * [backup-simplify]: Simplify 1/2 into 1/2
2.114 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
2.114 * [taylor]: Taking taylor expansion of 1 in n
2.114 * [backup-simplify]: Simplify 1 into 1
2.114 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.114 * [taylor]: Taking taylor expansion of k in n
2.114 * [backup-simplify]: Simplify k into k
2.114 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.114 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.114 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.114 * [taylor]: Taking taylor expansion of 2 in n
2.114 * [backup-simplify]: Simplify 2 into 2
2.114 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.114 * [taylor]: Taking taylor expansion of PI in n
2.114 * [backup-simplify]: Simplify PI into PI
2.114 * [taylor]: Taking taylor expansion of n in n
2.114 * [backup-simplify]: Simplify 0 into 0
2.114 * [backup-simplify]: Simplify 1 into 1
2.115 * [backup-simplify]: Simplify (/ PI 1) into PI
2.115 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.117 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.117 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
2.117 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
2.117 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
2.118 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.120 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
2.121 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
2.121 * [taylor]: Taking taylor expansion of (sqrt k) in n
2.121 * [taylor]: Taking taylor expansion of k in n
2.121 * [backup-simplify]: Simplify k into k
2.121 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
2.121 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
2.121 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
2.121 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
2.121 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.121 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.121 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
2.121 * [taylor]: Taking taylor expansion of 1/2 in n
2.121 * [backup-simplify]: Simplify 1/2 into 1/2
2.122 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
2.122 * [taylor]: Taking taylor expansion of 1 in n
2.122 * [backup-simplify]: Simplify 1 into 1
2.122 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.122 * [taylor]: Taking taylor expansion of k in n
2.122 * [backup-simplify]: Simplify k into k
2.122 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.122 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.122 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.122 * [taylor]: Taking taylor expansion of 2 in n
2.122 * [backup-simplify]: Simplify 2 into 2
2.122 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.122 * [taylor]: Taking taylor expansion of PI in n
2.122 * [backup-simplify]: Simplify PI into PI
2.122 * [taylor]: Taking taylor expansion of n in n
2.122 * [backup-simplify]: Simplify 0 into 0
2.122 * [backup-simplify]: Simplify 1 into 1
2.123 * [backup-simplify]: Simplify (/ PI 1) into PI
2.123 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.124 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.124 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
2.124 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
2.125 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
2.127 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.128 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
2.129 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
2.129 * [taylor]: Taking taylor expansion of (sqrt k) in n
2.129 * [taylor]: Taking taylor expansion of k in n
2.129 * [backup-simplify]: Simplify k into k
2.129 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
2.129 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
2.130 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))
2.131 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k
2.131 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
2.131 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
2.131 * [taylor]: Taking taylor expansion of 1/2 in k
2.131 * [backup-simplify]: Simplify 1/2 into 1/2
2.131 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
2.131 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
2.131 * [taylor]: Taking taylor expansion of 1 in k
2.131 * [backup-simplify]: Simplify 1 into 1
2.131 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.131 * [taylor]: Taking taylor expansion of k in k
2.131 * [backup-simplify]: Simplify 0 into 0
2.131 * [backup-simplify]: Simplify 1 into 1
2.131 * [backup-simplify]: Simplify (/ 1 1) into 1
2.131 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
2.131 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.131 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.131 * [taylor]: Taking taylor expansion of 2 in k
2.131 * [backup-simplify]: Simplify 2 into 2
2.132 * [taylor]: Taking taylor expansion of PI in k
2.132 * [backup-simplify]: Simplify PI into PI
2.132 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.133 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.133 * [taylor]: Taking taylor expansion of (log n) in k
2.133 * [taylor]: Taking taylor expansion of n in k
2.133 * [backup-simplify]: Simplify n into n
2.133 * [backup-simplify]: Simplify (log n) into (log n)
2.134 * [backup-simplify]: Simplify (- 1) into -1
2.134 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.134 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.135 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
2.136 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
2.138 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
2.139 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
2.139 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.139 * [taylor]: Taking taylor expansion of k in k
2.139 * [backup-simplify]: Simplify 0 into 0
2.139 * [backup-simplify]: Simplify 1 into 1
2.139 * [backup-simplify]: Simplify (sqrt 0) into 0
2.141 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.142 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) into 0
2.142 * [backup-simplify]: Simplify 0 into 0
2.143 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.144 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.146 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.146 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.146 * [backup-simplify]: Simplify (- 0) into 0
2.147 * [backup-simplify]: Simplify (+ 0 0) into 0
2.147 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
2.149 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.150 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
2.152 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.154 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
2.154 * [taylor]: Taking taylor expansion of 0 in k
2.154 * [backup-simplify]: Simplify 0 into 0
2.154 * [backup-simplify]: Simplify 0 into 0
2.156 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
2.157 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
2.158 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
2.159 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.160 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.164 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
2.164 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.165 * [backup-simplify]: Simplify (- 0) into 0
2.165 * [backup-simplify]: Simplify (+ 0 0) into 0
2.166 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
2.168 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.170 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
2.173 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.174 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
2.174 * [taylor]: Taking taylor expansion of 0 in k
2.174 * [backup-simplify]: Simplify 0 into 0
2.175 * [backup-simplify]: Simplify 0 into 0
2.175 * [backup-simplify]: Simplify 0 into 0
2.178 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.180 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
2.181 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
2.182 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
2.184 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.185 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.191 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
2.191 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.192 * [backup-simplify]: Simplify (- 0) into 0
2.192 * [backup-simplify]: Simplify (+ 0 0) into 0
2.194 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
2.196 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.198 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
2.201 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.203 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
2.203 * [taylor]: Taking taylor expansion of 0 in k
2.203 * [backup-simplify]: Simplify 0 into 0
2.203 * [backup-simplify]: Simplify 0 into 0
2.203 * [backup-simplify]: Simplify 0 into 0
2.203 * [backup-simplify]: Simplify 0 into 0
2.208 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.210 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
2.212 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
2.216 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
2.217 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1 (/ 1 (- k))) 2)) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
2.217 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (n k) around 0
2.217 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
2.217 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
2.217 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
2.217 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
2.217 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
2.217 * [taylor]: Taking taylor expansion of 1/2 in k
2.217 * [backup-simplify]: Simplify 1/2 into 1/2
2.217 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
2.217 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.217 * [taylor]: Taking taylor expansion of k in k
2.217 * [backup-simplify]: Simplify 0 into 0
2.217 * [backup-simplify]: Simplify 1 into 1
2.218 * [backup-simplify]: Simplify (/ 1 1) into 1
2.218 * [taylor]: Taking taylor expansion of 1 in k
2.218 * [backup-simplify]: Simplify 1 into 1
2.218 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
2.218 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
2.218 * [taylor]: Taking taylor expansion of -2 in k
2.218 * [backup-simplify]: Simplify -2 into -2
2.218 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.218 * [taylor]: Taking taylor expansion of PI in k
2.218 * [backup-simplify]: Simplify PI into PI
2.218 * [taylor]: Taking taylor expansion of n in k
2.218 * [backup-simplify]: Simplify n into n
2.218 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.218 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
2.218 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
2.219 * [backup-simplify]: Simplify (+ 1 0) into 1
2.219 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.219 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
2.220 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
2.220 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.220 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.220 * [taylor]: Taking taylor expansion of -1 in k
2.220 * [backup-simplify]: Simplify -1 into -1
2.220 * [taylor]: Taking taylor expansion of k in k
2.220 * [backup-simplify]: Simplify 0 into 0
2.220 * [backup-simplify]: Simplify 1 into 1
2.220 * [backup-simplify]: Simplify (/ -1 1) into -1
2.221 * [backup-simplify]: Simplify (sqrt 0) into 0
2.222 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.222 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
2.223 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
2.223 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
2.223 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
2.223 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
2.223 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
2.223 * [taylor]: Taking taylor expansion of 1/2 in n
2.223 * [backup-simplify]: Simplify 1/2 into 1/2
2.223 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
2.223 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.223 * [taylor]: Taking taylor expansion of k in n
2.223 * [backup-simplify]: Simplify k into k
2.223 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.223 * [taylor]: Taking taylor expansion of 1 in n
2.223 * [backup-simplify]: Simplify 1 into 1
2.223 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.223 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.223 * [taylor]: Taking taylor expansion of -2 in n
2.223 * [backup-simplify]: Simplify -2 into -2
2.223 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.223 * [taylor]: Taking taylor expansion of PI in n
2.223 * [backup-simplify]: Simplify PI into PI
2.223 * [taylor]: Taking taylor expansion of n in n
2.223 * [backup-simplify]: Simplify 0 into 0
2.223 * [backup-simplify]: Simplify 1 into 1
2.224 * [backup-simplify]: Simplify (/ PI 1) into PI
2.224 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.225 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.225 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
2.226 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
2.233 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.234 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
2.235 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
2.235 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.235 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.235 * [taylor]: Taking taylor expansion of -1 in n
2.235 * [backup-simplify]: Simplify -1 into -1
2.235 * [taylor]: Taking taylor expansion of k in n
2.235 * [backup-simplify]: Simplify k into k
2.235 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.236 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.236 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.236 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.237 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
2.237 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
2.237 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
2.237 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
2.237 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
2.237 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
2.237 * [taylor]: Taking taylor expansion of 1/2 in n
2.237 * [backup-simplify]: Simplify 1/2 into 1/2
2.237 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
2.237 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.237 * [taylor]: Taking taylor expansion of k in n
2.237 * [backup-simplify]: Simplify k into k
2.238 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.238 * [taylor]: Taking taylor expansion of 1 in n
2.238 * [backup-simplify]: Simplify 1 into 1
2.238 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.238 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.238 * [taylor]: Taking taylor expansion of -2 in n
2.238 * [backup-simplify]: Simplify -2 into -2
2.238 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.238 * [taylor]: Taking taylor expansion of PI in n
2.238 * [backup-simplify]: Simplify PI into PI
2.238 * [taylor]: Taking taylor expansion of n in n
2.238 * [backup-simplify]: Simplify 0 into 0
2.238 * [backup-simplify]: Simplify 1 into 1
2.238 * [backup-simplify]: Simplify (/ PI 1) into PI
2.239 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.240 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.240 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
2.240 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
2.242 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.243 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
2.244 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
2.244 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.244 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.244 * [taylor]: Taking taylor expansion of -1 in n
2.244 * [backup-simplify]: Simplify -1 into -1
2.244 * [taylor]: Taking taylor expansion of k in n
2.244 * [backup-simplify]: Simplify k into k
2.244 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.245 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.245 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.245 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.246 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
2.246 * [taylor]: Taking taylor expansion of (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k
2.246 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
2.247 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
2.247 * [taylor]: Taking taylor expansion of 1/2 in k
2.247 * [backup-simplify]: Simplify 1/2 into 1/2
2.247 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
2.247 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
2.247 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.247 * [taylor]: Taking taylor expansion of k in k
2.247 * [backup-simplify]: Simplify 0 into 0
2.247 * [backup-simplify]: Simplify 1 into 1
2.247 * [backup-simplify]: Simplify (/ 1 1) into 1
2.247 * [taylor]: Taking taylor expansion of 1 in k
2.247 * [backup-simplify]: Simplify 1 into 1
2.247 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
2.247 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
2.247 * [taylor]: Taking taylor expansion of (* -2 PI) in k
2.247 * [taylor]: Taking taylor expansion of -2 in k
2.247 * [backup-simplify]: Simplify -2 into -2
2.247 * [taylor]: Taking taylor expansion of PI in k
2.247 * [backup-simplify]: Simplify PI into PI
2.248 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.249 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.249 * [taylor]: Taking taylor expansion of (log n) in k
2.249 * [taylor]: Taking taylor expansion of n in k
2.249 * [backup-simplify]: Simplify n into n
2.249 * [backup-simplify]: Simplify (log n) into (log n)
2.250 * [backup-simplify]: Simplify (+ 1 0) into 1
2.250 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.251 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
2.252 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
2.254 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
2.255 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
2.255 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.255 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.255 * [taylor]: Taking taylor expansion of -1 in k
2.255 * [backup-simplify]: Simplify -1 into -1
2.255 * [taylor]: Taking taylor expansion of k in k
2.255 * [backup-simplify]: Simplify 0 into 0
2.255 * [backup-simplify]: Simplify 1 into 1
2.256 * [backup-simplify]: Simplify (/ -1 1) into -1
2.256 * [backup-simplify]: Simplify (sqrt 0) into 0
2.257 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.259 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
2.260 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
2.261 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.262 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.264 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
2.264 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.264 * [backup-simplify]: Simplify (+ 0 0) into 0
2.265 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
2.266 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.268 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
2.270 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.271 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
2.271 * [taylor]: Taking taylor expansion of 0 in k
2.271 * [backup-simplify]: Simplify 0 into 0
2.271 * [backup-simplify]: Simplify 0 into 0
2.272 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
2.275 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.277 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
2.279 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
2.280 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.281 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.285 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
2.285 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.286 * [backup-simplify]: Simplify (+ 0 0) into 0
2.287 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
2.288 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.290 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
2.291 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.292 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.292 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
2.293 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
2.293 * [taylor]: Taking taylor expansion of 0 in k
2.293 * [backup-simplify]: Simplify 0 into 0
2.293 * [backup-simplify]: Simplify 0 into 0
2.293 * [backup-simplify]: Simplify 0 into 0
2.294 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.296 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.298 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
2.299 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
2.302 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
2.302 * * * [progress]: simplifying candidates
2.302 * * * * [progress]: [ 1 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (log1p (expm1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
2.302 * * * * [progress]: [ 2 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (expm1 (log1p (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
2.302 * * * * [progress]: [ 3 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))) (sqrt k)))>
2.302 * * * * [progress]: [ 4 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))) (sqrt k)))>
2.302 * * * * [progress]: [ 5 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (/ (- 1 k) 2))) (sqrt k)))>
2.302 * * * * [progress]: [ 6 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (/ (- 1 k) 2))) (sqrt k)))>
2.302 * * * * [progress]: [ 7 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
2.302 * * * * [progress]: [ 8 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
2.302 * * * * [progress]: [ 9 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))) (sqrt k)))>
2.302 * * * * [progress]: [ 10 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ 1 2)) (pow (* n (* 2 PI)) (/ k 2))) (sqrt k)))>
2.302 * * * * [progress]: [ 11 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt k)))>
2.302 * * * * [progress]: [ 12 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt k)))>
2.302 * * * * [progress]: [ 13 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2))) (sqrt k)))>
2.302 * * * * [progress]: [ 14 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2))) (sqrt k)))>
2.302 * * * * [progress]: [ 15 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2)) (sqrt k)))>
2.302 * * * * [progress]: [ 16 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2))) (sqrt k)))>
2.302 * * * * [progress]: [ 17 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2))) (sqrt k)))>
2.302 * * * * [progress]: [ 18 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2)) (sqrt k)))>
2.302 * * * * [progress]: [ 19 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (sqrt k)))>
2.302 * * * * [progress]: [ 20 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (sqrt k)))>
2.303 * * * * [progress]: [ 21 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1 k) 2)) (sqrt k)))>
2.303 * * * * [progress]: [ 22 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2))) (sqrt k)))>
2.303 * * * * [progress]: [ 23 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2))) (sqrt k)))>
2.303 * * * * [progress]: [ 24 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2)) (sqrt k)))>
2.303 * * * * [progress]: [ 25 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2))) (sqrt k)))>
2.303 * * * * [progress]: [ 26 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2))) (sqrt k)))>
2.303 * * * * [progress]: [ 27 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (sqrt k)))>
2.303 * * * * [progress]: [ 28 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (sqrt k)))>
2.303 * * * * [progress]: [ 29 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (sqrt k)))>
2.303 * * * * [progress]: [ 30 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1 k) 2)) (sqrt k)))>
2.303 * * * * [progress]: [ 31 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt k)))>
2.303 * * * * [progress]: [ 32 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (- 1 k)) (/ 1 2)) (sqrt k)))>
2.303 * * * * [progress]: [ 33 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt k)))>
2.303 * * * * [progress]: [ 34 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1) (sqrt k)))>
2.303 * * * * [progress]: [ 35 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
2.303 * * * * [progress]: [ 36 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
2.303 * * * * [progress]: [ 37 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
2.303 * * * * [progress]: [ 38 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
2.303 * * * * [progress]: [ 39 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
2.303 * * * * [progress]: [ 40 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k)))>
2.303 * * * * [progress]: [ 41 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
2.303 * * * * [progress]: [ 42 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k)))>
2.303 * * * * [progress]: [ 43 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log1p (expm1 (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.303 * * * * [progress]: [ 44 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (expm1 (log1p (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.303 * * * * [progress]: [ 45 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt k)))>
2.303 * * * * [progress]: [ 46 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt k)))>
2.304 * * * * [progress]: [ 47 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt k)))>
2.304 * * * * [progress]: [ 48 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.304 * * * * [progress]: [ 49 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (log (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.304 * * * * [progress]: [ 50 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.304 * * * * [progress]: [ 51 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.304 * * * * [progress]: [ 52 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.304 * * * * [progress]: [ 53 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.304 * * * * [progress]: [ 54 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.304 * * * * [progress]: [ 55 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.304 * * * * [progress]: [ 56 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.304 * * * * [progress]: [ 57 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))>
2.304 * * * * [progress]: [ 58 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))>
2.304 * * * * [progress]: [ 59 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))>
2.304 * * * * [progress]: [ 60 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))>
2.304 * * * * [progress]: [ 61 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (/ (- 1 k) 2)) (sqrt k)))>
2.304 * * * * [progress]: [ 62 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt k)))>
2.304 * * * * [progress]: [ 63 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt k)))>
2.304 * * * * [progress]: [ 64 / 133 ] simplifiying candidate #<alt (λ (k n) (log1p (expm1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
2.304 * * * * [progress]: [ 65 / 133 ] simplifiying candidate #<alt (λ (k n) (expm1 (log1p (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
2.304 * * * * [progress]: [ 66 / 133 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) 1))>
2.304 * * * * [progress]: [ 67 / 133 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (log (sqrt k)))))>
2.304 * * * * [progress]: [ 68 / 133 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))>
2.304 * * * * [progress]: [ 69 / 133 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))>
2.304 * * * * [progress]: [ 70 / 133 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))))>
2.304 * * * * [progress]: [ 71 / 133 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (log (sqrt k)))))>
2.304 * * * * [progress]: [ 72 / 133 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
2.304 * * * * [progress]: [ 73 / 133 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
2.304 * * * * [progress]: [ 74 / 133 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
2.305 * * * * [progress]: [ 75 / 133 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
2.305 * * * * [progress]: [ 76 / 133 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
2.305 * * * * [progress]: [ 77 / 133 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
2.305 * * * * [progress]: [ 78 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (- (sqrt k))))>
2.305 * * * * [progress]: [ 79 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
2.305 * * * * [progress]: [ 80 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))))>
2.305 * * * * [progress]: [ 81 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
2.305 * * * * [progress]: [ 82 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt 1)) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
2.305 * * * * [progress]: [ 83 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
2.305 * * * * [progress]: [ 84 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) 1) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))))>
2.305 * * * * [progress]: [ 85 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
2.305 * * * * [progress]: [ 86 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))))>
2.305 * * * * [progress]: [ 87 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
2.305 * * * * [progress]: [ 88 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt 1)) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))>
2.305 * * * * [progress]: [ 89 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
2.305 * * * * [progress]: [ 90 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) 1) (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))>
2.305 * * * * [progress]: [ 91 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))))>
2.305 * * * * [progress]: [ 92 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))))>
2.305 * * * * [progress]: [ 93 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
2.305 * * * * [progress]: [ 94 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1)) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))>
2.305 * * * * [progress]: [ 95 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))))>
2.305 * * * * [progress]: [ 96 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))))>
2.305 * * * * [progress]: [ 97 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))))>
2.305 * * * * [progress]: [ 98 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))))>
2.305 * * * * [progress]: [ 99 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
2.305 * * * * [progress]: [ 100 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))>
2.306 * * * * [progress]: [ 101 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))))>
2.306 * * * * [progress]: [ 102 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))>
2.306 * * * * [progress]: [ 103 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k)))))>
2.306 * * * * [progress]: [ 104 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))))>
2.306 * * * * [progress]: [ 105 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))>
2.306 * * * * [progress]: [ 106 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1)) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))))>
2.306 * * * * [progress]: [ 107 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))))>
2.306 * * * * [progress]: [ 108 / 133 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))))>
2.306 * * * * [progress]: [ 109 / 133 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))>
2.306 * * * * [progress]: [ 110 / 133 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
2.306 * * * * [progress]: [ 111 / 133 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
2.306 * * * * [progress]: [ 112 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
2.306 * * * * [progress]: [ 113 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))>
2.306 * * * * [progress]: [ 114 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.306 * * * * [progress]: [ 115 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt 1)) (sqrt k)))>
2.306 * * * * [progress]: [ 116 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.306 * * * * [progress]: [ 117 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1) (sqrt k)))>
2.306 * * * * [progress]: [ 118 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow n (/ (- 1 k) 2)) (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))))>
2.306 * * * * [progress]: [ 119 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
2.306 * * * * [progress]: [ 120 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))))>
2.306 * * * * [progress]: [ 121 / 133 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))>
2.306 * * * * [progress]: [ 122 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))))>
2.306 * * * * [progress]: [ 123 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ 1 2)) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))>
2.306 * * * * [progress]: [ 124 / 133 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))))>
2.306 * * * * [progress]: [ 125 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (sqrt k)))>
2.307 * * * * [progress]: [ 126 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k)))>
2.307 * * * * [progress]: [ 127 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k)))>
2.307 * * * * [progress]: [ 128 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
2.307 * * * * [progress]: [ 129 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
2.307 * * * * [progress]: [ 130 / 133 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt k)))>
2.307 * * * * [progress]: [ 131 / 133 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))))>
2.307 * * * * [progress]: [ 132 / 133 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))))>
2.307 * * * * [progress]: [ 133 / 133 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))>
2.308 * [simplify]: Simplifying:
  (expm1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (log1p (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))
  (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))
  (* (log (* n (* 2 PI))) (/ (- 1 k) 2))
  (* (log (* n (* 2 PI))) (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (pow (* n (* 2 PI)) (/ 1 2))
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) 1))
  (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (pow (* n (* 2 PI)) (/ 1 1))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) 1))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
  (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (pow (* n (* 2 PI)) (/ 1 1))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (- 1 k))
  (pow n (/ (- 1 k) 2))
  (pow (* 2 PI) (/ (- 1 k) 2))
  (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
  (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
  (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (expm1 (* n (* 2 PI)))
  (log1p (* n (* 2 PI)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (expm1 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (log1p (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (- (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (sqrt k)))
  (- (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (log (sqrt k)))
  (log (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (exp (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (/ (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))
  (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (* (* (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (- (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (- (sqrt k))
  (/ (pow n (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt 1))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) 1)
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt 1))
  (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) 1)
  (/ (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) 1)
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ 1 1)
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1)
  (/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1)
  (/ (sqrt k) (pow (* 2 PI) (/ (- 1 k) 2)))
  (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))
  (real->posit16 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
2.312 * * [simplify]: iteration 1: (293 enodes)
2.443 * * [simplify]: iteration 2: (1281 enodes)
2.806 * * [simplify]: Extracting #0: cost 113 inf + 0
2.807 * * [simplify]: Extracting #1: cost 565 inf + 1
2.811 * * [simplify]: Extracting #2: cost 882 inf + 17584
2.845 * * [simplify]: Extracting #3: cost 810 inf + 105795
2.912 * * [simplify]: Extracting #4: cost 417 inf + 285399
3.019 * * [simplify]: Extracting #5: cost 181 inf + 403264
3.121 * * [simplify]: Extracting #6: cost 138 inf + 433414
3.222 * * [simplify]: Extracting #7: cost 97 inf + 451390
3.391 * * [simplify]: Extracting #8: cost 29 inf + 507695
3.524 * * [simplify]: Extracting #9: cost 3 inf + 526780
3.658 * * [simplify]: Extracting #10: cost 0 inf + 525069
3.767 * * [simplify]: Extracting #11: cost 0 inf + 524199
3.901 * * [simplify]: Extracting #12: cost 0 inf + 524079
4.033 * [simplify]: Simplified to:
  (expm1 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (log1p (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (log (* (* PI 2) n)) (/ 2 (- 1 k)))
  (/ (log (* (* PI 2) n)) (/ 2 (- 1 k)))
  (/ (log (* (* PI 2) n)) (/ 2 (- 1 k)))
  (/ (log (* (* PI 2) n)) (/ 2 (- 1 k)))
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (pow (* (* PI 2) n) (/ 1 2))
  (pow (* (* PI 2) n) (/ k 2))
  (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (cbrt (- 1 k)) (/ (sqrt 2) (cbrt (- 1 k)))))
  (pow (* (* PI 2) n) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* (* PI 2) n) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* PI 2) n) (sqrt (- 1 k)))
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (/ (+ (sqrt k) (sqrt 1)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) (sqrt 1)) (sqrt 2)))
  (pow (* (* PI 2) n) (+ (sqrt k) (sqrt 1)))
  (pow (* (* PI 2) n) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* (* PI 2) n) (+ (sqrt k) 1))
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (- 1 k))
  (pow n (/ (- 1 k) 2))
  (pow (* PI 2) (/ (- 1 k) 2))
  (/ (log (* (* PI 2) n)) (/ 2 (- 1 k)))
  (exp (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (pow (pow (* (* PI 2) n) (/ (- 1 k) 2)) 3)
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2))
  (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2))
  (real->posit16 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (expm1 (* (* PI 2) n))
  (log1p (* (* PI 2) n))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (* (exp (* n PI)) (exp (* n PI)))
  (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n)))
  (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n)))
  (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n)))
  (cbrt (* (* PI 2) n))
  (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n)))
  (sqrt (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (* n 2)
  (* (* PI 2) (cbrt n))
  (* (* (sqrt n) PI) 2)
  (* (* PI 2) n)
  (real->posit16 (* (* PI 2) n))
  (expm1 (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (log1p (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (- (/ (log (* (* PI 2) n)) (/ 2 (- 1 k))) (log (sqrt k)))
  (- (/ (log (* (* PI 2) n)) (/ 2 (- 1 k))) (log (sqrt k)))
  (- (/ (log (* (* PI 2) n)) (/ 2 (- 1 k))) (log (sqrt k)))
  (- (/ (log (* (* PI 2) n)) (/ 2 (- 1 k))) (log (sqrt k)))
  (- (/ (log (* (* PI 2) n)) (/ 2 (- 1 k))) (log (sqrt k)))
  (- (/ (log (* (* PI 2) n)) (/ 2 (- 1 k))) (log (sqrt k)))
  (exp (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (/ (/ (pow (pow (* (* PI 2) n) (/ (- 1 k) 2)) 3) k) (sqrt k))
  (* (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))))
  (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (* (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (- (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (- (sqrt k))
  (/ (/ (pow n (/ (- 1 k) 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) (fabs (cbrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow n (/ (- 1 k) 2)) (sqrt 1))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow n (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow n (/ (- 1 k) 2))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
  (* (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (fabs (cbrt k)))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt 1))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (fabs (cbrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt 1))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  1
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt 1))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt k))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2))
  (/ (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt 1))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (/ (- 1 k) 2))
  (/ (sqrt k) (pow (* PI 2) (/ (- 1 k) 2)))
  (/ (sqrt k) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (sqrt k) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (sqrt k) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (sqrt k) (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2)))
  (* (pow (* (* PI 2) n) (/ k 2)) (sqrt k))
  (real->posit16 (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (+ (* (* (exp (* (log (* (* PI 2) n)) 1/2)) (log (* PI 2))) (* (* (* k k) (log n)) 1/4)) (- (fma (* 1/8 (exp (* (log (* (* PI 2) n)) 1/2))) (* (* (log n) k) (* (log n) k)) (fma (* (* (log (* PI 2)) (* (exp (* (log (* (* PI 2) n)) 1/2)) (log (* PI 2)))) (* k k)) 1/8 (exp (* (log (* (* PI 2) n)) 1/2)))) (* (* k (+ (* (log n) (exp (* (log (* (* PI 2) n)) 1/2))) (* (exp (* (log (* (* PI 2) n)) 1/2)) (log (* PI 2))))) 1/2)))
  (exp (* (* 1/2 (- 1 k)) (log (* (* PI 2) n))))
  (exp (* (- 1 k) (* (- (log (* PI -2)) (log (/ -1 n))) 1/2)))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (* (* PI 2) n)
  (+ (fma (* (log (* PI 2)) +nan.0) (* (* k k) (exp (* (log (* (* PI 2) n)) 1/2))) (+ (+ (- (* (* (exp (* (log (* (* PI 2) n)) 1/2)) +nan.0) k) (* (exp (* (log (* (* PI 2) n)) 1/2)) +nan.0)) (- (* (* (* k k) (exp (* (log (* (* PI 2) n)) 1/2))) (* (* (log (* PI 2)) +nan.0) (log (* PI 2)))) (- (* (* +nan.0 (* (* k k) (log n))) (exp (* (log (* (* PI 2) n)) 1/2))) (fma (* (exp (* (log (* (* PI 2) n)) 1/2)) +nan.0) (* k k) (- (- (* (log (* PI 2)) (* (* (exp (* (log (* (* PI 2) n)) 1/2)) +nan.0) k)) (* (* (log n) k) (* (exp (* (log (* (* PI 2) n)) 1/2)) +nan.0)))))))) (* (* (exp (* (log (* (* PI 2) n)) 1/2)) +nan.0) (- (* (* (log n) k) (* (log n) k)))))) (- (* (log (* PI 2)) (* (* +nan.0 (* (* k k) (log n))) (exp (* (log (* (* PI 2) n)) 1/2))))))
  (+ (- (* +nan.0 (/ (exp (* (* 1/2 (- 1 k)) (log (* (* PI 2) n)))) k))) (- (/ (* (exp (* (* 1/2 (- 1 k)) (log (* (* PI 2) n)))) +nan.0) (* k k)) (/ (/ (* (exp (* (* 1/2 (- 1 k)) (log (* (* PI 2) n)))) +nan.0) (* k k)) k)))
  (+ (* +nan.0 (- (/ (exp (* (- 1 k) (* (- (log (* PI -2)) (log (/ -1 n))) 1/2))) (* k k)) (exp (* (- 1 k) (* (- (log (* PI -2)) (log (/ -1 n))) 1/2))))) (- (/ (exp (* (- 1 k) (* (- (log (* PI -2)) (log (/ -1 n))) 1/2))) (/ k +nan.0))))
4.051 * * * [progress]: adding candidates to table
5.901 * * [progress]: iteration 2 / 4
5.901 * * * [progress]: picking best candidate
5.942 * * * * [pick]: Picked  #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
5.942 * * * [progress]: localizing error
6.006 * * * [progress]: generating rewritten candidates
6.006 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1)
6.020 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2)
6.025 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 1)
6.041 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
6.086 * * * [progress]: generating series expansions
6.086 * * * * [progress]: [ 1 / 4 ] generating series at (2 1)
6.087 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
6.087 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
6.087 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
6.087 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
6.087 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
6.087 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
6.087 * [taylor]: Taking taylor expansion of 1/2 in k
6.087 * [backup-simplify]: Simplify 1/2 into 1/2
6.087 * [taylor]: Taking taylor expansion of (- 1 k) in k
6.087 * [taylor]: Taking taylor expansion of 1 in k
6.087 * [backup-simplify]: Simplify 1 into 1
6.087 * [taylor]: Taking taylor expansion of k in k
6.087 * [backup-simplify]: Simplify 0 into 0
6.087 * [backup-simplify]: Simplify 1 into 1
6.087 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
6.087 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
6.087 * [taylor]: Taking taylor expansion of 2 in k
6.087 * [backup-simplify]: Simplify 2 into 2
6.087 * [taylor]: Taking taylor expansion of (* n PI) in k
6.087 * [taylor]: Taking taylor expansion of n in k
6.087 * [backup-simplify]: Simplify n into n
6.087 * [taylor]: Taking taylor expansion of PI in k
6.087 * [backup-simplify]: Simplify PI into PI
6.087 * [backup-simplify]: Simplify (* n PI) into (* n PI)
6.087 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
6.088 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
6.088 * [backup-simplify]: Simplify (- 0) into 0
6.088 * [backup-simplify]: Simplify (+ 1 0) into 1
6.088 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
6.088 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
6.088 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
6.088 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
6.089 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
6.089 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
6.089 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
6.089 * [taylor]: Taking taylor expansion of 1/2 in n
6.089 * [backup-simplify]: Simplify 1/2 into 1/2
6.089 * [taylor]: Taking taylor expansion of (- 1 k) in n
6.089 * [taylor]: Taking taylor expansion of 1 in n
6.089 * [backup-simplify]: Simplify 1 into 1
6.089 * [taylor]: Taking taylor expansion of k in n
6.089 * [backup-simplify]: Simplify k into k
6.089 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
6.089 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
6.089 * [taylor]: Taking taylor expansion of 2 in n
6.089 * [backup-simplify]: Simplify 2 into 2
6.089 * [taylor]: Taking taylor expansion of (* n PI) in n
6.089 * [taylor]: Taking taylor expansion of n in n
6.089 * [backup-simplify]: Simplify 0 into 0
6.089 * [backup-simplify]: Simplify 1 into 1
6.089 * [taylor]: Taking taylor expansion of PI in n
6.089 * [backup-simplify]: Simplify PI into PI
6.089 * [backup-simplify]: Simplify (* 0 PI) into 0
6.089 * [backup-simplify]: Simplify (* 2 0) into 0
6.090 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.091 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
6.092 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.092 * [backup-simplify]: Simplify (- k) into (- k)
6.092 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
6.092 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
6.093 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.094 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
6.094 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
6.095 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
6.095 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
6.095 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
6.095 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
6.095 * [taylor]: Taking taylor expansion of 1/2 in n
6.095 * [backup-simplify]: Simplify 1/2 into 1/2
6.095 * [taylor]: Taking taylor expansion of (- 1 k) in n
6.095 * [taylor]: Taking taylor expansion of 1 in n
6.095 * [backup-simplify]: Simplify 1 into 1
6.095 * [taylor]: Taking taylor expansion of k in n
6.095 * [backup-simplify]: Simplify k into k
6.095 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
6.095 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
6.095 * [taylor]: Taking taylor expansion of 2 in n
6.095 * [backup-simplify]: Simplify 2 into 2
6.095 * [taylor]: Taking taylor expansion of (* n PI) in n
6.095 * [taylor]: Taking taylor expansion of n in n
6.095 * [backup-simplify]: Simplify 0 into 0
6.095 * [backup-simplify]: Simplify 1 into 1
6.095 * [taylor]: Taking taylor expansion of PI in n
6.095 * [backup-simplify]: Simplify PI into PI
6.095 * [backup-simplify]: Simplify (* 0 PI) into 0
6.095 * [backup-simplify]: Simplify (* 2 0) into 0
6.096 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.097 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
6.098 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.098 * [backup-simplify]: Simplify (- k) into (- k)
6.098 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
6.098 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
6.099 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.100 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
6.100 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
6.100 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
6.100 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
6.100 * [taylor]: Taking taylor expansion of 1/2 in k
6.100 * [backup-simplify]: Simplify 1/2 into 1/2
6.100 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
6.100 * [taylor]: Taking taylor expansion of (- 1 k) in k
6.100 * [taylor]: Taking taylor expansion of 1 in k
6.100 * [backup-simplify]: Simplify 1 into 1
6.100 * [taylor]: Taking taylor expansion of k in k
6.100 * [backup-simplify]: Simplify 0 into 0
6.100 * [backup-simplify]: Simplify 1 into 1
6.100 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
6.100 * [taylor]: Taking taylor expansion of (log n) in k
6.101 * [taylor]: Taking taylor expansion of n in k
6.101 * [backup-simplify]: Simplify n into n
6.101 * [backup-simplify]: Simplify (log n) into (log n)
6.101 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
6.101 * [taylor]: Taking taylor expansion of (* 2 PI) in k
6.101 * [taylor]: Taking taylor expansion of 2 in k
6.101 * [backup-simplify]: Simplify 2 into 2
6.101 * [taylor]: Taking taylor expansion of PI in k
6.101 * [backup-simplify]: Simplify PI into PI
6.101 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.102 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.102 * [backup-simplify]: Simplify (- 0) into 0
6.102 * [backup-simplify]: Simplify (+ 1 0) into 1
6.103 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.103 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
6.104 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
6.105 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
6.105 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
6.106 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
6.106 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
6.107 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
6.108 * [backup-simplify]: Simplify (- 0) into 0
6.108 * [backup-simplify]: Simplify (+ 0 0) into 0
6.108 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
6.109 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.110 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
6.111 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
6.111 * [taylor]: Taking taylor expansion of 0 in k
6.111 * [backup-simplify]: Simplify 0 into 0
6.111 * [backup-simplify]: Simplify 0 into 0
6.112 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
6.112 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
6.113 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
6.113 * [backup-simplify]: Simplify (+ 0 0) into 0
6.113 * [backup-simplify]: Simplify (- 1) into -1
6.114 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.115 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
6.116 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
6.118 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
6.119 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
6.120 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
6.121 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
6.123 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
6.123 * [backup-simplify]: Simplify (- 0) into 0
6.124 * [backup-simplify]: Simplify (+ 0 0) into 0
6.124 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
6.125 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.126 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
6.127 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
6.127 * [taylor]: Taking taylor expansion of 0 in k
6.127 * [backup-simplify]: Simplify 0 into 0
6.127 * [backup-simplify]: Simplify 0 into 0
6.127 * [backup-simplify]: Simplify 0 into 0
6.128 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
6.129 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
6.131 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
6.131 * [backup-simplify]: Simplify (+ 0 0) into 0
6.131 * [backup-simplify]: Simplify (- 0) into 0
6.131 * [backup-simplify]: Simplify (+ 0 0) into 0
6.133 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
6.134 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
6.136 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
6.139 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
6.145 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
6.145 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
6.145 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
6.145 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
6.145 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
6.145 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
6.145 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
6.145 * [taylor]: Taking taylor expansion of 1/2 in k
6.145 * [backup-simplify]: Simplify 1/2 into 1/2
6.145 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
6.145 * [taylor]: Taking taylor expansion of 1 in k
6.145 * [backup-simplify]: Simplify 1 into 1
6.145 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.145 * [taylor]: Taking taylor expansion of k in k
6.146 * [backup-simplify]: Simplify 0 into 0
6.146 * [backup-simplify]: Simplify 1 into 1
6.146 * [backup-simplify]: Simplify (/ 1 1) into 1
6.146 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
6.146 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
6.146 * [taylor]: Taking taylor expansion of 2 in k
6.146 * [backup-simplify]: Simplify 2 into 2
6.146 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.146 * [taylor]: Taking taylor expansion of PI in k
6.146 * [backup-simplify]: Simplify PI into PI
6.146 * [taylor]: Taking taylor expansion of n in k
6.146 * [backup-simplify]: Simplify n into n
6.146 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.146 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
6.146 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
6.146 * [backup-simplify]: Simplify (- 1) into -1
6.147 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.147 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
6.147 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
6.147 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
6.147 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
6.147 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
6.147 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
6.147 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
6.147 * [taylor]: Taking taylor expansion of 1/2 in n
6.147 * [backup-simplify]: Simplify 1/2 into 1/2
6.147 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
6.147 * [taylor]: Taking taylor expansion of 1 in n
6.147 * [backup-simplify]: Simplify 1 into 1
6.147 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.147 * [taylor]: Taking taylor expansion of k in n
6.147 * [backup-simplify]: Simplify k into k
6.147 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.147 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
6.147 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
6.147 * [taylor]: Taking taylor expansion of 2 in n
6.147 * [backup-simplify]: Simplify 2 into 2
6.147 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.147 * [taylor]: Taking taylor expansion of PI in n
6.147 * [backup-simplify]: Simplify PI into PI
6.147 * [taylor]: Taking taylor expansion of n in n
6.147 * [backup-simplify]: Simplify 0 into 0
6.147 * [backup-simplify]: Simplify 1 into 1
6.148 * [backup-simplify]: Simplify (/ PI 1) into PI
6.148 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.149 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.149 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.149 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
6.149 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
6.150 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.150 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
6.151 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
6.151 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
6.151 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
6.151 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
6.151 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
6.151 * [taylor]: Taking taylor expansion of 1/2 in n
6.151 * [backup-simplify]: Simplify 1/2 into 1/2
6.151 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
6.151 * [taylor]: Taking taylor expansion of 1 in n
6.151 * [backup-simplify]: Simplify 1 into 1
6.151 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.151 * [taylor]: Taking taylor expansion of k in n
6.151 * [backup-simplify]: Simplify k into k
6.151 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.151 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
6.151 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
6.151 * [taylor]: Taking taylor expansion of 2 in n
6.151 * [backup-simplify]: Simplify 2 into 2
6.151 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.151 * [taylor]: Taking taylor expansion of PI in n
6.151 * [backup-simplify]: Simplify PI into PI
6.151 * [taylor]: Taking taylor expansion of n in n
6.151 * [backup-simplify]: Simplify 0 into 0
6.151 * [backup-simplify]: Simplify 1 into 1
6.152 * [backup-simplify]: Simplify (/ PI 1) into PI
6.152 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.153 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.153 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.153 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
6.153 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
6.154 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.154 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
6.155 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
6.155 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
6.155 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
6.155 * [taylor]: Taking taylor expansion of 1/2 in k
6.155 * [backup-simplify]: Simplify 1/2 into 1/2
6.155 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
6.155 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
6.155 * [taylor]: Taking taylor expansion of 1 in k
6.155 * [backup-simplify]: Simplify 1 into 1
6.155 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.155 * [taylor]: Taking taylor expansion of k in k
6.155 * [backup-simplify]: Simplify 0 into 0
6.155 * [backup-simplify]: Simplify 1 into 1
6.155 * [backup-simplify]: Simplify (/ 1 1) into 1
6.156 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
6.156 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
6.156 * [taylor]: Taking taylor expansion of (* 2 PI) in k
6.156 * [taylor]: Taking taylor expansion of 2 in k
6.156 * [backup-simplify]: Simplify 2 into 2
6.156 * [taylor]: Taking taylor expansion of PI in k
6.156 * [backup-simplify]: Simplify PI into PI
6.156 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.157 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.157 * [taylor]: Taking taylor expansion of (log n) in k
6.157 * [taylor]: Taking taylor expansion of n in k
6.157 * [backup-simplify]: Simplify n into n
6.157 * [backup-simplify]: Simplify (log n) into (log n)
6.157 * [backup-simplify]: Simplify (- 1) into -1
6.157 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.157 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
6.158 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
6.159 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
6.160 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
6.161 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
6.168 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
6.169 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.170 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
6.172 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
6.172 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.173 * [backup-simplify]: Simplify (- 0) into 0
6.173 * [backup-simplify]: Simplify (+ 0 0) into 0
6.174 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
6.175 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.176 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
6.178 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
6.178 * [taylor]: Taking taylor expansion of 0 in k
6.178 * [backup-simplify]: Simplify 0 into 0
6.178 * [backup-simplify]: Simplify 0 into 0
6.179 * [backup-simplify]: Simplify 0 into 0
6.180 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.181 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
6.184 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
6.184 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
6.184 * [backup-simplify]: Simplify (- 0) into 0
6.185 * [backup-simplify]: Simplify (+ 0 0) into 0
6.186 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
6.187 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.189 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
6.191 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
6.191 * [taylor]: Taking taylor expansion of 0 in k
6.191 * [backup-simplify]: Simplify 0 into 0
6.191 * [backup-simplify]: Simplify 0 into 0
6.191 * [backup-simplify]: Simplify 0 into 0
6.191 * [backup-simplify]: Simplify 0 into 0
6.192 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.193 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
6.199 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
6.200 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
6.200 * [backup-simplify]: Simplify (- 0) into 0
6.200 * [backup-simplify]: Simplify (+ 0 0) into 0
6.202 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
6.203 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.205 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
6.208 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
6.208 * [taylor]: Taking taylor expansion of 0 in k
6.208 * [backup-simplify]: Simplify 0 into 0
6.208 * [backup-simplify]: Simplify 0 into 0
6.209 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
6.210 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
6.210 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
6.210 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
6.210 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
6.210 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
6.210 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
6.210 * [taylor]: Taking taylor expansion of 1/2 in k
6.210 * [backup-simplify]: Simplify 1/2 into 1/2
6.210 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
6.210 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.210 * [taylor]: Taking taylor expansion of k in k
6.210 * [backup-simplify]: Simplify 0 into 0
6.210 * [backup-simplify]: Simplify 1 into 1
6.211 * [backup-simplify]: Simplify (/ 1 1) into 1
6.211 * [taylor]: Taking taylor expansion of 1 in k
6.211 * [backup-simplify]: Simplify 1 into 1
6.211 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
6.211 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
6.211 * [taylor]: Taking taylor expansion of -2 in k
6.211 * [backup-simplify]: Simplify -2 into -2
6.211 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.211 * [taylor]: Taking taylor expansion of PI in k
6.211 * [backup-simplify]: Simplify PI into PI
6.211 * [taylor]: Taking taylor expansion of n in k
6.211 * [backup-simplify]: Simplify n into n
6.211 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.211 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
6.211 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
6.212 * [backup-simplify]: Simplify (+ 1 0) into 1
6.212 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
6.212 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
6.212 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
6.213 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
6.213 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
6.213 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
6.213 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
6.213 * [taylor]: Taking taylor expansion of 1/2 in n
6.213 * [backup-simplify]: Simplify 1/2 into 1/2
6.213 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
6.213 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.213 * [taylor]: Taking taylor expansion of k in n
6.213 * [backup-simplify]: Simplify k into k
6.213 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.213 * [taylor]: Taking taylor expansion of 1 in n
6.213 * [backup-simplify]: Simplify 1 into 1
6.213 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
6.213 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
6.213 * [taylor]: Taking taylor expansion of -2 in n
6.213 * [backup-simplify]: Simplify -2 into -2
6.213 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.213 * [taylor]: Taking taylor expansion of PI in n
6.213 * [backup-simplify]: Simplify PI into PI
6.213 * [taylor]: Taking taylor expansion of n in n
6.213 * [backup-simplify]: Simplify 0 into 0
6.213 * [backup-simplify]: Simplify 1 into 1
6.214 * [backup-simplify]: Simplify (/ PI 1) into PI
6.214 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
6.215 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
6.215 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
6.215 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
6.217 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.218 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
6.219 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
6.219 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
6.219 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
6.219 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
6.219 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
6.219 * [taylor]: Taking taylor expansion of 1/2 in n
6.219 * [backup-simplify]: Simplify 1/2 into 1/2
6.219 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
6.219 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.219 * [taylor]: Taking taylor expansion of k in n
6.219 * [backup-simplify]: Simplify k into k
6.219 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.219 * [taylor]: Taking taylor expansion of 1 in n
6.219 * [backup-simplify]: Simplify 1 into 1
6.220 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
6.220 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
6.220 * [taylor]: Taking taylor expansion of -2 in n
6.220 * [backup-simplify]: Simplify -2 into -2
6.220 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.220 * [taylor]: Taking taylor expansion of PI in n
6.220 * [backup-simplify]: Simplify PI into PI
6.220 * [taylor]: Taking taylor expansion of n in n
6.220 * [backup-simplify]: Simplify 0 into 0
6.220 * [backup-simplify]: Simplify 1 into 1
6.220 * [backup-simplify]: Simplify (/ PI 1) into PI
6.221 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
6.222 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
6.222 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
6.222 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
6.224 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.225 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
6.226 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
6.226 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
6.226 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
6.226 * [taylor]: Taking taylor expansion of 1/2 in k
6.226 * [backup-simplify]: Simplify 1/2 into 1/2
6.226 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
6.226 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
6.226 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.226 * [taylor]: Taking taylor expansion of k in k
6.226 * [backup-simplify]: Simplify 0 into 0
6.226 * [backup-simplify]: Simplify 1 into 1
6.227 * [backup-simplify]: Simplify (/ 1 1) into 1
6.227 * [taylor]: Taking taylor expansion of 1 in k
6.227 * [backup-simplify]: Simplify 1 into 1
6.227 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
6.227 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
6.227 * [taylor]: Taking taylor expansion of (* -2 PI) in k
6.227 * [taylor]: Taking taylor expansion of -2 in k
6.227 * [backup-simplify]: Simplify -2 into -2
6.227 * [taylor]: Taking taylor expansion of PI in k
6.227 * [backup-simplify]: Simplify PI into PI
6.227 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
6.228 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
6.229 * [taylor]: Taking taylor expansion of (log n) in k
6.229 * [taylor]: Taking taylor expansion of n in k
6.229 * [backup-simplify]: Simplify n into n
6.229 * [backup-simplify]: Simplify (log n) into (log n)
6.229 * [backup-simplify]: Simplify (+ 1 0) into 1
6.229 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
6.230 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
6.231 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
6.232 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
6.233 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
6.235 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
6.236 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.236 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
6.238 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
6.238 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.239 * [backup-simplify]: Simplify (+ 0 0) into 0
6.239 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
6.240 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.241 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
6.242 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
6.242 * [taylor]: Taking taylor expansion of 0 in k
6.242 * [backup-simplify]: Simplify 0 into 0
6.242 * [backup-simplify]: Simplify 0 into 0
6.242 * [backup-simplify]: Simplify 0 into 0
6.242 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.243 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
6.245 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
6.245 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
6.245 * [backup-simplify]: Simplify (+ 0 0) into 0
6.246 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
6.247 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.248 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
6.249 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
6.249 * [taylor]: Taking taylor expansion of 0 in k
6.249 * [backup-simplify]: Simplify 0 into 0
6.249 * [backup-simplify]: Simplify 0 into 0
6.249 * [backup-simplify]: Simplify 0 into 0
6.249 * [backup-simplify]: Simplify 0 into 0
6.250 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.251 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
6.254 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
6.254 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
6.254 * [backup-simplify]: Simplify (+ 0 0) into 0
6.255 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
6.256 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.257 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
6.259 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
6.259 * [taylor]: Taking taylor expansion of 0 in k
6.259 * [backup-simplify]: Simplify 0 into 0
6.259 * [backup-simplify]: Simplify 0 into 0
6.259 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
6.260 * * * * [progress]: [ 2 / 4 ] generating series at (2 2)
6.260 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k))
6.260 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0
6.260 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
6.260 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.260 * [taylor]: Taking taylor expansion of k in k
6.260 * [backup-simplify]: Simplify 0 into 0
6.260 * [backup-simplify]: Simplify 1 into 1
6.260 * [backup-simplify]: Simplify (/ 1 1) into 1
6.260 * [backup-simplify]: Simplify (sqrt 0) into 0
6.261 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.261 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
6.261 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.261 * [taylor]: Taking taylor expansion of k in k
6.261 * [backup-simplify]: Simplify 0 into 0
6.261 * [backup-simplify]: Simplify 1 into 1
6.261 * [backup-simplify]: Simplify (/ 1 1) into 1
6.262 * [backup-simplify]: Simplify (sqrt 0) into 0
6.262 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.263 * [backup-simplify]: Simplify 0 into 0
6.263 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.263 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
6.265 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.265 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.266 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.268 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.268 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.268 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
6.268 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k)
6.268 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0
6.268 * [taylor]: Taking taylor expansion of (sqrt k) in k
6.268 * [taylor]: Taking taylor expansion of k in k
6.268 * [backup-simplify]: Simplify 0 into 0
6.268 * [backup-simplify]: Simplify 1 into 1
6.269 * [backup-simplify]: Simplify (sqrt 0) into 0
6.269 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.269 * [taylor]: Taking taylor expansion of (sqrt k) in k
6.269 * [taylor]: Taking taylor expansion of k in k
6.269 * [backup-simplify]: Simplify 0 into 0
6.270 * [backup-simplify]: Simplify 1 into 1
6.270 * [backup-simplify]: Simplify (sqrt 0) into 0
6.271 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.271 * [backup-simplify]: Simplify 0 into 0
6.271 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.273 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.273 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.275 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.275 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.275 * [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))))))))
6.275 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k)))
6.275 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0
6.275 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
6.275 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
6.275 * [taylor]: Taking taylor expansion of (/ -1 k) in k
6.275 * [taylor]: Taking taylor expansion of -1 in k
6.275 * [backup-simplify]: Simplify -1 into -1
6.276 * [taylor]: Taking taylor expansion of k in k
6.276 * [backup-simplify]: Simplify 0 into 0
6.276 * [backup-simplify]: Simplify 1 into 1
6.276 * [backup-simplify]: Simplify (/ -1 1) into -1
6.276 * [backup-simplify]: Simplify (sqrt 0) into 0
6.277 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
6.277 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
6.277 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
6.277 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
6.277 * [taylor]: Taking taylor expansion of (/ -1 k) in k
6.277 * [taylor]: Taking taylor expansion of -1 in k
6.277 * [backup-simplify]: Simplify -1 into -1
6.277 * [taylor]: Taking taylor expansion of k in k
6.277 * [backup-simplify]: Simplify 0 into 0
6.277 * [backup-simplify]: Simplify 1 into 1
6.278 * [backup-simplify]: Simplify (/ -1 1) into -1
6.278 * [backup-simplify]: Simplify (sqrt 0) into 0
6.279 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
6.279 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
6.279 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.279 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
6.286 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.287 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
6.288 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
6.288 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.291 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.293 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
6.293 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
6.294 * [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)))))
6.294 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 1)
6.295 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
6.295 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
6.295 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
6.295 * [taylor]: Taking taylor expansion of 2 in n
6.295 * [backup-simplify]: Simplify 2 into 2
6.295 * [taylor]: Taking taylor expansion of (* n PI) in n
6.295 * [taylor]: Taking taylor expansion of n in n
6.295 * [backup-simplify]: Simplify 0 into 0
6.295 * [backup-simplify]: Simplify 1 into 1
6.295 * [taylor]: Taking taylor expansion of PI in n
6.295 * [backup-simplify]: Simplify PI into PI
6.295 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
6.295 * [taylor]: Taking taylor expansion of 2 in n
6.295 * [backup-simplify]: Simplify 2 into 2
6.295 * [taylor]: Taking taylor expansion of (* n PI) in n
6.295 * [taylor]: Taking taylor expansion of n in n
6.295 * [backup-simplify]: Simplify 0 into 0
6.295 * [backup-simplify]: Simplify 1 into 1
6.295 * [taylor]: Taking taylor expansion of PI in n
6.295 * [backup-simplify]: Simplify PI into PI
6.296 * [backup-simplify]: Simplify (* 0 PI) into 0
6.296 * [backup-simplify]: Simplify (* 2 0) into 0
6.296 * [backup-simplify]: Simplify 0 into 0
6.298 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.299 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
6.300 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.301 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
6.302 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
6.302 * [backup-simplify]: Simplify 0 into 0
6.303 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
6.304 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
6.304 * [backup-simplify]: Simplify 0 into 0
6.306 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
6.307 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
6.307 * [backup-simplify]: Simplify 0 into 0
6.309 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
6.310 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
6.310 * [backup-simplify]: Simplify 0 into 0
6.311 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
6.312 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
6.312 * [backup-simplify]: Simplify 0 into 0
6.313 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
6.314 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
6.314 * [backup-simplify]: Simplify 0 into 0
6.315 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
6.315 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
6.315 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
6.315 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
6.315 * [taylor]: Taking taylor expansion of 2 in n
6.315 * [backup-simplify]: Simplify 2 into 2
6.315 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.315 * [taylor]: Taking taylor expansion of PI in n
6.315 * [backup-simplify]: Simplify PI into PI
6.315 * [taylor]: Taking taylor expansion of n in n
6.315 * [backup-simplify]: Simplify 0 into 0
6.315 * [backup-simplify]: Simplify 1 into 1
6.315 * [backup-simplify]: Simplify (/ PI 1) into PI
6.316 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
6.316 * [taylor]: Taking taylor expansion of 2 in n
6.316 * [backup-simplify]: Simplify 2 into 2
6.316 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.316 * [taylor]: Taking taylor expansion of PI in n
6.316 * [backup-simplify]: Simplify PI into PI
6.316 * [taylor]: Taking taylor expansion of n in n
6.316 * [backup-simplify]: Simplify 0 into 0
6.316 * [backup-simplify]: Simplify 1 into 1
6.316 * [backup-simplify]: Simplify (/ PI 1) into PI
6.316 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.317 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.317 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.318 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
6.318 * [backup-simplify]: Simplify 0 into 0
6.318 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.319 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
6.319 * [backup-simplify]: Simplify 0 into 0
6.320 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.320 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
6.320 * [backup-simplify]: Simplify 0 into 0
6.321 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.322 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
6.322 * [backup-simplify]: Simplify 0 into 0
6.323 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.324 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
6.324 * [backup-simplify]: Simplify 0 into 0
6.324 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.325 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
6.325 * [backup-simplify]: Simplify 0 into 0
6.326 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
6.326 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
6.326 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
6.326 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
6.326 * [taylor]: Taking taylor expansion of -2 in n
6.326 * [backup-simplify]: Simplify -2 into -2
6.326 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.326 * [taylor]: Taking taylor expansion of PI in n
6.326 * [backup-simplify]: Simplify PI into PI
6.326 * [taylor]: Taking taylor expansion of n in n
6.326 * [backup-simplify]: Simplify 0 into 0
6.326 * [backup-simplify]: Simplify 1 into 1
6.327 * [backup-simplify]: Simplify (/ PI 1) into PI
6.327 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
6.327 * [taylor]: Taking taylor expansion of -2 in n
6.327 * [backup-simplify]: Simplify -2 into -2
6.327 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.327 * [taylor]: Taking taylor expansion of PI in n
6.327 * [backup-simplify]: Simplify PI into PI
6.327 * [taylor]: Taking taylor expansion of n in n
6.327 * [backup-simplify]: Simplify 0 into 0
6.327 * [backup-simplify]: Simplify 1 into 1
6.327 * [backup-simplify]: Simplify (/ PI 1) into PI
6.327 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
6.328 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
6.328 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.329 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
6.329 * [backup-simplify]: Simplify 0 into 0
6.329 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.330 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
6.330 * [backup-simplify]: Simplify 0 into 0
6.331 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.331 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
6.331 * [backup-simplify]: Simplify 0 into 0
6.332 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.333 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
6.333 * [backup-simplify]: Simplify 0 into 0
6.333 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.334 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
6.334 * [backup-simplify]: Simplify 0 into 0
6.335 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.336 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
6.336 * [backup-simplify]: Simplify 0 into 0
6.336 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
6.336 * * * * [progress]: [ 4 / 4 ] generating series at (2)
6.337 * [backup-simplify]: Simplify (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
6.337 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (n k) around 0
6.337 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
6.337 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
6.337 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
6.337 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
6.337 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
6.337 * [taylor]: Taking taylor expansion of 1/2 in k
6.337 * [backup-simplify]: Simplify 1/2 into 1/2
6.337 * [taylor]: Taking taylor expansion of (- 1 k) in k
6.337 * [taylor]: Taking taylor expansion of 1 in k
6.337 * [backup-simplify]: Simplify 1 into 1
6.337 * [taylor]: Taking taylor expansion of k in k
6.337 * [backup-simplify]: Simplify 0 into 0
6.337 * [backup-simplify]: Simplify 1 into 1
6.337 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
6.337 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
6.337 * [taylor]: Taking taylor expansion of 2 in k
6.337 * [backup-simplify]: Simplify 2 into 2
6.337 * [taylor]: Taking taylor expansion of (* n PI) in k
6.337 * [taylor]: Taking taylor expansion of n in k
6.337 * [backup-simplify]: Simplify n into n
6.337 * [taylor]: Taking taylor expansion of PI in k
6.337 * [backup-simplify]: Simplify PI into PI
6.337 * [backup-simplify]: Simplify (* n PI) into (* n PI)
6.337 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
6.337 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
6.337 * [backup-simplify]: Simplify (- 0) into 0
6.338 * [backup-simplify]: Simplify (+ 1 0) into 1
6.338 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
6.338 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
6.338 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
6.338 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
6.338 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.338 * [taylor]: Taking taylor expansion of k in k
6.338 * [backup-simplify]: Simplify 0 into 0
6.338 * [backup-simplify]: Simplify 1 into 1
6.338 * [backup-simplify]: Simplify (/ 1 1) into 1
6.339 * [backup-simplify]: Simplify (sqrt 0) into 0
6.340 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.340 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
6.340 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
6.340 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
6.340 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
6.340 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
6.340 * [taylor]: Taking taylor expansion of 1/2 in n
6.340 * [backup-simplify]: Simplify 1/2 into 1/2
6.340 * [taylor]: Taking taylor expansion of (- 1 k) in n
6.340 * [taylor]: Taking taylor expansion of 1 in n
6.340 * [backup-simplify]: Simplify 1 into 1
6.340 * [taylor]: Taking taylor expansion of k in n
6.340 * [backup-simplify]: Simplify k into k
6.340 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
6.340 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
6.340 * [taylor]: Taking taylor expansion of 2 in n
6.340 * [backup-simplify]: Simplify 2 into 2
6.340 * [taylor]: Taking taylor expansion of (* n PI) in n
6.340 * [taylor]: Taking taylor expansion of n in n
6.340 * [backup-simplify]: Simplify 0 into 0
6.340 * [backup-simplify]: Simplify 1 into 1
6.340 * [taylor]: Taking taylor expansion of PI in n
6.340 * [backup-simplify]: Simplify PI into PI
6.340 * [backup-simplify]: Simplify (* 0 PI) into 0
6.341 * [backup-simplify]: Simplify (* 2 0) into 0
6.341 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.343 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
6.344 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.344 * [backup-simplify]: Simplify (- k) into (- k)
6.344 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
6.344 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
6.345 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.346 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
6.347 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
6.348 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
6.348 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.348 * [taylor]: Taking taylor expansion of k in n
6.348 * [backup-simplify]: Simplify k into k
6.348 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.348 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
6.348 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.348 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
6.348 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
6.348 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
6.348 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
6.348 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
6.348 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
6.348 * [taylor]: Taking taylor expansion of 1/2 in n
6.348 * [backup-simplify]: Simplify 1/2 into 1/2
6.348 * [taylor]: Taking taylor expansion of (- 1 k) in n
6.348 * [taylor]: Taking taylor expansion of 1 in n
6.348 * [backup-simplify]: Simplify 1 into 1
6.348 * [taylor]: Taking taylor expansion of k in n
6.348 * [backup-simplify]: Simplify k into k
6.348 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
6.348 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
6.348 * [taylor]: Taking taylor expansion of 2 in n
6.348 * [backup-simplify]: Simplify 2 into 2
6.348 * [taylor]: Taking taylor expansion of (* n PI) in n
6.348 * [taylor]: Taking taylor expansion of n in n
6.348 * [backup-simplify]: Simplify 0 into 0
6.348 * [backup-simplify]: Simplify 1 into 1
6.349 * [taylor]: Taking taylor expansion of PI in n
6.349 * [backup-simplify]: Simplify PI into PI
6.349 * [backup-simplify]: Simplify (* 0 PI) into 0
6.349 * [backup-simplify]: Simplify (* 2 0) into 0
6.351 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.353 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
6.354 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.354 * [backup-simplify]: Simplify (- k) into (- k)
6.354 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
6.354 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
6.355 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.356 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
6.357 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
6.357 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
6.357 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.357 * [taylor]: Taking taylor expansion of k in n
6.357 * [backup-simplify]: Simplify k into k
6.357 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.357 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
6.358 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.358 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
6.359 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) into (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k)))
6.359 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) in k
6.359 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
6.359 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
6.359 * [taylor]: Taking taylor expansion of 1/2 in k
6.359 * [backup-simplify]: Simplify 1/2 into 1/2
6.359 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
6.359 * [taylor]: Taking taylor expansion of (- 1 k) in k
6.359 * [taylor]: Taking taylor expansion of 1 in k
6.359 * [backup-simplify]: Simplify 1 into 1
6.359 * [taylor]: Taking taylor expansion of k in k
6.359 * [backup-simplify]: Simplify 0 into 0
6.359 * [backup-simplify]: Simplify 1 into 1
6.359 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
6.359 * [taylor]: Taking taylor expansion of (log n) in k
6.359 * [taylor]: Taking taylor expansion of n in k
6.359 * [backup-simplify]: Simplify n into n
6.359 * [backup-simplify]: Simplify (log n) into (log n)
6.359 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
6.359 * [taylor]: Taking taylor expansion of (* 2 PI) in k
6.359 * [taylor]: Taking taylor expansion of 2 in k
6.359 * [backup-simplify]: Simplify 2 into 2
6.359 * [taylor]: Taking taylor expansion of PI in k
6.359 * [backup-simplify]: Simplify PI into PI
6.360 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.361 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.361 * [backup-simplify]: Simplify (- 0) into 0
6.362 * [backup-simplify]: Simplify (+ 1 0) into 1
6.363 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.364 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
6.365 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
6.366 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
6.366 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
6.366 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.366 * [taylor]: Taking taylor expansion of k in k
6.366 * [backup-simplify]: Simplify 0 into 0
6.366 * [backup-simplify]: Simplify 1 into 1
6.366 * [backup-simplify]: Simplify (/ 1 1) into 1
6.367 * [backup-simplify]: Simplify (sqrt 0) into 0
6.368 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.369 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
6.369 * [backup-simplify]: Simplify 0 into 0
6.370 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
6.372 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
6.374 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
6.374 * [backup-simplify]: Simplify (- 0) into 0
6.374 * [backup-simplify]: Simplify (+ 0 0) into 0
6.375 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
6.376 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.377 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
6.380 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
6.381 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
6.381 * [taylor]: Taking taylor expansion of 0 in k
6.381 * [backup-simplify]: Simplify 0 into 0
6.382 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
6.382 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
6.384 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
6.385 * [backup-simplify]: Simplify (+ 0 0) into 0
6.385 * [backup-simplify]: Simplify (- 1) into -1
6.386 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.388 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
6.390 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
6.393 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
6.397 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
6.398 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
6.398 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
6.399 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
6.405 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
6.407 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
6.410 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
6.411 * [backup-simplify]: Simplify (- 0) into 0
6.411 * [backup-simplify]: Simplify (+ 0 0) into 0
6.412 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
6.413 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.415 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
6.417 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
6.419 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
6.419 * [taylor]: Taking taylor expansion of 0 in k
6.419 * [backup-simplify]: Simplify 0 into 0
6.419 * [backup-simplify]: Simplify 0 into 0
6.420 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
6.423 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.425 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
6.426 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
6.429 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
6.429 * [backup-simplify]: Simplify (+ 0 0) into 0
6.430 * [backup-simplify]: Simplify (- 0) into 0
6.430 * [backup-simplify]: Simplify (+ 0 0) into 0
6.432 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
6.434 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
6.438 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
6.445 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
6.447 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
6.448 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
6.448 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
6.449 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
6.450 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
6.453 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
6.454 * [backup-simplify]: Simplify (- 0) into 0
6.454 * [backup-simplify]: Simplify (+ 0 0) into 0
6.455 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 k))))) into 0
6.456 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
6.457 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
6.459 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
6.460 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
6.460 * [taylor]: Taking taylor expansion of 0 in k
6.460 * [backup-simplify]: Simplify 0 into 0
6.460 * [backup-simplify]: Simplify 0 into 0
6.460 * [backup-simplify]: Simplify 0 into 0
6.461 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.463 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.465 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
6.466 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
6.469 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
6.469 * [backup-simplify]: Simplify (+ 0 0) into 0
6.470 * [backup-simplify]: Simplify (- 0) into 0
6.470 * [backup-simplify]: Simplify (+ 0 0) into 0
6.471 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
6.473 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
6.477 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
6.487 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
6.494 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
6.509 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
6.509 * [backup-simplify]: Simplify (* (pow (* (/ 1 n) (* 2 PI)) (/ (- 1 (/ 1 k)) 2)) (/ 1 (sqrt (/ 1 k)))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
6.509 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (n k) around 0
6.509 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
6.509 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
6.509 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
6.509 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
6.509 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
6.509 * [taylor]: Taking taylor expansion of 1/2 in k
6.509 * [backup-simplify]: Simplify 1/2 into 1/2
6.509 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
6.509 * [taylor]: Taking taylor expansion of 1 in k
6.509 * [backup-simplify]: Simplify 1 into 1
6.509 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.509 * [taylor]: Taking taylor expansion of k in k
6.509 * [backup-simplify]: Simplify 0 into 0
6.509 * [backup-simplify]: Simplify 1 into 1
6.510 * [backup-simplify]: Simplify (/ 1 1) into 1
6.510 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
6.510 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
6.510 * [taylor]: Taking taylor expansion of 2 in k
6.510 * [backup-simplify]: Simplify 2 into 2
6.510 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.510 * [taylor]: Taking taylor expansion of PI in k
6.510 * [backup-simplify]: Simplify PI into PI
6.510 * [taylor]: Taking taylor expansion of n in k
6.510 * [backup-simplify]: Simplify n into n
6.510 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.510 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
6.510 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
6.510 * [backup-simplify]: Simplify (- 1) into -1
6.510 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.511 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
6.511 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
6.511 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
6.511 * [taylor]: Taking taylor expansion of (sqrt k) in k
6.511 * [taylor]: Taking taylor expansion of k in k
6.511 * [backup-simplify]: Simplify 0 into 0
6.511 * [backup-simplify]: Simplify 1 into 1
6.511 * [backup-simplify]: Simplify (sqrt 0) into 0
6.512 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.512 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
6.512 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
6.512 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
6.512 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
6.512 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
6.512 * [taylor]: Taking taylor expansion of 1/2 in n
6.512 * [backup-simplify]: Simplify 1/2 into 1/2
6.512 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
6.512 * [taylor]: Taking taylor expansion of 1 in n
6.512 * [backup-simplify]: Simplify 1 into 1
6.512 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.512 * [taylor]: Taking taylor expansion of k in n
6.512 * [backup-simplify]: Simplify k into k
6.512 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.512 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
6.512 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
6.512 * [taylor]: Taking taylor expansion of 2 in n
6.512 * [backup-simplify]: Simplify 2 into 2
6.513 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.513 * [taylor]: Taking taylor expansion of PI in n
6.513 * [backup-simplify]: Simplify PI into PI
6.513 * [taylor]: Taking taylor expansion of n in n
6.513 * [backup-simplify]: Simplify 0 into 0
6.513 * [backup-simplify]: Simplify 1 into 1
6.513 * [backup-simplify]: Simplify (/ PI 1) into PI
6.513 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.514 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.514 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.514 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
6.514 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
6.515 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.515 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
6.516 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
6.516 * [taylor]: Taking taylor expansion of (sqrt k) in n
6.516 * [taylor]: Taking taylor expansion of k in n
6.516 * [backup-simplify]: Simplify k into k
6.516 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
6.516 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
6.516 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
6.516 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
6.516 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
6.516 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
6.516 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
6.516 * [taylor]: Taking taylor expansion of 1/2 in n
6.516 * [backup-simplify]: Simplify 1/2 into 1/2
6.516 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
6.516 * [taylor]: Taking taylor expansion of 1 in n
6.516 * [backup-simplify]: Simplify 1 into 1
6.516 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.516 * [taylor]: Taking taylor expansion of k in n
6.516 * [backup-simplify]: Simplify k into k
6.517 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.517 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
6.517 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
6.517 * [taylor]: Taking taylor expansion of 2 in n
6.517 * [backup-simplify]: Simplify 2 into 2
6.517 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.517 * [taylor]: Taking taylor expansion of PI in n
6.517 * [backup-simplify]: Simplify PI into PI
6.517 * [taylor]: Taking taylor expansion of n in n
6.517 * [backup-simplify]: Simplify 0 into 0
6.517 * [backup-simplify]: Simplify 1 into 1
6.517 * [backup-simplify]: Simplify (/ PI 1) into PI
6.517 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.518 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.518 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.518 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
6.518 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
6.519 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.520 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
6.520 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
6.520 * [taylor]: Taking taylor expansion of (sqrt 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 (sqrt k) into (sqrt k)
6.520 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
6.521 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k))
6.521 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k
6.521 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
6.521 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
6.521 * [taylor]: Taking taylor expansion of 1/2 in k
6.521 * [backup-simplify]: Simplify 1/2 into 1/2
6.521 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
6.521 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
6.521 * [taylor]: Taking taylor expansion of 1 in k
6.521 * [backup-simplify]: Simplify 1 into 1
6.521 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.521 * [taylor]: Taking taylor expansion of k in k
6.521 * [backup-simplify]: Simplify 0 into 0
6.521 * [backup-simplify]: Simplify 1 into 1
6.522 * [backup-simplify]: Simplify (/ 1 1) into 1
6.522 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
6.522 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
6.522 * [taylor]: Taking taylor expansion of (* 2 PI) in k
6.522 * [taylor]: Taking taylor expansion of 2 in k
6.522 * [backup-simplify]: Simplify 2 into 2
6.522 * [taylor]: Taking taylor expansion of PI in k
6.522 * [backup-simplify]: Simplify PI into PI
6.522 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
6.523 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
6.523 * [taylor]: Taking taylor expansion of (log n) in k
6.523 * [taylor]: Taking taylor expansion of n in k
6.523 * [backup-simplify]: Simplify n into n
6.524 * [backup-simplify]: Simplify (log n) into (log n)
6.524 * [backup-simplify]: Simplify (- 1) into -1
6.524 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.524 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
6.525 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
6.526 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
6.527 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
6.529 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
6.529 * [taylor]: Taking taylor expansion of (sqrt k) in k
6.529 * [taylor]: Taking taylor expansion of k in k
6.529 * [backup-simplify]: Simplify 0 into 0
6.529 * [backup-simplify]: Simplify 1 into 1
6.529 * [backup-simplify]: Simplify (sqrt 0) into 0
6.531 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.532 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) into 0
6.532 * [backup-simplify]: Simplify 0 into 0
6.533 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.533 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
6.535 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
6.535 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.536 * [backup-simplify]: Simplify (- 0) into 0
6.536 * [backup-simplify]: Simplify (+ 0 0) into 0
6.537 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
6.538 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.539 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
6.541 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
6.542 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
6.542 * [taylor]: Taking taylor expansion of 0 in k
6.542 * [backup-simplify]: Simplify 0 into 0
6.542 * [backup-simplify]: Simplify 0 into 0
6.544 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
6.545 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
6.546 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
6.547 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.548 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
6.551 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
6.551 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
6.551 * [backup-simplify]: Simplify (- 0) into 0
6.551 * [backup-simplify]: Simplify (+ 0 0) into 0
6.552 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
6.553 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.554 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
6.555 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
6.556 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
6.556 * [taylor]: Taking taylor expansion of 0 in k
6.556 * [backup-simplify]: Simplify 0 into 0
6.556 * [backup-simplify]: Simplify 0 into 0
6.556 * [backup-simplify]: Simplify 0 into 0
6.558 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.559 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
6.560 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
6.560 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
6.561 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.562 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
6.565 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
6.565 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
6.565 * [backup-simplify]: Simplify (- 0) into 0
6.566 * [backup-simplify]: Simplify (+ 0 0) into 0
6.566 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
6.567 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
6.568 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
6.570 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
6.571 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
6.571 * [taylor]: Taking taylor expansion of 0 in k
6.571 * [backup-simplify]: Simplify 0 into 0
6.571 * [backup-simplify]: Simplify 0 into 0
6.571 * [backup-simplify]: Simplify 0 into 0
6.572 * [backup-simplify]: Simplify 0 into 0
6.574 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.576 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
6.576 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
6.579 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
6.579 * [backup-simplify]: Simplify (* (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1 (/ 1 (- k))) 2)) (/ 1 (sqrt (/ 1 (- k))))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
6.579 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (n k) around 0
6.579 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
6.579 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
6.579 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
6.579 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
6.579 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
6.579 * [taylor]: Taking taylor expansion of 1/2 in k
6.579 * [backup-simplify]: Simplify 1/2 into 1/2
6.579 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
6.579 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.579 * [taylor]: Taking taylor expansion of k in k
6.579 * [backup-simplify]: Simplify 0 into 0
6.579 * [backup-simplify]: Simplify 1 into 1
6.580 * [backup-simplify]: Simplify (/ 1 1) into 1
6.580 * [taylor]: Taking taylor expansion of 1 in k
6.580 * [backup-simplify]: Simplify 1 into 1
6.580 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
6.580 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
6.580 * [taylor]: Taking taylor expansion of -2 in k
6.580 * [backup-simplify]: Simplify -2 into -2
6.580 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.580 * [taylor]: Taking taylor expansion of PI in k
6.580 * [backup-simplify]: Simplify PI into PI
6.580 * [taylor]: Taking taylor expansion of n in k
6.580 * [backup-simplify]: Simplify n into n
6.580 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.580 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
6.580 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
6.580 * [backup-simplify]: Simplify (+ 1 0) into 1
6.581 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
6.581 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
6.581 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
6.581 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
6.581 * [taylor]: Taking taylor expansion of (/ -1 k) in k
6.581 * [taylor]: Taking taylor expansion of -1 in k
6.581 * [backup-simplify]: Simplify -1 into -1
6.581 * [taylor]: Taking taylor expansion of k in k
6.581 * [backup-simplify]: Simplify 0 into 0
6.581 * [backup-simplify]: Simplify 1 into 1
6.581 * [backup-simplify]: Simplify (/ -1 1) into -1
6.581 * [backup-simplify]: Simplify (sqrt 0) into 0
6.582 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
6.582 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
6.582 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
6.582 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
6.582 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
6.582 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
6.582 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
6.582 * [taylor]: Taking taylor expansion of 1/2 in n
6.583 * [backup-simplify]: Simplify 1/2 into 1/2
6.583 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
6.583 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.583 * [taylor]: Taking taylor expansion of k in n
6.583 * [backup-simplify]: Simplify k into k
6.583 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.583 * [taylor]: Taking taylor expansion of 1 in n
6.583 * [backup-simplify]: Simplify 1 into 1
6.583 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
6.583 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
6.583 * [taylor]: Taking taylor expansion of -2 in n
6.583 * [backup-simplify]: Simplify -2 into -2
6.583 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.583 * [taylor]: Taking taylor expansion of PI in n
6.583 * [backup-simplify]: Simplify PI into PI
6.583 * [taylor]: Taking taylor expansion of n in n
6.583 * [backup-simplify]: Simplify 0 into 0
6.583 * [backup-simplify]: Simplify 1 into 1
6.583 * [backup-simplify]: Simplify (/ PI 1) into PI
6.584 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
6.584 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
6.584 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
6.584 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
6.585 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.586 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
6.586 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
6.587 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
6.587 * [taylor]: Taking taylor expansion of (/ -1 k) in n
6.587 * [taylor]: Taking taylor expansion of -1 in n
6.587 * [backup-simplify]: Simplify -1 into -1
6.587 * [taylor]: Taking taylor expansion of k in n
6.587 * [backup-simplify]: Simplify k into k
6.587 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
6.587 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
6.587 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
6.587 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
6.587 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
6.588 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
6.588 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
6.588 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
6.588 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
6.588 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
6.588 * [taylor]: Taking taylor expansion of 1/2 in n
6.588 * [backup-simplify]: Simplify 1/2 into 1/2
6.588 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
6.588 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.588 * [taylor]: Taking taylor expansion of k in n
6.588 * [backup-simplify]: Simplify k into k
6.588 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.588 * [taylor]: Taking taylor expansion of 1 in n
6.588 * [backup-simplify]: Simplify 1 into 1
6.588 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
6.588 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
6.588 * [taylor]: Taking taylor expansion of -2 in n
6.588 * [backup-simplify]: Simplify -2 into -2
6.588 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.588 * [taylor]: Taking taylor expansion of PI in n
6.588 * [backup-simplify]: Simplify PI into PI
6.588 * [taylor]: Taking taylor expansion of n in n
6.588 * [backup-simplify]: Simplify 0 into 0
6.588 * [backup-simplify]: Simplify 1 into 1
6.588 * [backup-simplify]: Simplify (/ PI 1) into PI
6.588 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
6.589 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
6.589 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
6.589 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
6.590 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.591 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
6.592 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
6.592 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
6.592 * [taylor]: Taking taylor expansion of (/ -1 k) in n
6.592 * [taylor]: Taking taylor expansion of -1 in n
6.592 * [backup-simplify]: Simplify -1 into -1
6.592 * [taylor]: Taking taylor expansion of k in n
6.592 * [backup-simplify]: Simplify k into k
6.592 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
6.592 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
6.592 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
6.592 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
6.593 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
6.593 * [taylor]: Taking taylor expansion of (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k
6.593 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
6.593 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
6.593 * [taylor]: Taking taylor expansion of 1/2 in k
6.593 * [backup-simplify]: Simplify 1/2 into 1/2
6.593 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
6.593 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
6.593 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.593 * [taylor]: Taking taylor expansion of k in k
6.593 * [backup-simplify]: Simplify 0 into 0
6.593 * [backup-simplify]: Simplify 1 into 1
6.593 * [backup-simplify]: Simplify (/ 1 1) into 1
6.593 * [taylor]: Taking taylor expansion of 1 in k
6.593 * [backup-simplify]: Simplify 1 into 1
6.593 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
6.593 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
6.593 * [taylor]: Taking taylor expansion of (* -2 PI) in k
6.593 * [taylor]: Taking taylor expansion of -2 in k
6.593 * [backup-simplify]: Simplify -2 into -2
6.593 * [taylor]: Taking taylor expansion of PI in k
6.593 * [backup-simplify]: Simplify PI into PI
6.594 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
6.594 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
6.594 * [taylor]: Taking taylor expansion of (log n) in k
6.594 * [taylor]: Taking taylor expansion of n in k
6.594 * [backup-simplify]: Simplify n into n
6.594 * [backup-simplify]: Simplify (log n) into (log n)
6.595 * [backup-simplify]: Simplify (+ 1 0) into 1
6.595 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
6.595 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
6.596 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
6.597 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
6.597 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
6.597 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
6.597 * [taylor]: Taking taylor expansion of (/ -1 k) in k
6.597 * [taylor]: Taking taylor expansion of -1 in k
6.597 * [backup-simplify]: Simplify -1 into -1
6.597 * [taylor]: Taking taylor expansion of k in k
6.597 * [backup-simplify]: Simplify 0 into 0
6.597 * [backup-simplify]: Simplify 1 into 1
6.598 * [backup-simplify]: Simplify (/ -1 1) into -1
6.598 * [backup-simplify]: Simplify (sqrt 0) into 0
6.599 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
6.603 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
6.604 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
6.605 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.606 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
6.607 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
6.607 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.607 * [backup-simplify]: Simplify (+ 0 0) into 0
6.607 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
6.608 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.609 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
6.610 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
6.611 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
6.611 * [taylor]: Taking taylor expansion of 0 in k
6.611 * [backup-simplify]: Simplify 0 into 0
6.611 * [backup-simplify]: Simplify 0 into 0
6.611 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
6.613 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.614 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
6.615 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
6.616 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.617 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
6.618 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
6.619 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
6.619 * [backup-simplify]: Simplify (+ 0 0) into 0
6.619 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
6.620 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
6.621 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
6.623 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
6.623 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
6.624 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
6.626 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
6.626 * [taylor]: Taking taylor expansion of 0 in k
6.626 * [backup-simplify]: Simplify 0 into 0
6.626 * [backup-simplify]: Simplify 0 into 0
6.626 * [backup-simplify]: Simplify 0 into 0
6.627 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.631 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.635 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
6.636 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
6.640 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
6.640 * * * [progress]: simplifying candidates
6.640 * * * * [progress]: [ 1 / 197 ] simplifiying candidate #<alt (λ (k n) (* (log1p (expm1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ 1 (sqrt k))))>
6.640 * * * * [progress]: [ 2 / 197 ] simplifiying candidate #<alt (λ (k n) (* (expm1 (log1p (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ 1 (sqrt k))))>
6.640 * * * * [progress]: [ 3 / 197 ] simplifiying candidate #<alt (λ (k n) (* (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k))))>
6.641 * * * * [progress]: [ 4 / 197 ] simplifiying candidate #<alt (λ (k n) (* (exp (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k))))>
6.641 * * * * [progress]: [ 5 / 197 ] simplifiying candidate #<alt (λ (k n) (* (exp (* (log (* n (* 2 PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k))))>
6.641 * * * * [progress]: [ 6 / 197 ] simplifiying candidate #<alt (λ (k n) (* (exp (* (log (* n (* 2 PI))) (/ (- 1 k) 2))) (/ 1 (sqrt k))))>
6.641 * * * * [progress]: [ 7 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))) (/ 1 (sqrt k))))>
6.641 * * * * [progress]: [ 8 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))) (/ 1 (sqrt k))))>
6.641 * * * * [progress]: [ 9 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))) (/ 1 (sqrt k))))>
6.641 * * * * [progress]: [ 10 / 197 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ 1 2)) (pow (* n (* 2 PI)) (/ k 2))) (/ 1 (sqrt k))))>
6.641 * * * * [progress]: [ 11 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (/ 1 (sqrt k))))>
6.641 * * * * [progress]: [ 12 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (/ 1 (sqrt k))))>
6.641 * * * * [progress]: [ 13 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2))) (/ 1 (sqrt k))))>
6.641 * * * * [progress]: [ 14 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2))) (/ 1 (sqrt k))))>
6.641 * * * * [progress]: [ 15 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2)) (/ 1 (sqrt k))))>
6.641 * * * * [progress]: [ 16 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2))) (/ 1 (sqrt k))))>
6.641 * * * * [progress]: [ 17 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2))) (/ 1 (sqrt k))))>
6.641 * * * * [progress]: [ 18 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2)) (/ 1 (sqrt k))))>
6.642 * * * * [progress]: [ 19 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (/ 1 (sqrt k))))>
6.642 * * * * [progress]: [ 20 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (/ 1 (sqrt k))))>
6.642 * * * * [progress]: [ 21 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.642 * * * * [progress]: [ 22 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2))) (/ 1 (sqrt k))))>
6.642 * * * * [progress]: [ 23 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2))) (/ 1 (sqrt k))))>
6.642 * * * * [progress]: [ 24 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2)) (/ 1 (sqrt k))))>
6.642 * * * * [progress]: [ 25 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2))) (/ 1 (sqrt k))))>
6.642 * * * * [progress]: [ 26 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2))) (/ 1 (sqrt k))))>
6.642 * * * * [progress]: [ 27 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (/ 1 (sqrt k))))>
6.642 * * * * [progress]: [ 28 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (/ 1 (sqrt k))))>
6.642 * * * * [progress]: [ 29 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (/ 1 (sqrt k))))>
6.642 * * * * [progress]: [ 30 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.642 * * * * [progress]: [ 31 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.642 * * * * [progress]: [ 32 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (- 1 k)) (/ 1 2)) (/ 1 (sqrt k))))>
6.642 * * * * [progress]: [ 33 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (/ 1 (sqrt k))))>
6.643 * * * * [progress]: [ 34 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1) (/ 1 (sqrt k))))>
6.643 * * * * [progress]: [ 35 / 197 ] simplifiying candidate #<alt (λ (k n) (* (exp (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ 1 (sqrt k))))>
6.643 * * * * [progress]: [ 36 / 197 ] simplifiying candidate #<alt (λ (k n) (* (log (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ 1 (sqrt k))))>
6.643 * * * * [progress]: [ 37 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ 1 (sqrt k))))>
6.643 * * * * [progress]: [ 38 / 197 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ 1 (sqrt k))))>
6.643 * * * * [progress]: [ 39 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ 1 (sqrt k))))>
6.643 * * * * [progress]: [ 40 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (sqrt k))))>
6.643 * * * * [progress]: [ 41 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (/ 1 (sqrt k))))>
6.643 * * * * [progress]: [ 42 / 197 ] simplifiying candidate #<alt (λ (k n) (* (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ 1 (sqrt k))))>
6.643 * * * * [progress]: [ 43 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (log1p (expm1 (/ 1 (sqrt k))))))>
6.643 * * * * [progress]: [ 44 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (expm1 (log1p (/ 1 (sqrt k))))))>
6.643 * * * * [progress]: [ 45 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (sqrt k) -1)))>
6.643 * * * * [progress]: [ 46 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k (- 1/2))))>
6.643 * * * * [progress]: [ 47 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (sqrt k) (- 1))))>
6.643 * * * * [progress]: [ 48 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k (- (/ 1 2)))))>
6.643 * * * * [progress]: [ 49 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (/ 1 (sqrt k)) 1)))>
6.644 * * * * [progress]: [ 50 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (exp (- (log (sqrt k))))))>
6.644 * * * * [progress]: [ 51 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (exp (- 0 (log (sqrt k))))))>
6.644 * * * * [progress]: [ 52 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (exp (- (log 1) (log (sqrt k))))))>
6.644 * * * * [progress]: [ 53 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (exp (log (/ 1 (sqrt k))))))>
6.644 * * * * [progress]: [ 54 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (log (exp (/ 1 (sqrt k))))))>
6.644 * * * * [progress]: [ 55 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
6.644 * * * * [progress]: [ 56 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k))))))>
6.644 * * * * [progress]: [ 57 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))))))>
6.644 * * * * [progress]: [ 58 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))))))>
6.644 * * * * [progress]: [ 59 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (- 1) (- (sqrt k)))))>
6.644 * * * * [progress]: [ 60 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1) (cbrt (sqrt k))))))>
6.644 * * * * [progress]: [ 61 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1) (sqrt (cbrt k))))))>
6.644 * * * * [progress]: [ 62 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k))))))>
6.644 * * * * [progress]: [ 63 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (/ (cbrt 1) (sqrt k)))))>
6.644 * * * * [progress]: [ 64 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k))))))>
6.644 * * * * [progress]: [ 65 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sqrt k)))))>
6.645 * * * * [progress]: [ 66 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1) (cbrt (sqrt k))))))>
6.645 * * * * [progress]: [ 67 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1) (sqrt (cbrt k))))))>
6.645 * * * * [progress]: [ 68 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k))))))>
6.645 * * * * [progress]: [ 69 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (/ (sqrt 1) (sqrt 1)) (/ (sqrt 1) (sqrt k)))))>
6.645 * * * * [progress]: [ 70 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k))))))>
6.645 * * * * [progress]: [ 71 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (/ (sqrt 1) 1) (/ (sqrt 1) (sqrt k)))))>
6.645 * * * * [progress]: [ 72 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1 (cbrt (sqrt k))))))>
6.645 * * * * [progress]: [ 73 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1 (sqrt (cbrt k))))))>
6.645 * * * * [progress]: [ 74 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))))))>
6.645 * * * * [progress]: [ 75 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (/ 1 (sqrt 1)) (/ 1 (sqrt k)))))>
6.645 * * * * [progress]: [ 76 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k))))))>
6.645 * * * * [progress]: [ 77 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (/ 1 1) (/ 1 (sqrt k)))))>
6.645 * * * * [progress]: [ 78 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* 1 (/ 1 (sqrt k)))))>
6.645 * * * * [progress]: [ 79 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* 1 (/ 1 (sqrt k)))))>
6.645 * * * * [progress]: [ 80 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (/ (sqrt k) 1))))>
6.645 * * * * [progress]: [ 81 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))))>
6.646 * * * * [progress]: [ 82 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k)))))>
6.646 * * * * [progress]: [ 83 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))))>
6.646 * * * * [progress]: [ 84 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (/ 1 (sqrt 1)) (sqrt k))))>
6.646 * * * * [progress]: [ 85 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))))>
6.646 * * * * [progress]: [ 86 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (/ 1 1) (sqrt k))))>
6.646 * * * * [progress]: [ 87 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt k) (cbrt 1)))))>
6.646 * * * * [progress]: [ 88 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (sqrt 1) (/ (sqrt k) (sqrt 1)))))>
6.646 * * * * [progress]: [ 89 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (/ (sqrt k) 1))))>
6.646 * * * * [progress]: [ 90 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (posit16->real (real->posit16 (/ 1 (sqrt k))))))>
6.646 * * * * [progress]: [ 91 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (log1p (expm1 (* n (* 2 PI)))) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.646 * * * * [progress]: [ 92 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (expm1 (log1p (* n (* 2 PI)))) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.646 * * * * [progress]: [ 93 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.646 * * * * [progress]: [ 94 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.646 * * * * [progress]: [ 95 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.646 * * * * [progress]: [ 96 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (exp (+ (log n) (+ (log 2) (log PI)))) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.647 * * * * [progress]: [ 97 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (exp (+ (log n) (log (* 2 PI)))) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.647 * * * * [progress]: [ 98 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (exp (log (* n (* 2 PI)))) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.647 * * * * [progress]: [ 99 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (log (exp (* n (* 2 PI)))) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.647 * * * * [progress]: [ 100 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.647 * * * * [progress]: [ 101 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.647 * * * * [progress]: [ 102 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.647 * * * * [progress]: [ 103 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.647 * * * * [progress]: [ 104 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.647 * * * * [progress]: [ 105 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* 1 (* n (* 2 PI))) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.647 * * * * [progress]: [ 106 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.647 * * * * [progress]: [ 107 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.647 * * * * [progress]: [ 108 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.647 * * * * [progress]: [ 109 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* 1 (* n (* 2 PI))) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.647 * * * * [progress]: [ 110 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.647 * * * * [progress]: [ 111 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.647 * * * * [progress]: [ 112 / 197 ] simplifiying candidate #<alt (λ (k n) (log1p (expm1 (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))))>
6.648 * * * * [progress]: [ 113 / 197 ] simplifiying candidate #<alt (λ (k n) (expm1 (log1p (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))))>
6.648 * * * * [progress]: [ 114 / 197 ] simplifiying candidate #<alt (λ (k n) (pow (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))) 1))>
6.648 * * * * [progress]: [ 115 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (- (log (sqrt k))))))>
6.648 * * * * [progress]: [ 116 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (- 0 (log (sqrt k))))))>
6.648 * * * * [progress]: [ 117 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (- (log 1) (log (sqrt k))))))>
6.648 * * * * [progress]: [ 118 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (log (/ 1 (sqrt k))))))>
6.648 * * * * [progress]: [ 119 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (- (log (sqrt k))))))>
6.648 * * * * [progress]: [ 120 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (- 0 (log (sqrt k))))))>
6.648 * * * * [progress]: [ 121 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (- (log 1) (log (sqrt k))))))>
6.648 * * * * [progress]: [ 122 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (/ 1 (sqrt k))))))>
6.648 * * * * [progress]: [ 123 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (- (log (sqrt k))))))>
6.648 * * * * [progress]: [ 124 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (- 0 (log (sqrt k))))))>
6.648 * * * * [progress]: [ 125 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (- (log 1) (log (sqrt k))))))>
6.648 * * * * [progress]: [ 126 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (/ 1 (sqrt k))))))>
6.648 * * * * [progress]: [ 127 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (- (log (sqrt k))))))>
6.648 * * * * [progress]: [ 128 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (- 0 (log (sqrt k))))))>
6.649 * * * * [progress]: [ 129 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (- (log 1) (log (sqrt k))))))>
6.649 * * * * [progress]: [ 130 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (/ 1 (sqrt k))))))>
6.649 * * * * [progress]: [ 131 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (- (log (sqrt k))))))>
6.649 * * * * [progress]: [ 132 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (- 0 (log (sqrt k))))))>
6.649 * * * * [progress]: [ 133 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (- (log 1) (log (sqrt k))))))>
6.649 * * * * [progress]: [ 134 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (log (/ 1 (sqrt k))))))>
6.649 * * * * [progress]: [ 135 / 197 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))))>
6.649 * * * * [progress]: [ 136 / 197 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))))>
6.649 * * * * [progress]: [ 137 / 197 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
6.649 * * * * [progress]: [ 138 / 197 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))))))>
6.649 * * * * [progress]: [ 139 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))) (cbrt (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))) (cbrt (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))))>
6.649 * * * * [progress]: [ 140 / 197 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))))>
6.649 * * * * [progress]: [ 141 / 197 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))) (sqrt (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))))>
6.649 * * * * [progress]: [ 142 / 197 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ 1 2)) 1) (* (pow (* n (* 2 PI)) (/ k 2)) (sqrt k))))>
6.649 * * * * [progress]: [ 143 / 197 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))))>
6.650 * * * * [progress]: [ 144 / 197 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))>
6.650 * * * * [progress]: [ 145 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k)))) (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k))))))>
6.650 * * * * [progress]: [ 146 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt 1) (sqrt (sqrt k)))) (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt 1) (sqrt (sqrt k))))))>
6.650 * * * * [progress]: [ 147 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt 1) (sqrt (sqrt k)))) (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt 1) (sqrt (sqrt k))))))>
6.650 * * * * [progress]: [ 148 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (sqrt (sqrt k)))) (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (sqrt (sqrt k))))))>
6.650 * * * * [progress]: [ 149 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (sqrt (sqrt k)))) (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (sqrt (sqrt k))))))>
6.650 * * * * [progress]: [ 150 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (/ 1 (sqrt k)))) (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (/ 1 (sqrt k))))))>
6.650 * * * * [progress]: [ 151 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ (sqrt 1) (sqrt (sqrt k)))) (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ (sqrt 1) (sqrt (sqrt k))))))>
6.650 * * * * [progress]: [ 152 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ (sqrt 1) (sqrt (sqrt k)))) (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ (sqrt 1) (sqrt (sqrt k))))))>
6.650 * * * * [progress]: [ 153 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ 1 (sqrt (sqrt k)))) (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ 1 (sqrt (sqrt k))))))>
6.650 * * * * [progress]: [ 154 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ 1 (sqrt (sqrt k)))) (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ 1 (sqrt (sqrt k))))))>
6.650 * * * * [progress]: [ 155 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))) (cbrt (/ 1 (sqrt k)))))>
6.650 * * * * [progress]: [ 156 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
6.650 * * * * [progress]: [ 157 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt 1) (cbrt (sqrt k)))))>
6.651 * * * * [progress]: [ 158 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt 1) (sqrt (cbrt k)))))>
6.651 * * * * [progress]: [ 159 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))) (/ (cbrt 1) (sqrt (sqrt k)))))>
6.651 * * * * [progress]: [ 160 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (* (cbrt 1) (cbrt 1)) (sqrt 1))) (/ (cbrt 1) (sqrt k))))>
6.651 * * * * [progress]: [ 161 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))) (/ (cbrt 1) (sqrt (sqrt k)))))>
6.651 * * * * [progress]: [ 162 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (* (cbrt 1) (cbrt 1)) 1)) (/ (cbrt 1) (sqrt k))))>
6.651 * * * * [progress]: [ 163 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt 1) (cbrt (sqrt k)))))>
6.651 * * * * [progress]: [ 164 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt 1) (sqrt (cbrt k)))))>
6.651 * * * * [progress]: [ 165 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (sqrt 1) (sqrt (sqrt k)))) (/ (sqrt 1) (sqrt (sqrt k)))))>
6.651 * * * * [progress]: [ 166 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (sqrt 1) (sqrt 1))) (/ (sqrt 1) (sqrt k))))>
6.651 * * * * [progress]: [ 167 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (sqrt 1) (sqrt (sqrt k)))) (/ (sqrt 1) (sqrt (sqrt k)))))>
6.651 * * * * [progress]: [ 168 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (sqrt 1) 1)) (/ (sqrt 1) (sqrt k))))>
6.652 * * * * [progress]: [ 169 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ 1 (cbrt (sqrt k)))))>
6.652 * * * * [progress]: [ 170 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (/ 1 (sqrt (cbrt k)))))>
6.652 * * * * [progress]: [ 171 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k)))))>
6.652 * * * * [progress]: [ 172 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt 1))) (/ 1 (sqrt k))))>
6.652 * * * * [progress]: [ 173 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k)))))>
6.652 * * * * [progress]: [ 174 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 1)) (/ 1 (sqrt k))))>
6.652 * * * * [progress]: [ 175 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1) (/ 1 (sqrt k))))>
6.653 * * * * [progress]: [ 176 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1) (/ 1 (sqrt k))))>
6.653 * * * * [progress]: [ 177 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow n (/ (- 1 k) 2)) (* (pow (* 2 PI) (/ (- 1 k) 2)) (/ 1 (sqrt k)))))>
6.653 * * * * [progress]: [ 178 / 197 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (sqrt k)))))>
6.653 * * * * [progress]: [ 179 / 197 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (sqrt k)))))>
6.653 * * * * [progress]: [ 180 / 197 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))))>
6.653 * * * * [progress]: [ 181 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ 1 (sqrt k)))))>
6.653 * * * * [progress]: [ 182 / 197 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1) (sqrt k)))>
6.653 * * * * [progress]: [ 183 / 197 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ 1 2)) (/ 1 (sqrt k))) (pow (* n (* 2 PI)) (/ k 2))))>
6.653 * * * * [progress]: [ 184 / 197 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))))>
6.653 * * * * [progress]: [ 185 / 197 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))>
6.653 * * * * [progress]: [ 186 / 197 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (/ 1 (sqrt k))))>
6.653 * * * * [progress]: [ 187 / 197 ] simplifiying candidate #<alt (λ (k n) (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (/ 1 (sqrt k))))>
6.654 * * * * [progress]: [ 188 / 197 ] simplifiying candidate #<alt (λ (k n) (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (/ 1 (sqrt k))))>
6.654 * * * * [progress]: [ 189 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))))>
6.654 * * * * [progress]: [ 190 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))))>
6.654 * * * * [progress]: [ 191 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))))>
6.654 * * * * [progress]: [ 192 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.654 * * * * [progress]: [ 193 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.654 * * * * [progress]: [ 194 / 197 ] simplifiying candidate #<alt (λ (k n) (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
6.654 * * * * [progress]: [ 195 / 197 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))))>
6.654 * * * * [progress]: [ 196 / 197 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))))>
6.654 * * * * [progress]: [ 197 / 197 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))>
6.657 * [simplify]: Simplifying:
  (expm1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (log1p (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))
  (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))
  (* (log (* n (* 2 PI))) (/ (- 1 k) 2))
  (* (log (* n (* 2 PI))) (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (pow (* n (* 2 PI)) (/ 1 2))
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) 1))
  (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (pow (* n (* 2 PI)) (/ 1 1))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) 1))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
  (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (pow (* n (* 2 PI)) (/ 1 1))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (- 1 k))
  (pow n (/ (- 1 k) 2))
  (pow (* 2 PI) (/ (- 1 k) 2))
  (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
  (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
  (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (expm1 (/ 1 (sqrt k)))
  (log1p (/ 1 (sqrt k)))
  (- 1/2)
  (- 1)
  (- (/ 1 2))
  (- (log (sqrt k)))
  (- 0 (log (sqrt k)))
  (- (log 1) (log (sqrt k)))
  (log (/ 1 (sqrt k)))
  (exp (/ 1 (sqrt k)))
  (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
  (cbrt (/ 1 (sqrt k)))
  (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (- 1)
  (- (sqrt k))
  (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt 1) (cbrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt 1) (sqrt (cbrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt 1))
  (/ (cbrt 1) (sqrt k))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) 1)
  (/ (cbrt 1) (sqrt k))
  (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1) (cbrt (sqrt k)))
  (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt 1) (sqrt (cbrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt 1))
  (/ (sqrt 1) (sqrt k))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) 1)
  (/ (sqrt 1) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 1)
  (/ 1 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1)
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 1)
  (/ (sqrt k) (cbrt 1))
  (/ (sqrt k) (sqrt 1))
  (/ (sqrt k) 1)
  (real->posit16 (/ 1 (sqrt k)))
  (expm1 (* n (* 2 PI)))
  (log1p (* n (* 2 PI)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (expm1 (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))
  (log1p (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))
  (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (- (log (sqrt k))))
  (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (- 0 (log (sqrt k))))
  (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (- (log 1) (log (sqrt k))))
  (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (log (/ 1 (sqrt k))))
  (+ (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (- (log (sqrt k))))
  (+ (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (- 0 (log (sqrt k))))
  (+ (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (- (log 1) (log (sqrt k))))
  (+ (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2)) (log (/ 1 (sqrt k))))
  (+ (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (- (log (sqrt k))))
  (+ (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (- 0 (log (sqrt k))))
  (+ (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (- (log 1) (log (sqrt k))))
  (+ (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (/ 1 (sqrt k))))
  (+ (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (- (log (sqrt k))))
  (+ (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (- 0 (log (sqrt k))))
  (+ (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (- (log 1) (log (sqrt k))))
  (+ (* (log (* n (* 2 PI))) (/ (- 1 k) 2)) (log (/ 1 (sqrt k))))
  (+ (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (- (log (sqrt k))))
  (+ (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (- 0 (log (sqrt k))))
  (+ (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (- (log 1) (log (sqrt k))))
  (+ (log (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (log (/ 1 (sqrt k))))
  (log (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))
  (exp (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))
  (* (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))))
  (* (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))))
  (* (cbrt (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))) (cbrt (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))))
  (cbrt (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))
  (* (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))
  (sqrt (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))
  (sqrt (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ 1 2)) 1)
  (* (pow (* n (* 2 PI)) (/ k 2)) (sqrt k))
  (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k))))
  (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k))))
  (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt 1) (sqrt (sqrt k))))
  (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt 1) (sqrt (sqrt k))))
  (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt 1) (sqrt (sqrt k))))
  (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt 1) (sqrt (sqrt k))))
  (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (sqrt (sqrt k))))
  (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (sqrt (sqrt k))))
  (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (sqrt (sqrt k))))
  (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (sqrt (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (/ 1 (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (/ 1 (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ (sqrt 1) (sqrt (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ (sqrt 1) (sqrt (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ (sqrt 1) (sqrt (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ (sqrt 1) (sqrt (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ 1 (sqrt (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ 1 (sqrt (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ 1 (sqrt (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ 1 (sqrt (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (* (cbrt 1) (cbrt 1)) 1))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (sqrt 1) (sqrt (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (sqrt 1) (sqrt 1)))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (sqrt 1) (sqrt (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ (sqrt 1) 1))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt (* (cbrt k) (cbrt k)))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt 1)))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 1))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1)
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1)
  (* (pow (* 2 PI) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
  (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (sqrt k)))
  (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ 1 (sqrt k)))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
  (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ 1 (sqrt k)))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1)
  (* (pow (* n (* 2 PI)) (/ 1 2)) (/ 1 (sqrt k)))
  (real->posit16 (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
  (- (+ (* +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 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
6.664 * * [simplify]: iteration 1: (357 enodes)
6.832 * * [simplify]: iteration 2: (1585 enodes)
7.420 * * [simplify]: Extracting #0: cost 135 inf + 0
7.423 * * [simplify]: Extracting #1: cost 788 inf + 42
7.431 * * [simplify]: Extracting #2: cost 1254 inf + 5236
7.460 * * [simplify]: Extracting #3: cost 1106 inf + 111691
7.515 * * [simplify]: Extracting #4: cost 506 inf + 357277
7.627 * * [simplify]: Extracting #5: cost 193 inf + 500122
7.746 * * [simplify]: Extracting #6: cost 127 inf + 540433
7.876 * * [simplify]: Extracting #7: cost 53 inf + 585487
8.013 * * [simplify]: Extracting #8: cost 6 inf + 624086
8.149 * * [simplify]: Extracting #9: cost 0 inf + 628169
8.283 * * [simplify]: Extracting #10: cost 0 inf + 627679
8.424 * * [simplify]: Extracting #11: cost 0 inf + 627629
8.585 * [simplify]: Simplified to:
  (expm1 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (log1p (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (* (log (* (* PI 2) n)) (- 1 k)) 2)
  (/ (* (log (* (* PI 2) n)) (- 1 k)) 2)
  (/ (* (log (* (* PI 2) n)) (- 1 k)) 2)
  (/ (* (log (* (* PI 2) n)) (- 1 k)) 2)
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (pow (* (* PI 2) n) (/ 1 2))
  (pow (* (* PI 2) n) (/ k 2))
  (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* (* PI 2) n) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* (* PI 2) n) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* PI 2) n) (sqrt (- 1 k)))
  (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (/ (/ (+ (sqrt 1) (sqrt k)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)))
  (pow (* (* PI 2) n) (+ (sqrt 1) (sqrt k)))
  (pow (* (* PI 2) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* (* PI 2) n) (+ 1 (sqrt k)))
  (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (- 1 k))
  (pow n (/ (- 1 k) 2))
  (pow (* PI 2) (/ (- 1 k) 2))
  (/ (* (log (* (* PI 2) n)) (- 1 k)) 2)
  (exp (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (pow (pow (* (* PI 2) n) (/ (- 1 k) 2)) 3)
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))
  (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))
  (real->posit16 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (expm1 (/ 1 (sqrt k)))
  (log1p (/ 1 (sqrt k)))
  (- 1/2)
  (- 1)
  (- (/ 1 2))
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (exp (/ 1 (sqrt k)))
  (/ (/ 1 k) (sqrt k))
  (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
  (cbrt (/ 1 (sqrt k)))
  (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (- 1)
  (- (sqrt k))
  (* (/ (cbrt 1) (cbrt (sqrt k))) (/ (cbrt 1) (cbrt (sqrt k))))
  (/ (cbrt 1) (cbrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (fabs (cbrt k)))
  (/ (cbrt 1) (sqrt (cbrt k)))
  (/ (cbrt 1) (/ (sqrt (sqrt k)) (cbrt 1)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (cbrt 1) (/ (sqrt 1) (cbrt 1)))
  (/ (cbrt 1) (sqrt k))
  (/ (cbrt 1) (/ (sqrt (sqrt k)) (cbrt 1)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (* (cbrt 1) (cbrt 1))
  (/ (cbrt 1) (sqrt k))
  (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1) (cbrt (sqrt k)))
  (/ (sqrt 1) (fabs (cbrt k)))
  (/ (sqrt 1) (sqrt (cbrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  1
  (/ (sqrt 1) (sqrt k))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (sqrt 1)
  (/ (sqrt 1) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt k))
  (sqrt k)
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ (sqrt k) (cbrt 1))
  (/ (sqrt k) (sqrt 1))
  (sqrt k)
  (real->posit16 (/ 1 (sqrt k)))
  (expm1 (* (* PI 2) n))
  (log1p (* (* PI 2) n))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (* (exp (* n PI)) (exp (* n PI)))
  (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n))
  (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n))
  (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n)))
  (cbrt (* (* PI 2) n))
  (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (* n 2)
  (* (* (cbrt n) 2) PI)
  (* PI (* (sqrt n) 2))
  (* (* PI 2) n)
  (real->posit16 (* (* PI 2) n))
  (expm1 (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (log1p (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (- (/ (* (log (* (* PI 2) n)) (- 1 k)) 2) (log (sqrt k)))
  (exp (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (/ (pow (pow (* (* PI 2) n) (/ (- 1 k) 2)) 3) (* k (sqrt k)))
  (* (pow (pow (* (* PI 2) n) (/ (- 1 k) 2)) 3) (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))))
  (* (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))))
  (cbrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (/ (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (* (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)) (pow (* (* PI 2) n) (/ (- 1 k) 2)))) (sqrt k))
  (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (pow (* (* PI 2) n) (/ 1 2))
  (* (pow (* (* PI 2) n) (/ k 2)) (sqrt k))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (/ (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt 1)) (sqrt (sqrt k)))
  (/ (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt 1)) (sqrt (sqrt k)))
  (/ (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt 1)) (sqrt (sqrt k)))
  (/ (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt 1)) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (* (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))) (sqrt (/ 1 (sqrt k))))
  (* (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))) (sqrt (/ 1 (sqrt k))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))) (sqrt (sqrt k)))
  (* (* (cbrt (/ 1 (sqrt k))) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (/ 1 (sqrt k))))
  (* (sqrt (/ 1 (sqrt k))) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (* (/ (cbrt 1) (cbrt (sqrt k))) (/ (cbrt 1) (cbrt (sqrt k)))) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (* (* (cbrt 1) (cbrt 1)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (fabs (cbrt k)))
  (/ (* (* (cbrt 1) (cbrt 1)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (/ (sqrt 1) (* (cbrt 1) (cbrt 1))))
  (/ (* (* (cbrt 1) (cbrt 1)) (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (* (* (cbrt 1) (cbrt 1)) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (/ (/ (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt 1)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (/ (sqrt 1) (fabs (cbrt k))))
  (/ (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt 1)) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (/ (- 1 k) 2))
  (/ (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt 1)) (sqrt (sqrt k)))
  (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt 1))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt 1))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (/ (- 1 k) 2))
  (pow (* (* PI 2) n) (/ (- 1 k) 2))
  (pow (* (* PI 2) n) (/ (- 1 k) 2))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
  (/ (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (sqrt k))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))) (sqrt k))
  (pow (* (* PI 2) n) (/ (- 1 k) 2))
  (/ (pow (* (* PI 2) n) (/ 1 2)) (sqrt k))
  (real->posit16 (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (sqrt k)))
  (fma 1/4 (* (exp (* 1/2 (log (* (* PI 2) n)))) (* (* (* (log n) k) k) (log (* PI 2)))) (- (fma (* 1/8 (exp (* 1/2 (log (* (* PI 2) n))))) (* (* (log n) k) (* (log n) k)) (fma (* (* (log (* PI 2)) (log (* PI 2))) 1/8) (* (exp (* 1/2 (log (* (* PI 2) n)))) (* k k)) (exp (* 1/2 (log (* (* PI 2) n)))))) (* (fma (* (log n) k) (exp (* 1/2 (log (* (* PI 2) n)))) (* (* (log (* PI 2)) k) (exp (* 1/2 (log (* (* PI 2) n)))))) 1/2)))
  (exp (* (* (- 1 k) 1/2) (log (* (* PI 2) n))))
  (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (- (- (* +nan.0 (* k k)) (- +nan.0 (* +nan.0 k))))
  (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ +nan.0 (* (* k k) k))))
  (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) +nan.0))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (* (* PI 2) n)
  (- (* (* (exp (* 1/2 (log (* (* PI 2) n)))) (* (* (* (log n) k) k) (log (* PI 2)))) (- +nan.0)) (+ (+ (- (* (* +nan.0 (exp (* 1/2 (log (* (* PI 2) n))))) (* (* (log n) k) (* (log n) k))) (* (* +nan.0 (exp (* 1/2 (log (* (* PI 2) n))))) k)) (+ (- (* +nan.0 (exp (* 1/2 (log (* (* PI 2) n))))) (* (* (log (* PI 2)) (log (* PI 2))) (* (* +nan.0 (exp (* 1/2 (log (* (* PI 2) n))))) (* k k)))) (+ (- (* (* (* (log n) k) k) (* +nan.0 (exp (* 1/2 (log (* (* PI 2) n)))))) (* (* +nan.0 (exp (* 1/2 (log (* (* PI 2) n))))) (* k k))) (* +nan.0 (- (* (* (log (* PI 2)) k) (exp (* 1/2 (log (* (* PI 2) n))))) (* (* (log n) k) (exp (* 1/2 (log (* (* PI 2) n)))))))))) (* (* (exp (* 1/2 (log (* (* PI 2) n)))) (* (* k k) (log (* PI 2)))) (- +nan.0))))
  (+ (* +nan.0 (- (/ (exp (* (* (- 1 k) 1/2) (log (* (* PI 2) n)))) (* k k)) (/ (exp (* (* (- 1 k) 1/2) (log (* (* PI 2) n)))) (* (* k k) k)))) (- (/ (* +nan.0 (exp (* (* (- 1 k) 1/2) (log (* (* PI 2) n))))) k)))
  (- (fma +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k) (- (* +nan.0 (- (/ (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k) k) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
8.610 * * * [progress]: adding candidates to table
11.232 * * [progress]: iteration 3 / 4
11.232 * * * [progress]: picking best candidate
11.262 * * * * [pick]: Picked  #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
11.262 * * * [progress]: localizing error
11.323 * * * [progress]: generating rewritten candidates
11.323 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 2)
11.353 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1)
11.383 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1)
11.463 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 2 1)
11.490 * * * [progress]: generating series expansions
11.490 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 2)
11.491 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) into (pow (* 2 (* n PI)) (* 1/4 (- 1 k)))
11.491 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in (n k) around 0
11.491 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in k
11.491 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in k
11.491 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in k
11.491 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in k
11.491 * [taylor]: Taking taylor expansion of 1/4 in k
11.491 * [backup-simplify]: Simplify 1/4 into 1/4
11.491 * [taylor]: Taking taylor expansion of (- 1 k) in k
11.491 * [taylor]: Taking taylor expansion of 1 in k
11.491 * [backup-simplify]: Simplify 1 into 1
11.491 * [taylor]: Taking taylor expansion of k in k
11.491 * [backup-simplify]: Simplify 0 into 0
11.491 * [backup-simplify]: Simplify 1 into 1
11.491 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
11.491 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
11.491 * [taylor]: Taking taylor expansion of 2 in k
11.491 * [backup-simplify]: Simplify 2 into 2
11.491 * [taylor]: Taking taylor expansion of (* n PI) in k
11.491 * [taylor]: Taking taylor expansion of n in k
11.491 * [backup-simplify]: Simplify n into n
11.491 * [taylor]: Taking taylor expansion of PI in k
11.491 * [backup-simplify]: Simplify PI into PI
11.491 * [backup-simplify]: Simplify (* n PI) into (* n PI)
11.491 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
11.491 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
11.492 * [backup-simplify]: Simplify (- 0) into 0
11.492 * [backup-simplify]: Simplify (+ 1 0) into 1
11.492 * [backup-simplify]: Simplify (* 1/4 1) into 1/4
11.492 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
11.492 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
11.492 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in n
11.492 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in n
11.492 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in n
11.492 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in n
11.492 * [taylor]: Taking taylor expansion of 1/4 in n
11.492 * [backup-simplify]: Simplify 1/4 into 1/4
11.492 * [taylor]: Taking taylor expansion of (- 1 k) in n
11.492 * [taylor]: Taking taylor expansion of 1 in n
11.492 * [backup-simplify]: Simplify 1 into 1
11.492 * [taylor]: Taking taylor expansion of k in n
11.492 * [backup-simplify]: Simplify k into k
11.492 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
11.492 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
11.493 * [taylor]: Taking taylor expansion of 2 in n
11.493 * [backup-simplify]: Simplify 2 into 2
11.493 * [taylor]: Taking taylor expansion of (* n PI) in n
11.493 * [taylor]: Taking taylor expansion of n in n
11.493 * [backup-simplify]: Simplify 0 into 0
11.493 * [backup-simplify]: Simplify 1 into 1
11.493 * [taylor]: Taking taylor expansion of PI in n
11.493 * [backup-simplify]: Simplify PI into PI
11.493 * [backup-simplify]: Simplify (* 0 PI) into 0
11.493 * [backup-simplify]: Simplify (* 2 0) into 0
11.494 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.495 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
11.499 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.500 * [backup-simplify]: Simplify (- k) into (- k)
11.500 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
11.500 * [backup-simplify]: Simplify (* 1/4 (- 1 k)) into (* 1/4 (- 1 k))
11.501 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.501 * [backup-simplify]: Simplify (* (* 1/4 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
11.502 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
11.502 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in n
11.502 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in n
11.502 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in n
11.502 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in n
11.502 * [taylor]: Taking taylor expansion of 1/4 in n
11.502 * [backup-simplify]: Simplify 1/4 into 1/4
11.502 * [taylor]: Taking taylor expansion of (- 1 k) in n
11.502 * [taylor]: Taking taylor expansion of 1 in n
11.502 * [backup-simplify]: Simplify 1 into 1
11.502 * [taylor]: Taking taylor expansion of k in n
11.502 * [backup-simplify]: Simplify k into k
11.502 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
11.502 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
11.502 * [taylor]: Taking taylor expansion of 2 in n
11.502 * [backup-simplify]: Simplify 2 into 2
11.502 * [taylor]: Taking taylor expansion of (* n PI) in n
11.502 * [taylor]: Taking taylor expansion of n in n
11.502 * [backup-simplify]: Simplify 0 into 0
11.502 * [backup-simplify]: Simplify 1 into 1
11.502 * [taylor]: Taking taylor expansion of PI in n
11.502 * [backup-simplify]: Simplify PI into PI
11.503 * [backup-simplify]: Simplify (* 0 PI) into 0
11.503 * [backup-simplify]: Simplify (* 2 0) into 0
11.504 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.505 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
11.505 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.505 * [backup-simplify]: Simplify (- k) into (- k)
11.505 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
11.505 * [backup-simplify]: Simplify (* 1/4 (- 1 k)) into (* 1/4 (- 1 k))
11.506 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.507 * [backup-simplify]: Simplify (* (* 1/4 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
11.508 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
11.508 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
11.508 * [taylor]: Taking taylor expansion of (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
11.508 * [taylor]: Taking taylor expansion of 1/4 in k
11.508 * [backup-simplify]: Simplify 1/4 into 1/4
11.508 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
11.508 * [taylor]: Taking taylor expansion of (- 1 k) in k
11.508 * [taylor]: Taking taylor expansion of 1 in k
11.508 * [backup-simplify]: Simplify 1 into 1
11.508 * [taylor]: Taking taylor expansion of k in k
11.508 * [backup-simplify]: Simplify 0 into 0
11.508 * [backup-simplify]: Simplify 1 into 1
11.508 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
11.508 * [taylor]: Taking taylor expansion of (log n) in k
11.508 * [taylor]: Taking taylor expansion of n in k
11.508 * [backup-simplify]: Simplify n into n
11.508 * [backup-simplify]: Simplify (log n) into (log n)
11.508 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
11.508 * [taylor]: Taking taylor expansion of (* 2 PI) in k
11.508 * [taylor]: Taking taylor expansion of 2 in k
11.508 * [backup-simplify]: Simplify 2 into 2
11.508 * [taylor]: Taking taylor expansion of PI in k
11.508 * [backup-simplify]: Simplify PI into PI
11.508 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.509 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.509 * [backup-simplify]: Simplify (- 0) into 0
11.510 * [backup-simplify]: Simplify (+ 1 0) into 1
11.510 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.511 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
11.511 * [backup-simplify]: Simplify (* 1/4 (+ (log n) (log (* 2 PI)))) into (* 1/4 (+ (log n) (log (* 2 PI))))
11.512 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
11.513 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
11.513 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.514 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
11.516 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
11.516 * [backup-simplify]: Simplify (- 0) into 0
11.517 * [backup-simplify]: Simplify (+ 0 0) into 0
11.517 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- 1 k))) into 0
11.518 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.520 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
11.521 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.521 * [taylor]: Taking taylor expansion of 0 in k
11.522 * [backup-simplify]: Simplify 0 into 0
11.522 * [backup-simplify]: Simplify 0 into 0
11.522 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
11.523 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
11.524 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
11.524 * [backup-simplify]: Simplify (+ 0 0) into 0
11.524 * [backup-simplify]: Simplify (- 1) into -1
11.525 * [backup-simplify]: Simplify (+ 0 -1) into -1
11.525 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
11.527 * [backup-simplify]: Simplify (+ (* 1/4 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))))
11.528 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
11.530 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
11.531 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
11.532 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
11.533 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
11.534 * [backup-simplify]: Simplify (- 0) into 0
11.534 * [backup-simplify]: Simplify (+ 0 0) into 0
11.535 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
11.536 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.537 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
11.538 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.538 * [taylor]: Taking taylor expansion of 0 in k
11.538 * [backup-simplify]: Simplify 0 into 0
11.538 * [backup-simplify]: Simplify 0 into 0
11.538 * [backup-simplify]: Simplify 0 into 0
11.539 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
11.540 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
11.542 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
11.542 * [backup-simplify]: Simplify (+ 0 0) into 0
11.542 * [backup-simplify]: Simplify (- 0) into 0
11.543 * [backup-simplify]: Simplify (+ 0 0) into 0
11.544 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
11.545 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
11.547 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
11.550 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
11.556 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
11.557 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (/ (- 1 (/ 1 k)) 2) 2)) into (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k))))
11.557 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in (n k) around 0
11.557 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in k
11.557 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
11.557 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
11.557 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in k
11.557 * [taylor]: Taking taylor expansion of 1/4 in k
11.557 * [backup-simplify]: Simplify 1/4 into 1/4
11.557 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
11.557 * [taylor]: Taking taylor expansion of 1 in k
11.557 * [backup-simplify]: Simplify 1 into 1
11.557 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.557 * [taylor]: Taking taylor expansion of k in k
11.557 * [backup-simplify]: Simplify 0 into 0
11.557 * [backup-simplify]: Simplify 1 into 1
11.557 * [backup-simplify]: Simplify (/ 1 1) into 1
11.557 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
11.557 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
11.557 * [taylor]: Taking taylor expansion of 2 in k
11.557 * [backup-simplify]: Simplify 2 into 2
11.557 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.557 * [taylor]: Taking taylor expansion of PI in k
11.557 * [backup-simplify]: Simplify PI into PI
11.557 * [taylor]: Taking taylor expansion of n in k
11.557 * [backup-simplify]: Simplify n into n
11.557 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.557 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
11.557 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
11.558 * [backup-simplify]: Simplify (- 1) into -1
11.558 * [backup-simplify]: Simplify (+ 0 -1) into -1
11.558 * [backup-simplify]: Simplify (* 1/4 -1) into -1/4
11.558 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
11.558 * [backup-simplify]: Simplify (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
11.558 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in n
11.558 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
11.558 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
11.558 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in n
11.558 * [taylor]: Taking taylor expansion of 1/4 in n
11.558 * [backup-simplify]: Simplify 1/4 into 1/4
11.558 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
11.558 * [taylor]: Taking taylor expansion of 1 in n
11.558 * [backup-simplify]: Simplify 1 into 1
11.558 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.558 * [taylor]: Taking taylor expansion of k in n
11.558 * [backup-simplify]: Simplify k into k
11.558 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.559 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
11.559 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
11.559 * [taylor]: Taking taylor expansion of 2 in n
11.559 * [backup-simplify]: Simplify 2 into 2
11.559 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.559 * [taylor]: Taking taylor expansion of PI in n
11.559 * [backup-simplify]: Simplify PI into PI
11.559 * [taylor]: Taking taylor expansion of n in n
11.559 * [backup-simplify]: Simplify 0 into 0
11.559 * [backup-simplify]: Simplify 1 into 1
11.559 * [backup-simplify]: Simplify (/ PI 1) into PI
11.559 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.560 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.560 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
11.560 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
11.560 * [backup-simplify]: Simplify (* 1/4 (- 1 (/ 1 k))) into (* 1/4 (- 1 (/ 1 k)))
11.561 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.562 * [backup-simplify]: Simplify (* (* 1/4 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
11.562 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
11.562 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in n
11.562 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
11.562 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
11.562 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in n
11.562 * [taylor]: Taking taylor expansion of 1/4 in n
11.562 * [backup-simplify]: Simplify 1/4 into 1/4
11.562 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
11.562 * [taylor]: Taking taylor expansion of 1 in n
11.562 * [backup-simplify]: Simplify 1 into 1
11.562 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.562 * [taylor]: Taking taylor expansion of k in n
11.562 * [backup-simplify]: Simplify k into k
11.562 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.563 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
11.563 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
11.563 * [taylor]: Taking taylor expansion of 2 in n
11.563 * [backup-simplify]: Simplify 2 into 2
11.563 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.563 * [taylor]: Taking taylor expansion of PI in n
11.563 * [backup-simplify]: Simplify PI into PI
11.563 * [taylor]: Taking taylor expansion of n in n
11.563 * [backup-simplify]: Simplify 0 into 0
11.563 * [backup-simplify]: Simplify 1 into 1
11.563 * [backup-simplify]: Simplify (/ PI 1) into PI
11.563 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.564 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.564 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
11.564 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
11.564 * [backup-simplify]: Simplify (* 1/4 (- 1 (/ 1 k))) into (* 1/4 (- 1 (/ 1 k)))
11.565 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.566 * [backup-simplify]: Simplify (* (* 1/4 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
11.566 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
11.566 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
11.566 * [taylor]: Taking taylor expansion of (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
11.566 * [taylor]: Taking taylor expansion of 1/4 in k
11.566 * [backup-simplify]: Simplify 1/4 into 1/4
11.566 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
11.566 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
11.566 * [taylor]: Taking taylor expansion of 1 in k
11.566 * [backup-simplify]: Simplify 1 into 1
11.566 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.566 * [taylor]: Taking taylor expansion of k in k
11.566 * [backup-simplify]: Simplify 0 into 0
11.566 * [backup-simplify]: Simplify 1 into 1
11.567 * [backup-simplify]: Simplify (/ 1 1) into 1
11.567 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
11.567 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
11.567 * [taylor]: Taking taylor expansion of (* 2 PI) in k
11.567 * [taylor]: Taking taylor expansion of 2 in k
11.567 * [backup-simplify]: Simplify 2 into 2
11.567 * [taylor]: Taking taylor expansion of PI in k
11.567 * [backup-simplify]: Simplify PI into PI
11.567 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.568 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.568 * [taylor]: Taking taylor expansion of (log n) in k
11.568 * [taylor]: Taking taylor expansion of n in k
11.568 * [backup-simplify]: Simplify n into n
11.568 * [backup-simplify]: Simplify (log n) into (log n)
11.568 * [backup-simplify]: Simplify (- 1) into -1
11.568 * [backup-simplify]: Simplify (+ 0 -1) into -1
11.568 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
11.569 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
11.570 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
11.570 * [backup-simplify]: Simplify (* 1/4 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
11.571 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
11.572 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
11.572 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.573 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
11.574 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
11.574 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.574 * [backup-simplify]: Simplify (- 0) into 0
11.574 * [backup-simplify]: Simplify (+ 0 0) into 0
11.575 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- 1 (/ 1 k)))) into 0
11.575 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.576 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
11.577 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.577 * [taylor]: Taking taylor expansion of 0 in k
11.577 * [backup-simplify]: Simplify 0 into 0
11.577 * [backup-simplify]: Simplify 0 into 0
11.577 * [backup-simplify]: Simplify 0 into 0
11.578 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.579 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
11.580 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
11.580 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.581 * [backup-simplify]: Simplify (- 0) into 0
11.581 * [backup-simplify]: Simplify (+ 0 0) into 0
11.581 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
11.582 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.583 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
11.585 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.585 * [taylor]: Taking taylor expansion of 0 in k
11.585 * [backup-simplify]: Simplify 0 into 0
11.585 * [backup-simplify]: Simplify 0 into 0
11.585 * [backup-simplify]: Simplify 0 into 0
11.585 * [backup-simplify]: Simplify 0 into 0
11.585 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.590 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.594 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
11.594 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.594 * [backup-simplify]: Simplify (- 0) into 0
11.594 * [backup-simplify]: Simplify (+ 0 0) into 0
11.595 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
11.596 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.597 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
11.599 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
11.599 * [taylor]: Taking taylor expansion of 0 in k
11.599 * [backup-simplify]: Simplify 0 into 0
11.599 * [backup-simplify]: Simplify 0 into 0
11.600 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
11.600 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (/ (- 1 (/ 1 (- k))) 2) 2)) into (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1)))
11.600 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in (n k) around 0
11.600 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in k
11.600 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
11.600 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
11.600 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in k
11.600 * [taylor]: Taking taylor expansion of 1/4 in k
11.600 * [backup-simplify]: Simplify 1/4 into 1/4
11.600 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
11.600 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.600 * [taylor]: Taking taylor expansion of k in k
11.600 * [backup-simplify]: Simplify 0 into 0
11.600 * [backup-simplify]: Simplify 1 into 1
11.600 * [backup-simplify]: Simplify (/ 1 1) into 1
11.600 * [taylor]: Taking taylor expansion of 1 in k
11.601 * [backup-simplify]: Simplify 1 into 1
11.601 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
11.601 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
11.601 * [taylor]: Taking taylor expansion of -2 in k
11.601 * [backup-simplify]: Simplify -2 into -2
11.601 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.601 * [taylor]: Taking taylor expansion of PI in k
11.601 * [backup-simplify]: Simplify PI into PI
11.601 * [taylor]: Taking taylor expansion of n in k
11.601 * [backup-simplify]: Simplify n into n
11.601 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.601 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
11.601 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
11.601 * [backup-simplify]: Simplify (+ 1 0) into 1
11.601 * [backup-simplify]: Simplify (* 1/4 1) into 1/4
11.601 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
11.602 * [backup-simplify]: Simplify (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/4 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
11.602 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in n
11.602 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
11.602 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
11.602 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in n
11.602 * [taylor]: Taking taylor expansion of 1/4 in n
11.602 * [backup-simplify]: Simplify 1/4 into 1/4
11.602 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
11.602 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.602 * [taylor]: Taking taylor expansion of k in n
11.602 * [backup-simplify]: Simplify k into k
11.602 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.602 * [taylor]: Taking taylor expansion of 1 in n
11.602 * [backup-simplify]: Simplify 1 into 1
11.602 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
11.602 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
11.602 * [taylor]: Taking taylor expansion of -2 in n
11.602 * [backup-simplify]: Simplify -2 into -2
11.602 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.602 * [taylor]: Taking taylor expansion of PI in n
11.602 * [backup-simplify]: Simplify PI into PI
11.602 * [taylor]: Taking taylor expansion of n in n
11.602 * [backup-simplify]: Simplify 0 into 0
11.602 * [backup-simplify]: Simplify 1 into 1
11.602 * [backup-simplify]: Simplify (/ PI 1) into PI
11.602 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
11.603 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
11.603 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
11.603 * [backup-simplify]: Simplify (* 1/4 (+ (/ 1 k) 1)) into (* 1/4 (+ (/ 1 k) 1))
11.604 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.605 * [backup-simplify]: Simplify (* (* 1/4 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
11.605 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
11.605 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in n
11.605 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
11.606 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
11.606 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in n
11.606 * [taylor]: Taking taylor expansion of 1/4 in n
11.606 * [backup-simplify]: Simplify 1/4 into 1/4
11.606 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
11.606 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.606 * [taylor]: Taking taylor expansion of k in n
11.606 * [backup-simplify]: Simplify k into k
11.606 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.606 * [taylor]: Taking taylor expansion of 1 in n
11.606 * [backup-simplify]: Simplify 1 into 1
11.606 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
11.606 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
11.606 * [taylor]: Taking taylor expansion of -2 in n
11.606 * [backup-simplify]: Simplify -2 into -2
11.606 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.606 * [taylor]: Taking taylor expansion of PI in n
11.606 * [backup-simplify]: Simplify PI into PI
11.606 * [taylor]: Taking taylor expansion of n in n
11.606 * [backup-simplify]: Simplify 0 into 0
11.606 * [backup-simplify]: Simplify 1 into 1
11.606 * [backup-simplify]: Simplify (/ PI 1) into PI
11.606 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
11.607 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
11.607 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
11.607 * [backup-simplify]: Simplify (* 1/4 (+ (/ 1 k) 1)) into (* 1/4 (+ (/ 1 k) 1))
11.608 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.609 * [backup-simplify]: Simplify (* (* 1/4 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
11.609 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
11.609 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
11.609 * [taylor]: Taking taylor expansion of (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
11.609 * [taylor]: Taking taylor expansion of 1/4 in k
11.610 * [backup-simplify]: Simplify 1/4 into 1/4
11.610 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
11.610 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
11.610 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.610 * [taylor]: Taking taylor expansion of k in k
11.610 * [backup-simplify]: Simplify 0 into 0
11.610 * [backup-simplify]: Simplify 1 into 1
11.610 * [backup-simplify]: Simplify (/ 1 1) into 1
11.610 * [taylor]: Taking taylor expansion of 1 in k
11.610 * [backup-simplify]: Simplify 1 into 1
11.610 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
11.610 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
11.610 * [taylor]: Taking taylor expansion of (* -2 PI) in k
11.610 * [taylor]: Taking taylor expansion of -2 in k
11.610 * [backup-simplify]: Simplify -2 into -2
11.610 * [taylor]: Taking taylor expansion of PI in k
11.610 * [backup-simplify]: Simplify PI into PI
11.610 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
11.611 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
11.611 * [taylor]: Taking taylor expansion of (log n) in k
11.611 * [taylor]: Taking taylor expansion of n in k
11.611 * [backup-simplify]: Simplify n into n
11.611 * [backup-simplify]: Simplify (log n) into (log n)
11.611 * [backup-simplify]: Simplify (+ 1 0) into 1
11.611 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
11.612 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
11.613 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
11.613 * [backup-simplify]: Simplify (* 1/4 (- (log (* -2 PI)) (log n))) into (* 1/4 (- (log (* -2 PI)) (log n)))
11.614 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
11.615 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
11.615 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.616 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
11.617 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
11.617 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.617 * [backup-simplify]: Simplify (+ 0 0) into 0
11.617 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (+ (/ 1 k) 1))) into 0
11.618 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.619 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
11.620 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.620 * [taylor]: Taking taylor expansion of 0 in k
11.620 * [backup-simplify]: Simplify 0 into 0
11.620 * [backup-simplify]: Simplify 0 into 0
11.620 * [backup-simplify]: Simplify 0 into 0
11.621 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.621 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
11.623 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
11.623 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.624 * [backup-simplify]: Simplify (+ 0 0) into 0
11.624 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
11.625 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.626 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
11.627 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.627 * [taylor]: Taking taylor expansion of 0 in k
11.627 * [backup-simplify]: Simplify 0 into 0
11.627 * [backup-simplify]: Simplify 0 into 0
11.627 * [backup-simplify]: Simplify 0 into 0
11.627 * [backup-simplify]: Simplify 0 into 0
11.628 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.629 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.632 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
11.633 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.633 * [backup-simplify]: Simplify (+ 0 0) into 0
11.634 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
11.635 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.636 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
11.637 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
11.637 * [taylor]: Taking taylor expansion of 0 in k
11.637 * [backup-simplify]: Simplify 0 into 0
11.638 * [backup-simplify]: Simplify 0 into 0
11.638 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
11.638 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1)
11.639 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) into (pow (* 2 (* n PI)) (* 1/4 (- 1 k)))
11.639 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in (n k) around 0
11.639 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in k
11.639 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in k
11.639 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in k
11.639 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in k
11.639 * [taylor]: Taking taylor expansion of 1/4 in k
11.639 * [backup-simplify]: Simplify 1/4 into 1/4
11.639 * [taylor]: Taking taylor expansion of (- 1 k) in k
11.639 * [taylor]: Taking taylor expansion of 1 in k
11.639 * [backup-simplify]: Simplify 1 into 1
11.639 * [taylor]: Taking taylor expansion of k in k
11.639 * [backup-simplify]: Simplify 0 into 0
11.639 * [backup-simplify]: Simplify 1 into 1
11.639 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
11.639 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
11.639 * [taylor]: Taking taylor expansion of 2 in k
11.639 * [backup-simplify]: Simplify 2 into 2
11.639 * [taylor]: Taking taylor expansion of (* n PI) in k
11.639 * [taylor]: Taking taylor expansion of n in k
11.639 * [backup-simplify]: Simplify n into n
11.639 * [taylor]: Taking taylor expansion of PI in k
11.639 * [backup-simplify]: Simplify PI into PI
11.639 * [backup-simplify]: Simplify (* n PI) into (* n PI)
11.639 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
11.639 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
11.639 * [backup-simplify]: Simplify (- 0) into 0
11.640 * [backup-simplify]: Simplify (+ 1 0) into 1
11.640 * [backup-simplify]: Simplify (* 1/4 1) into 1/4
11.640 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
11.640 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
11.640 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in n
11.640 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in n
11.640 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in n
11.640 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in n
11.640 * [taylor]: Taking taylor expansion of 1/4 in n
11.640 * [backup-simplify]: Simplify 1/4 into 1/4
11.640 * [taylor]: Taking taylor expansion of (- 1 k) in n
11.640 * [taylor]: Taking taylor expansion of 1 in n
11.640 * [backup-simplify]: Simplify 1 into 1
11.640 * [taylor]: Taking taylor expansion of k in n
11.640 * [backup-simplify]: Simplify k into k
11.640 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
11.640 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
11.640 * [taylor]: Taking taylor expansion of 2 in n
11.640 * [backup-simplify]: Simplify 2 into 2
11.640 * [taylor]: Taking taylor expansion of (* n PI) in n
11.640 * [taylor]: Taking taylor expansion of n in n
11.640 * [backup-simplify]: Simplify 0 into 0
11.640 * [backup-simplify]: Simplify 1 into 1
11.640 * [taylor]: Taking taylor expansion of PI in n
11.640 * [backup-simplify]: Simplify PI into PI
11.641 * [backup-simplify]: Simplify (* 0 PI) into 0
11.641 * [backup-simplify]: Simplify (* 2 0) into 0
11.642 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.643 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
11.644 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.644 * [backup-simplify]: Simplify (- k) into (- k)
11.644 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
11.644 * [backup-simplify]: Simplify (* 1/4 (- 1 k)) into (* 1/4 (- 1 k))
11.645 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.645 * [backup-simplify]: Simplify (* (* 1/4 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
11.646 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
11.646 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in n
11.646 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in n
11.646 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in n
11.646 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in n
11.646 * [taylor]: Taking taylor expansion of 1/4 in n
11.646 * [backup-simplify]: Simplify 1/4 into 1/4
11.646 * [taylor]: Taking taylor expansion of (- 1 k) in n
11.646 * [taylor]: Taking taylor expansion of 1 in n
11.646 * [backup-simplify]: Simplify 1 into 1
11.646 * [taylor]: Taking taylor expansion of k in n
11.646 * [backup-simplify]: Simplify k into k
11.646 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
11.646 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
11.646 * [taylor]: Taking taylor expansion of 2 in n
11.646 * [backup-simplify]: Simplify 2 into 2
11.646 * [taylor]: Taking taylor expansion of (* n PI) in n
11.646 * [taylor]: Taking taylor expansion of n in n
11.646 * [backup-simplify]: Simplify 0 into 0
11.646 * [backup-simplify]: Simplify 1 into 1
11.646 * [taylor]: Taking taylor expansion of PI in n
11.646 * [backup-simplify]: Simplify PI into PI
11.647 * [backup-simplify]: Simplify (* 0 PI) into 0
11.647 * [backup-simplify]: Simplify (* 2 0) into 0
11.648 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.649 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
11.649 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.649 * [backup-simplify]: Simplify (- k) into (- k)
11.649 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
11.649 * [backup-simplify]: Simplify (* 1/4 (- 1 k)) into (* 1/4 (- 1 k))
11.650 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.651 * [backup-simplify]: Simplify (* (* 1/4 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
11.652 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
11.652 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
11.652 * [taylor]: Taking taylor expansion of (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
11.652 * [taylor]: Taking taylor expansion of 1/4 in k
11.652 * [backup-simplify]: Simplify 1/4 into 1/4
11.652 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
11.652 * [taylor]: Taking taylor expansion of (- 1 k) in k
11.652 * [taylor]: Taking taylor expansion of 1 in k
11.652 * [backup-simplify]: Simplify 1 into 1
11.652 * [taylor]: Taking taylor expansion of k in k
11.652 * [backup-simplify]: Simplify 0 into 0
11.652 * [backup-simplify]: Simplify 1 into 1
11.652 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
11.652 * [taylor]: Taking taylor expansion of (log n) in k
11.652 * [taylor]: Taking taylor expansion of n in k
11.652 * [backup-simplify]: Simplify n into n
11.652 * [backup-simplify]: Simplify (log n) into (log n)
11.652 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
11.652 * [taylor]: Taking taylor expansion of (* 2 PI) in k
11.652 * [taylor]: Taking taylor expansion of 2 in k
11.652 * [backup-simplify]: Simplify 2 into 2
11.652 * [taylor]: Taking taylor expansion of PI in k
11.652 * [backup-simplify]: Simplify PI into PI
11.652 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.653 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.653 * [backup-simplify]: Simplify (- 0) into 0
11.654 * [backup-simplify]: Simplify (+ 1 0) into 1
11.654 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.655 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
11.656 * [backup-simplify]: Simplify (* 1/4 (+ (log n) (log (* 2 PI)))) into (* 1/4 (+ (log n) (log (* 2 PI))))
11.656 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
11.657 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
11.657 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.658 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
11.659 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
11.659 * [backup-simplify]: Simplify (- 0) into 0
11.660 * [backup-simplify]: Simplify (+ 0 0) into 0
11.660 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- 1 k))) into 0
11.661 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.661 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
11.663 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.663 * [taylor]: Taking taylor expansion of 0 in k
11.663 * [backup-simplify]: Simplify 0 into 0
11.663 * [backup-simplify]: Simplify 0 into 0
11.664 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
11.665 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
11.666 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
11.667 * [backup-simplify]: Simplify (+ 0 0) into 0
11.667 * [backup-simplify]: Simplify (- 1) into -1
11.668 * [backup-simplify]: Simplify (+ 0 -1) into -1
11.669 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
11.671 * [backup-simplify]: Simplify (+ (* 1/4 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))))
11.674 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
11.677 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
11.678 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
11.679 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
11.688 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
11.689 * [backup-simplify]: Simplify (- 0) into 0
11.689 * [backup-simplify]: Simplify (+ 0 0) into 0
11.690 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
11.692 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.693 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
11.695 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.695 * [taylor]: Taking taylor expansion of 0 in k
11.695 * [backup-simplify]: Simplify 0 into 0
11.695 * [backup-simplify]: Simplify 0 into 0
11.695 * [backup-simplify]: Simplify 0 into 0
11.696 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
11.697 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
11.698 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
11.699 * [backup-simplify]: Simplify (+ 0 0) into 0
11.699 * [backup-simplify]: Simplify (- 0) into 0
11.699 * [backup-simplify]: Simplify (+ 0 0) into 0
11.700 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
11.702 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
11.704 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
11.707 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
11.713 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
11.713 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (/ (- 1 (/ 1 k)) 2) 2)) into (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k))))
11.713 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in (n k) around 0
11.713 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in k
11.713 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
11.713 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
11.713 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in k
11.713 * [taylor]: Taking taylor expansion of 1/4 in k
11.713 * [backup-simplify]: Simplify 1/4 into 1/4
11.713 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
11.713 * [taylor]: Taking taylor expansion of 1 in k
11.713 * [backup-simplify]: Simplify 1 into 1
11.713 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.713 * [taylor]: Taking taylor expansion of k in k
11.713 * [backup-simplify]: Simplify 0 into 0
11.713 * [backup-simplify]: Simplify 1 into 1
11.714 * [backup-simplify]: Simplify (/ 1 1) into 1
11.714 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
11.714 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
11.714 * [taylor]: Taking taylor expansion of 2 in k
11.714 * [backup-simplify]: Simplify 2 into 2
11.714 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.714 * [taylor]: Taking taylor expansion of PI in k
11.714 * [backup-simplify]: Simplify PI into PI
11.714 * [taylor]: Taking taylor expansion of n in k
11.714 * [backup-simplify]: Simplify n into n
11.714 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.714 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
11.714 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
11.714 * [backup-simplify]: Simplify (- 1) into -1
11.715 * [backup-simplify]: Simplify (+ 0 -1) into -1
11.715 * [backup-simplify]: Simplify (* 1/4 -1) into -1/4
11.715 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
11.715 * [backup-simplify]: Simplify (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
11.715 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in n
11.715 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
11.715 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
11.715 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in n
11.715 * [taylor]: Taking taylor expansion of 1/4 in n
11.715 * [backup-simplify]: Simplify 1/4 into 1/4
11.715 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
11.715 * [taylor]: Taking taylor expansion of 1 in n
11.715 * [backup-simplify]: Simplify 1 into 1
11.715 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.715 * [taylor]: Taking taylor expansion of k in n
11.715 * [backup-simplify]: Simplify k into k
11.715 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.715 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
11.715 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
11.715 * [taylor]: Taking taylor expansion of 2 in n
11.715 * [backup-simplify]: Simplify 2 into 2
11.715 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.715 * [taylor]: Taking taylor expansion of PI in n
11.715 * [backup-simplify]: Simplify PI into PI
11.715 * [taylor]: Taking taylor expansion of n in n
11.715 * [backup-simplify]: Simplify 0 into 0
11.715 * [backup-simplify]: Simplify 1 into 1
11.716 * [backup-simplify]: Simplify (/ PI 1) into PI
11.716 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.717 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.717 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
11.717 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
11.717 * [backup-simplify]: Simplify (* 1/4 (- 1 (/ 1 k))) into (* 1/4 (- 1 (/ 1 k)))
11.718 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.718 * [backup-simplify]: Simplify (* (* 1/4 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
11.719 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
11.719 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in n
11.719 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
11.719 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
11.719 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in n
11.719 * [taylor]: Taking taylor expansion of 1/4 in n
11.719 * [backup-simplify]: Simplify 1/4 into 1/4
11.719 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
11.719 * [taylor]: Taking taylor expansion of 1 in n
11.719 * [backup-simplify]: Simplify 1 into 1
11.719 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.719 * [taylor]: Taking taylor expansion of k in n
11.719 * [backup-simplify]: Simplify k into k
11.719 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.719 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
11.719 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
11.719 * [taylor]: Taking taylor expansion of 2 in n
11.719 * [backup-simplify]: Simplify 2 into 2
11.719 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.719 * [taylor]: Taking taylor expansion of PI in n
11.719 * [backup-simplify]: Simplify PI into PI
11.719 * [taylor]: Taking taylor expansion of n in n
11.719 * [backup-simplify]: Simplify 0 into 0
11.719 * [backup-simplify]: Simplify 1 into 1
11.720 * [backup-simplify]: Simplify (/ PI 1) into PI
11.720 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.721 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.721 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
11.721 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
11.721 * [backup-simplify]: Simplify (* 1/4 (- 1 (/ 1 k))) into (* 1/4 (- 1 (/ 1 k)))
11.722 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.722 * [backup-simplify]: Simplify (* (* 1/4 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
11.723 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
11.723 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
11.723 * [taylor]: Taking taylor expansion of (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
11.723 * [taylor]: Taking taylor expansion of 1/4 in k
11.723 * [backup-simplify]: Simplify 1/4 into 1/4
11.723 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
11.723 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
11.723 * [taylor]: Taking taylor expansion of 1 in k
11.723 * [backup-simplify]: Simplify 1 into 1
11.723 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.723 * [taylor]: Taking taylor expansion of k in k
11.723 * [backup-simplify]: Simplify 0 into 0
11.723 * [backup-simplify]: Simplify 1 into 1
11.724 * [backup-simplify]: Simplify (/ 1 1) into 1
11.724 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
11.724 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
11.724 * [taylor]: Taking taylor expansion of (* 2 PI) in k
11.724 * [taylor]: Taking taylor expansion of 2 in k
11.724 * [backup-simplify]: Simplify 2 into 2
11.724 * [taylor]: Taking taylor expansion of PI in k
11.724 * [backup-simplify]: Simplify PI into PI
11.724 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.725 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.725 * [taylor]: Taking taylor expansion of (log n) in k
11.725 * [taylor]: Taking taylor expansion of n in k
11.725 * [backup-simplify]: Simplify n into n
11.725 * [backup-simplify]: Simplify (log n) into (log n)
11.725 * [backup-simplify]: Simplify (- 1) into -1
11.725 * [backup-simplify]: Simplify (+ 0 -1) into -1
11.725 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
11.726 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
11.726 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
11.727 * [backup-simplify]: Simplify (* 1/4 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
11.728 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
11.728 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
11.729 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.730 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
11.730 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
11.731 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.731 * [backup-simplify]: Simplify (- 0) into 0
11.731 * [backup-simplify]: Simplify (+ 0 0) into 0
11.731 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- 1 (/ 1 k)))) into 0
11.732 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.733 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
11.734 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.734 * [taylor]: Taking taylor expansion of 0 in k
11.734 * [backup-simplify]: Simplify 0 into 0
11.734 * [backup-simplify]: Simplify 0 into 0
11.734 * [backup-simplify]: Simplify 0 into 0
11.736 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.737 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
11.740 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
11.741 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.741 * [backup-simplify]: Simplify (- 0) into 0
11.741 * [backup-simplify]: Simplify (+ 0 0) into 0
11.742 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
11.744 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.746 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
11.748 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.748 * [taylor]: Taking taylor expansion of 0 in k
11.748 * [backup-simplify]: Simplify 0 into 0
11.748 * [backup-simplify]: Simplify 0 into 0
11.748 * [backup-simplify]: Simplify 0 into 0
11.748 * [backup-simplify]: Simplify 0 into 0
11.749 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.751 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.757 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
11.757 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.758 * [backup-simplify]: Simplify (- 0) into 0
11.758 * [backup-simplify]: Simplify (+ 0 0) into 0
11.759 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
11.761 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.763 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
11.765 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
11.766 * [taylor]: Taking taylor expansion of 0 in k
11.766 * [backup-simplify]: Simplify 0 into 0
11.766 * [backup-simplify]: Simplify 0 into 0
11.767 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
11.768 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (/ (- 1 (/ 1 (- k))) 2) 2)) into (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1)))
11.768 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in (n k) around 0
11.768 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in k
11.768 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
11.768 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
11.768 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in k
11.768 * [taylor]: Taking taylor expansion of 1/4 in k
11.768 * [backup-simplify]: Simplify 1/4 into 1/4
11.768 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
11.768 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.768 * [taylor]: Taking taylor expansion of k in k
11.768 * [backup-simplify]: Simplify 0 into 0
11.768 * [backup-simplify]: Simplify 1 into 1
11.768 * [backup-simplify]: Simplify (/ 1 1) into 1
11.768 * [taylor]: Taking taylor expansion of 1 in k
11.768 * [backup-simplify]: Simplify 1 into 1
11.768 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
11.768 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
11.768 * [taylor]: Taking taylor expansion of -2 in k
11.768 * [backup-simplify]: Simplify -2 into -2
11.769 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.769 * [taylor]: Taking taylor expansion of PI in k
11.769 * [backup-simplify]: Simplify PI into PI
11.769 * [taylor]: Taking taylor expansion of n in k
11.769 * [backup-simplify]: Simplify n into n
11.769 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.769 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
11.769 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
11.769 * [backup-simplify]: Simplify (+ 1 0) into 1
11.770 * [backup-simplify]: Simplify (* 1/4 1) into 1/4
11.770 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
11.770 * [backup-simplify]: Simplify (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/4 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
11.770 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in n
11.770 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
11.770 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
11.770 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in n
11.770 * [taylor]: Taking taylor expansion of 1/4 in n
11.770 * [backup-simplify]: Simplify 1/4 into 1/4
11.770 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
11.770 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.770 * [taylor]: Taking taylor expansion of k in n
11.770 * [backup-simplify]: Simplify k into k
11.770 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.770 * [taylor]: Taking taylor expansion of 1 in n
11.771 * [backup-simplify]: Simplify 1 into 1
11.771 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
11.771 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
11.771 * [taylor]: Taking taylor expansion of -2 in n
11.771 * [backup-simplify]: Simplify -2 into -2
11.771 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.771 * [taylor]: Taking taylor expansion of PI in n
11.771 * [backup-simplify]: Simplify PI into PI
11.771 * [taylor]: Taking taylor expansion of n in n
11.771 * [backup-simplify]: Simplify 0 into 0
11.771 * [backup-simplify]: Simplify 1 into 1
11.771 * [backup-simplify]: Simplify (/ PI 1) into PI
11.772 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
11.773 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
11.773 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
11.773 * [backup-simplify]: Simplify (* 1/4 (+ (/ 1 k) 1)) into (* 1/4 (+ (/ 1 k) 1))
11.774 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.775 * [backup-simplify]: Simplify (* (* 1/4 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
11.777 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
11.777 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in n
11.777 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
11.777 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
11.777 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in n
11.777 * [taylor]: Taking taylor expansion of 1/4 in n
11.777 * [backup-simplify]: Simplify 1/4 into 1/4
11.777 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
11.777 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.777 * [taylor]: Taking taylor expansion of k in n
11.777 * [backup-simplify]: Simplify k into k
11.777 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.777 * [taylor]: Taking taylor expansion of 1 in n
11.777 * [backup-simplify]: Simplify 1 into 1
11.777 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
11.777 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
11.777 * [taylor]: Taking taylor expansion of -2 in n
11.777 * [backup-simplify]: Simplify -2 into -2
11.777 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.777 * [taylor]: Taking taylor expansion of PI in n
11.777 * [backup-simplify]: Simplify PI into PI
11.777 * [taylor]: Taking taylor expansion of n in n
11.777 * [backup-simplify]: Simplify 0 into 0
11.777 * [backup-simplify]: Simplify 1 into 1
11.778 * [backup-simplify]: Simplify (/ PI 1) into PI
11.778 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
11.779 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
11.779 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
11.779 * [backup-simplify]: Simplify (* 1/4 (+ (/ 1 k) 1)) into (* 1/4 (+ (/ 1 k) 1))
11.781 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.782 * [backup-simplify]: Simplify (* (* 1/4 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
11.783 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
11.783 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
11.783 * [taylor]: Taking taylor expansion of (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
11.783 * [taylor]: Taking taylor expansion of 1/4 in k
11.783 * [backup-simplify]: Simplify 1/4 into 1/4
11.783 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
11.783 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
11.783 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.783 * [taylor]: Taking taylor expansion of k in k
11.783 * [backup-simplify]: Simplify 0 into 0
11.783 * [backup-simplify]: Simplify 1 into 1
11.784 * [backup-simplify]: Simplify (/ 1 1) into 1
11.784 * [taylor]: Taking taylor expansion of 1 in k
11.784 * [backup-simplify]: Simplify 1 into 1
11.784 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
11.784 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
11.784 * [taylor]: Taking taylor expansion of (* -2 PI) in k
11.784 * [taylor]: Taking taylor expansion of -2 in k
11.784 * [backup-simplify]: Simplify -2 into -2
11.784 * [taylor]: Taking taylor expansion of PI in k
11.784 * [backup-simplify]: Simplify PI into PI
11.785 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
11.786 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
11.786 * [taylor]: Taking taylor expansion of (log n) in k
11.786 * [taylor]: Taking taylor expansion of n in k
11.786 * [backup-simplify]: Simplify n into n
11.786 * [backup-simplify]: Simplify (log n) into (log n)
11.786 * [backup-simplify]: Simplify (+ 1 0) into 1
11.786 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
11.787 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
11.788 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
11.789 * [backup-simplify]: Simplify (* 1/4 (- (log (* -2 PI)) (log n))) into (* 1/4 (- (log (* -2 PI)) (log n)))
11.791 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
11.792 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
11.793 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.794 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
11.795 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
11.796 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.796 * [backup-simplify]: Simplify (+ 0 0) into 0
11.797 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (+ (/ 1 k) 1))) into 0
11.798 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.799 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
11.801 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.801 * [taylor]: Taking taylor expansion of 0 in k
11.801 * [backup-simplify]: Simplify 0 into 0
11.801 * [backup-simplify]: Simplify 0 into 0
11.801 * [backup-simplify]: Simplify 0 into 0
11.802 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.809 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
11.813 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
11.814 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.814 * [backup-simplify]: Simplify (+ 0 0) into 0
11.815 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
11.816 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.817 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
11.818 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.818 * [taylor]: Taking taylor expansion of 0 in k
11.818 * [backup-simplify]: Simplify 0 into 0
11.818 * [backup-simplify]: Simplify 0 into 0
11.818 * [backup-simplify]: Simplify 0 into 0
11.818 * [backup-simplify]: Simplify 0 into 0
11.819 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.820 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.823 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
11.823 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.823 * [backup-simplify]: Simplify (+ 0 0) into 0
11.824 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
11.825 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.826 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
11.828 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
11.828 * [taylor]: Taking taylor expansion of 0 in k
11.828 * [backup-simplify]: Simplify 0 into 0
11.828 * [backup-simplify]: Simplify 0 into 0
11.829 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
11.829 * * * * [progress]: [ 3 / 4 ] generating series at (2 1)
11.830 * [backup-simplify]: Simplify (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) into (pow (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) 2)
11.830 * [approximate]: Taking taylor expansion of (pow (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) 2) in (n k) around 0
11.830 * [taylor]: Taking taylor expansion of (pow (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) 2) in k
11.830 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in k
11.830 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in k
11.830 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in k
11.830 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in k
11.830 * [taylor]: Taking taylor expansion of 1/4 in k
11.830 * [backup-simplify]: Simplify 1/4 into 1/4
11.830 * [taylor]: Taking taylor expansion of (- 1 k) in k
11.830 * [taylor]: Taking taylor expansion of 1 in k
11.830 * [backup-simplify]: Simplify 1 into 1
11.830 * [taylor]: Taking taylor expansion of k in k
11.830 * [backup-simplify]: Simplify 0 into 0
11.830 * [backup-simplify]: Simplify 1 into 1
11.830 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
11.830 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
11.830 * [taylor]: Taking taylor expansion of 2 in k
11.830 * [backup-simplify]: Simplify 2 into 2
11.830 * [taylor]: Taking taylor expansion of (* n PI) in k
11.830 * [taylor]: Taking taylor expansion of n in k
11.830 * [backup-simplify]: Simplify n into n
11.830 * [taylor]: Taking taylor expansion of PI in k
11.830 * [backup-simplify]: Simplify PI into PI
11.830 * [backup-simplify]: Simplify (* n PI) into (* n PI)
11.830 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
11.830 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
11.830 * [backup-simplify]: Simplify (- 0) into 0
11.831 * [backup-simplify]: Simplify (+ 1 0) into 1
11.831 * [backup-simplify]: Simplify (* 1/4 1) into 1/4
11.831 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
11.831 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
11.831 * [taylor]: Taking taylor expansion of (pow (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) 2) in n
11.831 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in n
11.831 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in n
11.831 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in n
11.831 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in n
11.831 * [taylor]: Taking taylor expansion of 1/4 in n
11.831 * [backup-simplify]: Simplify 1/4 into 1/4
11.831 * [taylor]: Taking taylor expansion of (- 1 k) in n
11.831 * [taylor]: Taking taylor expansion of 1 in n
11.831 * [backup-simplify]: Simplify 1 into 1
11.831 * [taylor]: Taking taylor expansion of k in n
11.831 * [backup-simplify]: Simplify k into k
11.831 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
11.831 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
11.831 * [taylor]: Taking taylor expansion of 2 in n
11.831 * [backup-simplify]: Simplify 2 into 2
11.831 * [taylor]: Taking taylor expansion of (* n PI) in n
11.831 * [taylor]: Taking taylor expansion of n in n
11.831 * [backup-simplify]: Simplify 0 into 0
11.831 * [backup-simplify]: Simplify 1 into 1
11.831 * [taylor]: Taking taylor expansion of PI in n
11.831 * [backup-simplify]: Simplify PI into PI
11.832 * [backup-simplify]: Simplify (* 0 PI) into 0
11.832 * [backup-simplify]: Simplify (* 2 0) into 0
11.833 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.834 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
11.834 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.835 * [backup-simplify]: Simplify (- k) into (- k)
11.835 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
11.835 * [backup-simplify]: Simplify (* 1/4 (- 1 k)) into (* 1/4 (- 1 k))
11.835 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.836 * [backup-simplify]: Simplify (* (* 1/4 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
11.837 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
11.837 * [taylor]: Taking taylor expansion of (pow (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) 2) in n
11.837 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/4 (- 1 k))) in n
11.837 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 k)) (log (* 2 (* n PI))))) in n
11.837 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 k)) (log (* 2 (* n PI)))) in n
11.837 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 k)) in n
11.837 * [taylor]: Taking taylor expansion of 1/4 in n
11.837 * [backup-simplify]: Simplify 1/4 into 1/4
11.837 * [taylor]: Taking taylor expansion of (- 1 k) in n
11.837 * [taylor]: Taking taylor expansion of 1 in n
11.837 * [backup-simplify]: Simplify 1 into 1
11.837 * [taylor]: Taking taylor expansion of k in n
11.837 * [backup-simplify]: Simplify k into k
11.837 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
11.837 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
11.837 * [taylor]: Taking taylor expansion of 2 in n
11.837 * [backup-simplify]: Simplify 2 into 2
11.837 * [taylor]: Taking taylor expansion of (* n PI) in n
11.837 * [taylor]: Taking taylor expansion of n in n
11.837 * [backup-simplify]: Simplify 0 into 0
11.837 * [backup-simplify]: Simplify 1 into 1
11.837 * [taylor]: Taking taylor expansion of PI in n
11.837 * [backup-simplify]: Simplify PI into PI
11.837 * [backup-simplify]: Simplify (* 0 PI) into 0
11.838 * [backup-simplify]: Simplify (* 2 0) into 0
11.839 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.840 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
11.840 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.840 * [backup-simplify]: Simplify (- k) into (- k)
11.840 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
11.840 * [backup-simplify]: Simplify (* 1/4 (- 1 k)) into (* 1/4 (- 1 k))
11.841 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.842 * [backup-simplify]: Simplify (* (* 1/4 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
11.843 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
11.844 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))) into (pow (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 2)
11.844 * [taylor]: Taking taylor expansion of (pow (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 2) in k
11.844 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
11.844 * [taylor]: Taking taylor expansion of (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
11.844 * [taylor]: Taking taylor expansion of 1/4 in k
11.844 * [backup-simplify]: Simplify 1/4 into 1/4
11.844 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
11.844 * [taylor]: Taking taylor expansion of (- 1 k) in k
11.844 * [taylor]: Taking taylor expansion of 1 in k
11.844 * [backup-simplify]: Simplify 1 into 1
11.844 * [taylor]: Taking taylor expansion of k in k
11.844 * [backup-simplify]: Simplify 0 into 0
11.844 * [backup-simplify]: Simplify 1 into 1
11.844 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
11.844 * [taylor]: Taking taylor expansion of (log n) in k
11.844 * [taylor]: Taking taylor expansion of n in k
11.844 * [backup-simplify]: Simplify n into n
11.844 * [backup-simplify]: Simplify (log n) into (log n)
11.844 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
11.844 * [taylor]: Taking taylor expansion of (* 2 PI) in k
11.844 * [taylor]: Taking taylor expansion of 2 in k
11.844 * [backup-simplify]: Simplify 2 into 2
11.844 * [taylor]: Taking taylor expansion of PI in k
11.845 * [backup-simplify]: Simplify PI into PI
11.845 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.845 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.846 * [backup-simplify]: Simplify (- 0) into 0
11.846 * [backup-simplify]: Simplify (+ 1 0) into 1
11.847 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.848 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
11.849 * [backup-simplify]: Simplify (* 1/4 (+ (log n) (log (* 2 PI)))) into (* 1/4 (+ (log n) (log (* 2 PI))))
11.850 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
11.852 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) into (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2)
11.854 * [backup-simplify]: Simplify (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) into (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2)
11.855 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.856 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
11.858 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
11.858 * [backup-simplify]: Simplify (- 0) into 0
11.859 * [backup-simplify]: Simplify (+ 0 0) into 0
11.859 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- 1 k))) into 0
11.861 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.862 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
11.864 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.866 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (* 0 (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))))) into 0
11.866 * [taylor]: Taking taylor expansion of 0 in k
11.866 * [backup-simplify]: Simplify 0 into 0
11.866 * [backup-simplify]: Simplify 0 into 0
11.867 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
11.868 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
11.870 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
11.870 * [backup-simplify]: Simplify (+ 0 0) into 0
11.870 * [backup-simplify]: Simplify (- 1) into -1
11.871 * [backup-simplify]: Simplify (+ 0 -1) into -1
11.872 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
11.874 * [backup-simplify]: Simplify (+ (* 1/4 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))))
11.876 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
11.881 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log n))) (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log (* 2 PI))))))
11.883 * [backup-simplify]: Simplify (- (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log n))) (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log (* 2 PI)))))) into (- (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log n))) (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log (* 2 PI))))))
11.884 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
11.885 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
11.886 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
11.887 * [backup-simplify]: Simplify (- 0) into 0
11.887 * [backup-simplify]: Simplify (+ 0 0) into 0
11.888 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
11.889 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.889 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
11.891 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.892 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (* 0 (exp (* 1/4 (* (- 1 k) (+ (log n) (log (* 2 PI))))))))) into 0
11.892 * [taylor]: Taking taylor expansion of 0 in k
11.893 * [backup-simplify]: Simplify 0 into 0
11.893 * [backup-simplify]: Simplify 0 into 0
11.893 * [backup-simplify]: Simplify 0 into 0
11.894 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
11.894 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
11.896 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
11.896 * [backup-simplify]: Simplify (+ 0 0) into 0
11.897 * [backup-simplify]: Simplify (- 0) into 0
11.897 * [backup-simplify]: Simplify (+ 0 0) into 0
11.898 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
11.899 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
11.902 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
11.924 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))) (+ (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) into (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log n) 2))) (+ (* 1/4 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI))))) (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2)))))
11.927 * [backup-simplify]: Simplify (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log n) 2))) (+ (* 1/4 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI))))) (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2))))) into (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log n) 2))) (+ (* 1/4 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI))))) (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2)))))
11.935 * [backup-simplify]: Simplify (+ (* (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log n) 2))) (+ (* 1/4 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI))))) (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (- (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log n))) (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (log (* 2 PI)))))) (* k 1)) (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2))) into (- (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/4 (* (pow k 2) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI)))))) (+ (* 1/8 (* (pow k 2) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2)))) (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2)))) (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) k)))))
11.936 * [backup-simplify]: Simplify (* (pow (* (/ 1 n) (* 2 PI)) (/ (/ (- 1 (/ 1 k)) 2) 2)) (pow (* (/ 1 n) (* 2 PI)) (/ (/ (- 1 (/ 1 k)) 2) 2))) into (pow (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) 2)
11.936 * [approximate]: Taking taylor expansion of (pow (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) 2) in (n k) around 0
11.936 * [taylor]: Taking taylor expansion of (pow (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) 2) in k
11.936 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in k
11.936 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
11.936 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
11.936 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in k
11.936 * [taylor]: Taking taylor expansion of 1/4 in k
11.936 * [backup-simplify]: Simplify 1/4 into 1/4
11.936 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
11.936 * [taylor]: Taking taylor expansion of 1 in k
11.936 * [backup-simplify]: Simplify 1 into 1
11.936 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.936 * [taylor]: Taking taylor expansion of k in k
11.936 * [backup-simplify]: Simplify 0 into 0
11.936 * [backup-simplify]: Simplify 1 into 1
11.936 * [backup-simplify]: Simplify (/ 1 1) into 1
11.936 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
11.936 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
11.936 * [taylor]: Taking taylor expansion of 2 in k
11.936 * [backup-simplify]: Simplify 2 into 2
11.936 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.936 * [taylor]: Taking taylor expansion of PI in k
11.936 * [backup-simplify]: Simplify PI into PI
11.936 * [taylor]: Taking taylor expansion of n in k
11.936 * [backup-simplify]: Simplify n into n
11.936 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.936 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
11.936 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
11.937 * [backup-simplify]: Simplify (- 1) into -1
11.937 * [backup-simplify]: Simplify (+ 0 -1) into -1
11.937 * [backup-simplify]: Simplify (* 1/4 -1) into -1/4
11.937 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
11.938 * [backup-simplify]: Simplify (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
11.938 * [taylor]: Taking taylor expansion of (pow (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) 2) in n
11.938 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in n
11.938 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
11.938 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
11.938 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in n
11.938 * [taylor]: Taking taylor expansion of 1/4 in n
11.938 * [backup-simplify]: Simplify 1/4 into 1/4
11.938 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
11.938 * [taylor]: Taking taylor expansion of 1 in n
11.938 * [backup-simplify]: Simplify 1 into 1
11.938 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.938 * [taylor]: Taking taylor expansion of k in n
11.938 * [backup-simplify]: Simplify k into k
11.938 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.938 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
11.938 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
11.938 * [taylor]: Taking taylor expansion of 2 in n
11.938 * [backup-simplify]: Simplify 2 into 2
11.938 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.938 * [taylor]: Taking taylor expansion of PI in n
11.938 * [backup-simplify]: Simplify PI into PI
11.938 * [taylor]: Taking taylor expansion of n in n
11.938 * [backup-simplify]: Simplify 0 into 0
11.938 * [backup-simplify]: Simplify 1 into 1
11.939 * [backup-simplify]: Simplify (/ PI 1) into PI
11.939 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.940 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.940 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
11.940 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
11.940 * [backup-simplify]: Simplify (* 1/4 (- 1 (/ 1 k))) into (* 1/4 (- 1 (/ 1 k)))
11.941 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.941 * [backup-simplify]: Simplify (* (* 1/4 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
11.942 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
11.942 * [taylor]: Taking taylor expansion of (pow (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) 2) in n
11.942 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/4 (- 1 (/ 1 k)))) in n
11.942 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
11.942 * [taylor]: Taking taylor expansion of (* (* 1/4 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
11.942 * [taylor]: Taking taylor expansion of (* 1/4 (- 1 (/ 1 k))) in n
11.942 * [taylor]: Taking taylor expansion of 1/4 in n
11.942 * [backup-simplify]: Simplify 1/4 into 1/4
11.942 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
11.942 * [taylor]: Taking taylor expansion of 1 in n
11.942 * [backup-simplify]: Simplify 1 into 1
11.942 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.942 * [taylor]: Taking taylor expansion of k in n
11.942 * [backup-simplify]: Simplify k into k
11.942 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.942 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
11.942 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
11.942 * [taylor]: Taking taylor expansion of 2 in n
11.942 * [backup-simplify]: Simplify 2 into 2
11.942 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.942 * [taylor]: Taking taylor expansion of PI in n
11.942 * [backup-simplify]: Simplify PI into PI
11.942 * [taylor]: Taking taylor expansion of n in n
11.942 * [backup-simplify]: Simplify 0 into 0
11.942 * [backup-simplify]: Simplify 1 into 1
11.943 * [backup-simplify]: Simplify (/ PI 1) into PI
11.943 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.944 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.944 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
11.944 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
11.944 * [backup-simplify]: Simplify (* 1/4 (- 1 (/ 1 k))) into (* 1/4 (- 1 (/ 1 k)))
11.945 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.945 * [backup-simplify]: Simplify (* (* 1/4 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
11.946 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
11.948 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (pow (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 2)
11.948 * [taylor]: Taking taylor expansion of (pow (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 2) in k
11.948 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
11.948 * [taylor]: Taking taylor expansion of (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
11.948 * [taylor]: Taking taylor expansion of 1/4 in k
11.948 * [backup-simplify]: Simplify 1/4 into 1/4
11.948 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
11.948 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
11.948 * [taylor]: Taking taylor expansion of 1 in k
11.948 * [backup-simplify]: Simplify 1 into 1
11.948 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.948 * [taylor]: Taking taylor expansion of k in k
11.948 * [backup-simplify]: Simplify 0 into 0
11.948 * [backup-simplify]: Simplify 1 into 1
11.948 * [backup-simplify]: Simplify (/ 1 1) into 1
11.948 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
11.948 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
11.948 * [taylor]: Taking taylor expansion of (* 2 PI) in k
11.948 * [taylor]: Taking taylor expansion of 2 in k
11.948 * [backup-simplify]: Simplify 2 into 2
11.948 * [taylor]: Taking taylor expansion of PI in k
11.948 * [backup-simplify]: Simplify PI into PI
11.949 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.949 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.949 * [taylor]: Taking taylor expansion of (log n) in k
11.949 * [taylor]: Taking taylor expansion of n in k
11.949 * [backup-simplify]: Simplify n into n
11.949 * [backup-simplify]: Simplify (log n) into (log n)
11.950 * [backup-simplify]: Simplify (- 1) into -1
11.950 * [backup-simplify]: Simplify (+ 0 -1) into -1
11.950 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
11.951 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
11.952 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
11.953 * [backup-simplify]: Simplify (* 1/4 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
11.954 * [backup-simplify]: Simplify (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
11.957 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (pow (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 2)
11.958 * [backup-simplify]: Simplify (pow (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 2) into (pow (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 2)
11.959 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.960 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
11.961 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
11.962 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.962 * [backup-simplify]: Simplify (- 0) into 0
11.962 * [backup-simplify]: Simplify (+ 0 0) into 0
11.963 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- 1 (/ 1 k)))) into 0
11.964 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.966 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
11.967 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.973 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (* 0 (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
11.973 * [taylor]: Taking taylor expansion of 0 in k
11.973 * [backup-simplify]: Simplify 0 into 0
11.973 * [backup-simplify]: Simplify 0 into 0
11.976 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (* 0 (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
11.976 * [backup-simplify]: Simplify 0 into 0
11.977 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.978 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
11.982 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
11.982 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.983 * [backup-simplify]: Simplify (- 0) into 0
11.983 * [backup-simplify]: Simplify (+ 0 0) into 0
11.984 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
11.985 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.987 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
11.989 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.992 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into 0
11.992 * [taylor]: Taking taylor expansion of 0 in k
11.992 * [backup-simplify]: Simplify 0 into 0
11.992 * [backup-simplify]: Simplify 0 into 0
11.992 * [backup-simplify]: Simplify 0 into 0
11.995 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))) into 0
11.995 * [backup-simplify]: Simplify 0 into 0
11.996 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.998 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.004 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
12.004 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.005 * [backup-simplify]: Simplify (- 0) into 0
12.005 * [backup-simplify]: Simplify (+ 0 0) into 0
12.006 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
12.008 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.010 * [backup-simplify]: Simplify (+ (* (* 1/4 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
12.011 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
12.013 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/4 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))))) into 0
12.013 * [taylor]: Taking taylor expansion of 0 in k
12.013 * [backup-simplify]: Simplify 0 into 0
12.013 * [backup-simplify]: Simplify 0 into 0
12.014 * [backup-simplify]: Simplify (pow (exp (* 1/4 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) 2) into (pow (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 2)
12.015 * [backup-simplify]: Simplify (* (pow (* (/ 1 (- n)) (* 2 PI)) (/ (/ (- 1 (/ 1 (- k))) 2) 2)) (pow (* (/ 1 (- n)) (* 2 PI)) (/ (/ (- 1 (/ 1 (- k))) 2) 2))) into (pow (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) 2)
12.015 * [approximate]: Taking taylor expansion of (pow (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) 2) in (n k) around 0
12.015 * [taylor]: Taking taylor expansion of (pow (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) 2) in k
12.015 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in k
12.015 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
12.015 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
12.015 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in k
12.015 * [taylor]: Taking taylor expansion of 1/4 in k
12.015 * [backup-simplify]: Simplify 1/4 into 1/4
12.015 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
12.015 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.015 * [taylor]: Taking taylor expansion of k in k
12.015 * [backup-simplify]: Simplify 0 into 0
12.015 * [backup-simplify]: Simplify 1 into 1
12.015 * [backup-simplify]: Simplify (/ 1 1) into 1
12.015 * [taylor]: Taking taylor expansion of 1 in k
12.015 * [backup-simplify]: Simplify 1 into 1
12.015 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
12.015 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
12.016 * [taylor]: Taking taylor expansion of -2 in k
12.016 * [backup-simplify]: Simplify -2 into -2
12.016 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.016 * [taylor]: Taking taylor expansion of PI in k
12.016 * [backup-simplify]: Simplify PI into PI
12.016 * [taylor]: Taking taylor expansion of n in k
12.016 * [backup-simplify]: Simplify n into n
12.016 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.016 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
12.016 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
12.016 * [backup-simplify]: Simplify (+ 1 0) into 1
12.016 * [backup-simplify]: Simplify (* 1/4 1) into 1/4
12.016 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
12.016 * [backup-simplify]: Simplify (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/4 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
12.016 * [taylor]: Taking taylor expansion of (pow (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) 2) in n
12.017 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in n
12.017 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
12.017 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
12.017 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in n
12.017 * [taylor]: Taking taylor expansion of 1/4 in n
12.017 * [backup-simplify]: Simplify 1/4 into 1/4
12.017 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
12.017 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.017 * [taylor]: Taking taylor expansion of k in n
12.017 * [backup-simplify]: Simplify k into k
12.017 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.017 * [taylor]: Taking taylor expansion of 1 in n
12.017 * [backup-simplify]: Simplify 1 into 1
12.017 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.017 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.017 * [taylor]: Taking taylor expansion of -2 in n
12.017 * [backup-simplify]: Simplify -2 into -2
12.017 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.017 * [taylor]: Taking taylor expansion of PI in n
12.017 * [backup-simplify]: Simplify PI into PI
12.017 * [taylor]: Taking taylor expansion of n in n
12.017 * [backup-simplify]: Simplify 0 into 0
12.017 * [backup-simplify]: Simplify 1 into 1
12.017 * [backup-simplify]: Simplify (/ PI 1) into PI
12.017 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.018 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.018 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
12.018 * [backup-simplify]: Simplify (* 1/4 (+ (/ 1 k) 1)) into (* 1/4 (+ (/ 1 k) 1))
12.019 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.020 * [backup-simplify]: Simplify (* (* 1/4 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
12.020 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
12.020 * [taylor]: Taking taylor expansion of (pow (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) 2) in n
12.020 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/4 (+ (/ 1 k) 1))) in n
12.020 * [taylor]: Taking taylor expansion of (exp (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
12.020 * [taylor]: Taking taylor expansion of (* (* 1/4 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
12.020 * [taylor]: Taking taylor expansion of (* 1/4 (+ (/ 1 k) 1)) in n
12.021 * [taylor]: Taking taylor expansion of 1/4 in n
12.021 * [backup-simplify]: Simplify 1/4 into 1/4
12.021 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
12.021 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.021 * [taylor]: Taking taylor expansion of k in n
12.021 * [backup-simplify]: Simplify k into k
12.021 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.021 * [taylor]: Taking taylor expansion of 1 in n
12.021 * [backup-simplify]: Simplify 1 into 1
12.021 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.021 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.021 * [taylor]: Taking taylor expansion of -2 in n
12.021 * [backup-simplify]: Simplify -2 into -2
12.021 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.021 * [taylor]: Taking taylor expansion of PI in n
12.021 * [backup-simplify]: Simplify PI into PI
12.021 * [taylor]: Taking taylor expansion of n in n
12.021 * [backup-simplify]: Simplify 0 into 0
12.021 * [backup-simplify]: Simplify 1 into 1
12.021 * [backup-simplify]: Simplify (/ PI 1) into PI
12.021 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.022 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.022 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
12.022 * [backup-simplify]: Simplify (* 1/4 (+ (/ 1 k) 1)) into (* 1/4 (+ (/ 1 k) 1))
12.023 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.024 * [backup-simplify]: Simplify (* (* 1/4 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
12.025 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
12.031 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (pow (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 2)
12.031 * [taylor]: Taking taylor expansion of (pow (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 2) in k
12.031 * [taylor]: Taking taylor expansion of (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
12.031 * [taylor]: Taking taylor expansion of (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
12.031 * [taylor]: Taking taylor expansion of 1/4 in k
12.031 * [backup-simplify]: Simplify 1/4 into 1/4
12.031 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
12.031 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
12.031 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.031 * [taylor]: Taking taylor expansion of k in k
12.031 * [backup-simplify]: Simplify 0 into 0
12.031 * [backup-simplify]: Simplify 1 into 1
12.031 * [backup-simplify]: Simplify (/ 1 1) into 1
12.031 * [taylor]: Taking taylor expansion of 1 in k
12.031 * [backup-simplify]: Simplify 1 into 1
12.031 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
12.031 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
12.031 * [taylor]: Taking taylor expansion of (* -2 PI) in k
12.031 * [taylor]: Taking taylor expansion of -2 in k
12.031 * [backup-simplify]: Simplify -2 into -2
12.031 * [taylor]: Taking taylor expansion of PI in k
12.031 * [backup-simplify]: Simplify PI into PI
12.032 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.032 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.032 * [taylor]: Taking taylor expansion of (log n) in k
12.032 * [taylor]: Taking taylor expansion of n in k
12.033 * [backup-simplify]: Simplify n into n
12.033 * [backup-simplify]: Simplify (log n) into (log n)
12.033 * [backup-simplify]: Simplify (+ 1 0) into 1
12.033 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.033 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
12.034 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
12.035 * [backup-simplify]: Simplify (* 1/4 (- (log (* -2 PI)) (log n))) into (* 1/4 (- (log (* -2 PI)) (log n)))
12.036 * [backup-simplify]: Simplify (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
12.037 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (pow (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 2)
12.038 * [backup-simplify]: Simplify (pow (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 2) into (pow (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 2)
12.038 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.039 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
12.040 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
12.040 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.040 * [backup-simplify]: Simplify (+ 0 0) into 0
12.041 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (+ (/ 1 k) 1))) into 0
12.041 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.042 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
12.044 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.047 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 0) (* 0 (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0
12.047 * [taylor]: Taking taylor expansion of 0 in k
12.047 * [backup-simplify]: Simplify 0 into 0
12.047 * [backup-simplify]: Simplify 0 into 0
12.049 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 0) (* 0 (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0
12.049 * [backup-simplify]: Simplify 0 into 0
12.050 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.051 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
12.054 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
12.055 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.055 * [backup-simplify]: Simplify (+ 0 0) into 0
12.056 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
12.056 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.057 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
12.059 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.061 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))) into 0
12.061 * [taylor]: Taking taylor expansion of 0 in k
12.061 * [backup-simplify]: Simplify 0 into 0
12.061 * [backup-simplify]: Simplify 0 into 0
12.061 * [backup-simplify]: Simplify 0 into 0
12.062 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))) into 0
12.062 * [backup-simplify]: Simplify 0 into 0
12.063 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.064 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.067 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
12.067 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.067 * [backup-simplify]: Simplify (+ 0 0) into 0
12.068 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
12.069 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.070 * [backup-simplify]: Simplify (+ (* (* 1/4 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
12.072 * [backup-simplify]: Simplify (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
12.074 * [backup-simplify]: Simplify (+ (* (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 1/4 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))))) into 0
12.074 * [taylor]: Taking taylor expansion of 0 in k
12.074 * [backup-simplify]: Simplify 0 into 0
12.074 * [backup-simplify]: Simplify 0 into 0
12.075 * [backup-simplify]: Simplify (pow (exp (* 1/4 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) 2) into (pow (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 2)
12.075 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 2 1)
12.075 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
12.075 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
12.075 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.075 * [taylor]: Taking taylor expansion of 2 in n
12.075 * [backup-simplify]: Simplify 2 into 2
12.075 * [taylor]: Taking taylor expansion of (* n PI) in n
12.075 * [taylor]: Taking taylor expansion of n in n
12.075 * [backup-simplify]: Simplify 0 into 0
12.075 * [backup-simplify]: Simplify 1 into 1
12.075 * [taylor]: Taking taylor expansion of PI in n
12.075 * [backup-simplify]: Simplify PI into PI
12.075 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.075 * [taylor]: Taking taylor expansion of 2 in n
12.075 * [backup-simplify]: Simplify 2 into 2
12.075 * [taylor]: Taking taylor expansion of (* n PI) in n
12.075 * [taylor]: Taking taylor expansion of n in n
12.075 * [backup-simplify]: Simplify 0 into 0
12.075 * [backup-simplify]: Simplify 1 into 1
12.076 * [taylor]: Taking taylor expansion of PI in n
12.076 * [backup-simplify]: Simplify PI into PI
12.076 * [backup-simplify]: Simplify (* 0 PI) into 0
12.076 * [backup-simplify]: Simplify (* 2 0) into 0
12.076 * [backup-simplify]: Simplify 0 into 0
12.077 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.078 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.078 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.079 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.080 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
12.080 * [backup-simplify]: Simplify 0 into 0
12.080 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.081 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.081 * [backup-simplify]: Simplify 0 into 0
12.082 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.083 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
12.083 * [backup-simplify]: Simplify 0 into 0
12.084 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.084 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
12.084 * [backup-simplify]: Simplify 0 into 0
12.085 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.087 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
12.087 * [backup-simplify]: Simplify 0 into 0
12.089 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
12.091 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
12.091 * [backup-simplify]: Simplify 0 into 0
12.092 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
12.092 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
12.092 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
12.092 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.092 * [taylor]: Taking taylor expansion of 2 in n
12.092 * [backup-simplify]: Simplify 2 into 2
12.092 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.092 * [taylor]: Taking taylor expansion of PI in n
12.092 * [backup-simplify]: Simplify PI into PI
12.092 * [taylor]: Taking taylor expansion of n in n
12.092 * [backup-simplify]: Simplify 0 into 0
12.092 * [backup-simplify]: Simplify 1 into 1
12.093 * [backup-simplify]: Simplify (/ PI 1) into PI
12.093 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.093 * [taylor]: Taking taylor expansion of 2 in n
12.093 * [backup-simplify]: Simplify 2 into 2
12.093 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.093 * [taylor]: Taking taylor expansion of PI in n
12.093 * [backup-simplify]: Simplify PI into PI
12.093 * [taylor]: Taking taylor expansion of n in n
12.093 * [backup-simplify]: Simplify 0 into 0
12.093 * [backup-simplify]: Simplify 1 into 1
12.094 * [backup-simplify]: Simplify (/ PI 1) into PI
12.094 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.095 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.096 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.096 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.096 * [backup-simplify]: Simplify 0 into 0
12.098 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.098 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.098 * [backup-simplify]: Simplify 0 into 0
12.099 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.100 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.100 * [backup-simplify]: Simplify 0 into 0
12.100 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.101 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.101 * [backup-simplify]: Simplify 0 into 0
12.102 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.103 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.103 * [backup-simplify]: Simplify 0 into 0
12.103 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.104 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.104 * [backup-simplify]: Simplify 0 into 0
12.105 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
12.105 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
12.105 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
12.105 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.105 * [taylor]: Taking taylor expansion of -2 in n
12.105 * [backup-simplify]: Simplify -2 into -2
12.105 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.105 * [taylor]: Taking taylor expansion of PI in n
12.105 * [backup-simplify]: Simplify PI into PI
12.105 * [taylor]: Taking taylor expansion of n in n
12.105 * [backup-simplify]: Simplify 0 into 0
12.105 * [backup-simplify]: Simplify 1 into 1
12.105 * [backup-simplify]: Simplify (/ PI 1) into PI
12.106 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.106 * [taylor]: Taking taylor expansion of -2 in n
12.106 * [backup-simplify]: Simplify -2 into -2
12.106 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.106 * [taylor]: Taking taylor expansion of PI in n
12.106 * [backup-simplify]: Simplify PI into PI
12.106 * [taylor]: Taking taylor expansion of n in n
12.106 * [backup-simplify]: Simplify 0 into 0
12.106 * [backup-simplify]: Simplify 1 into 1
12.106 * [backup-simplify]: Simplify (/ PI 1) into PI
12.106 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.107 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.107 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.108 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
12.108 * [backup-simplify]: Simplify 0 into 0
12.108 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.109 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
12.109 * [backup-simplify]: Simplify 0 into 0
12.109 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.110 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.110 * [backup-simplify]: Simplify 0 into 0
12.111 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.112 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.112 * [backup-simplify]: Simplify 0 into 0
12.113 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.114 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.114 * [backup-simplify]: Simplify 0 into 0
12.114 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.115 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.115 * [backup-simplify]: Simplify 0 into 0
12.116 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
12.116 * * * [progress]: simplifying candidates
12.116 * * * * [progress]: [ 1 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (log1p (expm1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.116 * * * * [progress]: [ 2 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (expm1 (log1p (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.116 * * * * [progress]: [ 3 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.116 * * * * [progress]: [ 4 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (exp (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.116 * * * * [progress]: [ 5 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (exp (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.116 * * * * [progress]: [ 6 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (exp (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.116 * * * * [progress]: [ 7 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (* 1 (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.116 * * * * [progress]: [ 8 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (* 1 (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.116 * * * * [progress]: [ 9 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (* 1 (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.116 * * * * [progress]: [ 10 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ (pow (* n (* 2 PI)) (/ (/ 1 2) 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2)))) (sqrt k)))>
12.116 * * * * [progress]: [ 11 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (* (cbrt (/ (/ (- 1 k) 2) 2)) (cbrt (/ (/ (- 1 k) 2) 2)))) (cbrt (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.116 * * * * [progress]: [ 12 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (sqrt (/ (/ (- 1 k) 2) 2))) (sqrt (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.116 * * * * [progress]: [ 13 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (/ (- 1 k) 2)) (cbrt 2)))) (sqrt k)))>
12.116 * * * * [progress]: [ 14 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (sqrt 2))) (/ (cbrt (/ (- 1 k) 2)) (sqrt 2)))) (sqrt k)))>
12.116 * * * * [progress]: [ 15 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) 1)) (/ (cbrt (/ (- 1 k) 2)) 2))) (sqrt k)))>
12.116 * * * * [progress]: [ 16 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (/ (- 1 k) 2)) (cbrt 2)))) (sqrt k)))>
12.116 * * * * [progress]: [ 17 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2))) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2)))) (sqrt k)))>
12.117 * * * * [progress]: [ 18 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) 1)) (/ (sqrt (/ (- 1 k) 2)) 2))) (sqrt k)))>
12.117 * * * * [progress]: [ 19 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (cbrt (- 1 k)) (cbrt 2)) (cbrt 2)))) (sqrt k)))>
12.117 * * * * [progress]: [ 20 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (cbrt (- 1 k)) (cbrt 2)) (sqrt 2)))) (sqrt k)))>
12.117 * * * * [progress]: [ 21 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (cbrt (- 1 k)) (cbrt 2)) 2))) (sqrt k)))>
12.117 * * * * [progress]: [ 22 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (cbrt (- 1 k)) (sqrt 2)) (cbrt 2)))) (sqrt k)))>
12.117 * * * * [progress]: [ 23 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) (sqrt 2))) (/ (/ (cbrt (- 1 k)) (sqrt 2)) (sqrt 2)))) (sqrt k)))>
12.117 * * * * [progress]: [ 24 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) 1)) (/ (/ (cbrt (- 1 k)) (sqrt 2)) 2))) (sqrt k)))>
12.117 * * * * [progress]: [ 25 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (cbrt (- 1 k)) 2) (cbrt 2)))) (sqrt k)))>
12.117 * * * * [progress]: [ 26 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) (sqrt 2))) (/ (/ (cbrt (- 1 k)) 2) (sqrt 2)))) (sqrt k)))>
12.117 * * * * [progress]: [ 27 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) 1)) (/ (/ (cbrt (- 1 k)) 2) 2))) (sqrt k)))>
12.117 * * * * [progress]: [ 28 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))) (sqrt k)))>
12.117 * * * * [progress]: [ 29 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (sqrt 2)))) (sqrt k)))>
12.117 * * * * [progress]: [ 30 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (sqrt (- 1 k)) (cbrt 2)) 2))) (sqrt k)))>
12.117 * * * * [progress]: [ 31 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (cbrt 2)))) (sqrt k)))>
12.117 * * * * [progress]: [ 32 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (sqrt 2))) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (sqrt 2)))) (sqrt k)))>
12.117 * * * * [progress]: [ 33 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) 1)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) 2))) (sqrt k)))>
12.117 * * * * [progress]: [ 34 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (sqrt (- 1 k)) 2) (cbrt 2)))) (sqrt k)))>
12.117 * * * * [progress]: [ 35 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) (sqrt 2))) (/ (/ (sqrt (- 1 k)) 2) (sqrt 2)))) (sqrt k)))>
12.117 * * * * [progress]: [ 36 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) 1)) (/ (/ (sqrt (- 1 k)) 2) 2))) (sqrt k)))>
12.117 * * * * [progress]: [ 37 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (cbrt 2)) (cbrt 2)))) (sqrt k)))>
12.117 * * * * [progress]: [ 38 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- 1 k) (cbrt 2)) (sqrt 2)))) (sqrt k)))>
12.118 * * * * [progress]: [ 39 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- 1 k) (cbrt 2)) 2))) (sqrt k)))>
12.118 * * * * [progress]: [ 40 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (sqrt 2)) (cbrt 2)))) (sqrt k)))>
12.118 * * * * [progress]: [ 41 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (sqrt 2))) (/ (/ (- 1 k) (sqrt 2)) (sqrt 2)))) (sqrt k)))>
12.118 * * * * [progress]: [ 42 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) 1)) (/ (/ (- 1 k) (sqrt 2)) 2))) (sqrt k)))>
12.118 * * * * [progress]: [ 43 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) 2) (cbrt 2)))) (sqrt k)))>
12.118 * * * * [progress]: [ 44 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 1) (sqrt 2))) (/ (/ (- 1 k) 2) (sqrt 2)))) (sqrt k)))>
12.118 * * * * [progress]: [ 45 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 1) 1)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.118 * * * * [progress]: [ 46 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- (sqrt 1) (sqrt k)) (cbrt 2)) (cbrt 2)))) (sqrt k)))>
12.118 * * * * [progress]: [ 47 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- (sqrt 1) (sqrt k)) (cbrt 2)) (sqrt 2)))) (sqrt k)))>
12.118 * * * * [progress]: [ 48 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- (sqrt 1) (sqrt k)) (cbrt 2)) 2))) (sqrt k)))>
12.118 * * * * [progress]: [ 49 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- (sqrt 1) (sqrt k)) (sqrt 2)) (cbrt 2)))) (sqrt k)))>
12.118 * * * * [progress]: [ 50 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) (sqrt 2))) (/ (/ (- (sqrt 1) (sqrt k)) (sqrt 2)) (sqrt 2)))) (sqrt k)))>
12.118 * * * * [progress]: [ 51 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) 1)) (/ (/ (- (sqrt 1) (sqrt k)) (sqrt 2)) 2))) (sqrt k)))>
12.118 * * * * [progress]: [ 52 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- (sqrt 1) (sqrt k)) 2) (cbrt 2)))) (sqrt k)))>
12.118 * * * * [progress]: [ 53 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) (sqrt 2))) (/ (/ (- (sqrt 1) (sqrt k)) 2) (sqrt 2)))) (sqrt k)))>
12.118 * * * * [progress]: [ 54 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) 1)) (/ (/ (- (sqrt 1) (sqrt k)) 2) 2))) (sqrt k)))>
12.118 * * * * [progress]: [ 55 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 (sqrt k)) (cbrt 2)) (cbrt 2)))) (sqrt k)))>
12.118 * * * * [progress]: [ 56 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- 1 (sqrt k)) (cbrt 2)) (sqrt 2)))) (sqrt k)))>
12.118 * * * * [progress]: [ 57 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- 1 (sqrt k)) (cbrt 2)) 2))) (sqrt k)))>
12.118 * * * * [progress]: [ 58 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 (sqrt k)) (sqrt 2)) (cbrt 2)))) (sqrt k)))>
12.119 * * * * [progress]: [ 59 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) (sqrt 2))) (/ (/ (- 1 (sqrt k)) (sqrt 2)) (sqrt 2)))) (sqrt k)))>
12.119 * * * * [progress]: [ 60 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) 1)) (/ (/ (- 1 (sqrt k)) (sqrt 2)) 2))) (sqrt k)))>
12.119 * * * * [progress]: [ 61 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 (sqrt k)) 2) (cbrt 2)))) (sqrt k)))>
12.119 * * * * [progress]: [ 62 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) (sqrt 2))) (/ (/ (- 1 (sqrt k)) 2) (sqrt 2)))) (sqrt k)))>
12.119 * * * * [progress]: [ 63 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) 1)) (/ (/ (- 1 (sqrt k)) 2) 2))) (sqrt k)))>
12.119 * * * * [progress]: [ 64 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (cbrt 2)) (cbrt 2)))) (sqrt k)))>
12.119 * * * * [progress]: [ 65 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- 1 k) (cbrt 2)) (sqrt 2)))) (sqrt k)))>
12.119 * * * * [progress]: [ 66 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- 1 k) (cbrt 2)) 2))) (sqrt k)))>
12.119 * * * * [progress]: [ 67 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (sqrt 2)) (cbrt 2)))) (sqrt k)))>
12.119 * * * * [progress]: [ 68 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (sqrt 2))) (/ (/ (- 1 k) (sqrt 2)) (sqrt 2)))) (sqrt k)))>
12.119 * * * * [progress]: [ 69 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) 1)) (/ (/ (- 1 k) (sqrt 2)) 2))) (sqrt k)))>
12.119 * * * * [progress]: [ 70 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) 2) (cbrt 2)))) (sqrt k)))>
12.119 * * * * [progress]: [ 71 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 1) (sqrt 2))) (/ (/ (- 1 k) 2) (sqrt 2)))) (sqrt k)))>
12.119 * * * * [progress]: [ 72 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ 1 1) 1)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.119 * * * * [progress]: [ 73 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) 2) (cbrt 2)))) (sqrt k)))>
12.119 * * * * [progress]: [ 74 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (/ (- 1 k) 2) (sqrt 2)))) (sqrt k)))>
12.119 * * * * [progress]: [ 75 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.119 * * * * [progress]: [ 76 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (- 1 k) (* (cbrt 2) (cbrt 2)))) (/ (/ 1 2) (cbrt 2)))) (sqrt k)))>
12.119 * * * * [progress]: [ 77 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (- 1 k) (sqrt 2))) (/ (/ 1 2) (sqrt 2)))) (sqrt k)))>
12.119 * * * * [progress]: [ 78 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (- 1 k) 1)) (/ (/ 1 2) 2))) (sqrt k)))>
12.119 * * * * [progress]: [ 79 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) 1) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.119 * * * * [progress]: [ 80 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 2))) (sqrt k)))>
12.120 * * * * [progress]: [ 81 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (pow n (/ (/ (- 1 k) 2) 2)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.120 * * * * [progress]: [ 82 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1)) (sqrt k)))>
12.120 * * * * [progress]: [ 83 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (exp (log (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.120 * * * * [progress]: [ 84 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (log (exp (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.120 * * * * [progress]: [ 85 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (* (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.120 * * * * [progress]: [ 86 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (cbrt (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.120 * * * * [progress]: [ 87 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.120 * * * * [progress]: [ 88 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* 1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.120 * * * * [progress]: [ 89 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)))) (sqrt k)))>
12.120 * * * * [progress]: [ 90 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.120 * * * * [progress]: [ 91 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (log1p (expm1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.120 * * * * [progress]: [ 92 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (expm1 (log1p (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.120 * * * * [progress]: [ 93 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.120 * * * * [progress]: [ 94 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.120 * * * * [progress]: [ 95 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.120 * * * * [progress]: [ 96 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.120 * * * * [progress]: [ 97 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (* 1 (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.120 * * * * [progress]: [ 98 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (* 1 (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.120 * * * * [progress]: [ 99 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (* 1 (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.120 * * * * [progress]: [ 100 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (/ (pow (* n (* 2 PI)) (/ (/ 1 2) 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.120 * * * * [progress]: [ 101 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (* (cbrt (/ (/ (- 1 k) 2) 2)) (cbrt (/ (/ (- 1 k) 2) 2)))) (cbrt (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.120 * * * * [progress]: [ 102 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (sqrt (/ (/ (- 1 k) 2) 2))) (sqrt (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.120 * * * * [progress]: [ 103 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (/ (- 1 k) 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.120 * * * * [progress]: [ 104 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (sqrt 2))) (/ (cbrt (/ (- 1 k) 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 105 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) 1)) (/ (cbrt (/ (- 1 k) 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 106 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (/ (- 1 k) 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 107 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2))) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 108 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) 1)) (/ (sqrt (/ (- 1 k) 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 109 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (cbrt (- 1 k)) (cbrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 110 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (cbrt (- 1 k)) (cbrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 111 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (cbrt (- 1 k)) (cbrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 112 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (cbrt (- 1 k)) (sqrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 113 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) (sqrt 2))) (/ (/ (cbrt (- 1 k)) (sqrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 114 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)) 1)) (/ (/ (cbrt (- 1 k)) (sqrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 115 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (cbrt (- 1 k)) 2) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 116 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) (sqrt 2))) (/ (/ (cbrt (- 1 k)) 2) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 117 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1) 1)) (/ (/ (cbrt (- 1 k)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 118 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 119 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 120 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (sqrt (- 1 k)) (cbrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 121 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 122 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (sqrt 2))) (/ (/ (sqrt (- 1 k)) (sqrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 123 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) 1)) (/ (/ (sqrt (- 1 k)) (sqrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 124 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (sqrt (- 1 k)) 2) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 125 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) (sqrt 2))) (/ (/ (sqrt (- 1 k)) 2) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.121 * * * * [progress]: [ 126 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) 1) 1)) (/ (/ (sqrt (- 1 k)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 127 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (cbrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 128 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- 1 k) (cbrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 129 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- 1 k) (cbrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 130 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (sqrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 131 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (sqrt 2))) (/ (/ (- 1 k) (sqrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 132 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) 1)) (/ (/ (- 1 k) (sqrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 133 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) 2) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 134 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 1) (sqrt 2))) (/ (/ (- 1 k) 2) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 135 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 1) 1)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 136 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- (sqrt 1) (sqrt k)) (cbrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 137 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- (sqrt 1) (sqrt k)) (cbrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 138 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- (sqrt 1) (sqrt k)) (cbrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 139 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- (sqrt 1) (sqrt k)) (sqrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 140 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) (sqrt 2))) (/ (/ (- (sqrt 1) (sqrt k)) (sqrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 141 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)) 1)) (/ (/ (- (sqrt 1) (sqrt k)) (sqrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 142 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- (sqrt 1) (sqrt k)) 2) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 143 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) (sqrt 2))) (/ (/ (- (sqrt 1) (sqrt k)) 2) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 144 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ (sqrt 1) (sqrt k)) 1) 1)) (/ (/ (- (sqrt 1) (sqrt k)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 145 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 (sqrt k)) (cbrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 146 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- 1 (sqrt k)) (cbrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 147 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- 1 (sqrt k)) (cbrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.122 * * * * [progress]: [ 148 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 (sqrt k)) (sqrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 149 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) (sqrt 2))) (/ (/ (- 1 (sqrt k)) (sqrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 150 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) (sqrt 2)) 1)) (/ (/ (- 1 (sqrt k)) (sqrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 151 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 (sqrt k)) 2) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 152 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) (sqrt 2))) (/ (/ (- 1 (sqrt k)) 2) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 153 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (+ 1 (sqrt k)) 1) 1)) (/ (/ (- 1 (sqrt k)) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 154 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (cbrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 155 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) (sqrt 2))) (/ (/ (- 1 k) (cbrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 156 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (* (cbrt 2) (cbrt 2))) 1)) (/ (/ (- 1 k) (cbrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 157 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) (sqrt 2)) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 158 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) (sqrt 2))) (/ (/ (- 1 k) (sqrt 2)) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 159 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 (sqrt 2)) 1)) (/ (/ (- 1 k) (sqrt 2)) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 160 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 1) (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) 2) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 161 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 1) (sqrt 2))) (/ (/ (- 1 k) 2) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 162 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ 1 1) 1)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 163 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (/ (- 1 k) 2) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 164 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (/ (- 1 k) 2) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 165 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 166 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (- 1 k) (* (cbrt 2) (cbrt 2)))) (/ (/ 1 2) (cbrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 167 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (- 1 k) (sqrt 2))) (/ (/ 1 2) (sqrt 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 168 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (- 1 k) 1)) (/ (/ 1 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 169 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) 1) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 170 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.123 * * * * [progress]: [ 171 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow n (/ (/ (- 1 k) 2) 2)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.124 * * * * [progress]: [ 172 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.124 * * * * [progress]: [ 173 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (log (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.124 * * * * [progress]: [ 174 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (log (exp (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.124 * * * * [progress]: [ 175 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (* (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.124 * * * * [progress]: [ 176 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.124 * * * * [progress]: [ 177 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.124 * * * * [progress]: [ 178 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* 1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.124 * * * * [progress]: [ 179 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.124 * * * * [progress]: [ 180 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.124 * * * * [progress]: [ 181 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (log1p (expm1 (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.124 * * * * [progress]: [ 182 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (expm1 (log1p (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.124 * * * * [progress]: [ 183 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (+ (/ (/ (- 1 k) 2) 2) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.124 * * * * [progress]: [ 184 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n (* 2 PI)) (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (sqrt k)))>
12.124 * * * * [progress]: [ 185 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 2) (sqrt k)))>
12.124 * * * * [progress]: [ 186 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) 1) (sqrt k)))>
12.124 * * * * [progress]: [ 187 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2)) (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.124 * * * * [progress]: [ 188 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2)) (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.124 * * * * [progress]: [ 189 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2)) (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.124 * * * * [progress]: [ 190 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2)) (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.124 * * * * [progress]: [ 191 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2)) (log (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.124 * * * * [progress]: [ 192 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.124 * * * * [progress]: [ 193 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.124 * * * * [progress]: [ 194 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.124 * * * * [progress]: [ 195 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.125 * * * * [progress]: [ 196 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (log (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.125 * * * * [progress]: [ 197 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.125 * * * * [progress]: [ 198 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.125 * * * * [progress]: [ 199 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.125 * * * * [progress]: [ 200 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.125 * * * * [progress]: [ 201 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (log (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.125 * * * * [progress]: [ 202 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.125 * * * * [progress]: [ 203 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.125 * * * * [progress]: [ 204 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.125 * * * * [progress]: [ 205 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.125 * * * * [progress]: [ 206 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)) (log (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.125 * * * * [progress]: [ 207 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (log (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.125 * * * * [progress]: [ 208 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (log (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.125 * * * * [progress]: [ 209 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (log (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.125 * * * * [progress]: [ 210 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (log (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.125 * * * * [progress]: [ 211 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (+ (log (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (log (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.125 * * * * [progress]: [ 212 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.125 * * * * [progress]: [ 213 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.125 * * * * [progress]: [ 214 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.125 * * * * [progress]: [ 215 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (cbrt (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (cbrt (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.126 * * * * [progress]: [ 216 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.126 * * * * [progress]: [ 217 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (sqrt (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.126 * * * * [progress]: [ 218 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (pow (* n (* 2 PI)) (/ (/ 1 2) 2)) (pow (* n (* 2 PI)) (/ (/ 1 2) 2))) (* (pow (* n (* 2 PI)) (/ (/ k 2) 2)) (pow (* n (* 2 PI)) (/ (/ k 2) 2)))) (sqrt k)))>
12.126 * * * * [progress]: [ 219 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.126 * * * * [progress]: [ 220 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow n (/ (/ (- 1 k) 2) 2)) (pow n (/ (/ (- 1 k) 2) 2))) (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.126 * * * * [progress]: [ 221 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (* (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (* (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (* (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.126 * * * * [progress]: [ 222 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (* (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.126 * * * * [progress]: [ 223 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* 1 1) (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.126 * * * * [progress]: [ 224 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))) (* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)))) (sqrt k)))>
12.126 * * * * [progress]: [ 225 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (* (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.126 * * * * [progress]: [ 226 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))) (* (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)))) (sqrt k)))>
12.126 * * * * [progress]: [ 227 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.126 * * * * [progress]: [ 228 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))) (* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)))) (sqrt k)))>
12.126 * * * * [progress]: [ 229 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 2 (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.126 * * * * [progress]: [ 230 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow n (/ (/ (- 1 k) 2) 2))) (pow (* 2 PI) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.126 * * * * [progress]: [ 231 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (* (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.126 * * * * [progress]: [ 232 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.126 * * * * [progress]: [ 233 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) 1) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.126 * * * * [progress]: [ 234 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))) (sqrt k)))>
12.126 * * * * [progress]: [ 235 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (/ (/ (- 1 k) 2) 2)) (* (pow (* 2 PI) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.126 * * * * [progress]: [ 236 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (* (cbrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.126 * * * * [progress]: [ 237 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (* (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.126 * * * * [progress]: [ 238 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.127 * * * * [progress]: [ 239 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))) (sqrt k)))>
12.127 * * * * [progress]: [ 240 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ 1 2) 2))) (pow (* n (* 2 PI)) (/ (/ k 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 241 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (/ (* (pow (* n (* 2 PI)) (/ (/ 1 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ k 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 242 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))) (sqrt k)))>
12.127 * * * * [progress]: [ 243 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 244 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (log1p (expm1 (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 245 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (expm1 (log1p (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 246 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) 1) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 247 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) 1) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 248 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (pow (* n (* 2 PI)) 1) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 249 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (exp (+ (log n) (+ (log 2) (log PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 250 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (exp (+ (log n) (log (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 251 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (exp (log (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 252 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (log (exp (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 253 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 254 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 255 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 256 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 257 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 258 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* 1 (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 259 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* (* n 2) PI) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 260 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 261 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 262 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* 1 (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.127 * * * * [progress]: [ 263 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.128 * * * * [progress]: [ 264 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.128 * * * * [progress]: [ 265 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))) (sqrt k)))>
12.128 * * * * [progress]: [ 266 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))) (sqrt k)))>
12.128 * * * * [progress]: [ 267 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))) (sqrt k)))>
12.128 * * * * [progress]: [ 268 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.128 * * * * [progress]: [ 269 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.128 * * * * [progress]: [ 270 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.128 * * * * [progress]: [ 271 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (- (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/4 (* (pow k 2) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI)))))) (+ (* 1/8 (* (pow k 2) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2)))) (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2)))) (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) k))))) (sqrt k)))>
12.128 * * * * [progress]: [ 272 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 2) (sqrt k)))>
12.128 * * * * [progress]: [ 273 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 2) (sqrt k)))>
12.128 * * * * [progress]: [ 274 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.128 * * * * [progress]: [ 275 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.128 * * * * [progress]: [ 276 / 276 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* 2 (* n PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))>
12.139 * [simplify]: Simplifying:
  (expm1 (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (log1p (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (* (+ (log n) (+ (log 2) (log PI))) (/ (/ (- 1 k) 2) 2))
  (* (+ (log n) (log (* 2 PI))) (/ (/ (- 1 k) 2) 2))
  (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2))
  (* (log (* n (* 2 PI))) (/ (/ (- 1 k) 2) 2))
  (* 1 (/ (/ (- 1 k) 2) 2))
  (* 1 (/ (/ (- 1 k) 2) 2))
  (* 1 (/ (/ (- 1 k) 2) 2))
  (pow (* n (* 2 PI)) (/ (/ 1 2) 2))
  (pow (* n (* 2 PI)) (/ (/ k 2) 2))
  (pow (* n (* 2 PI)) (* (cbrt (/ (/ (- 1 k) 2) 2)) (cbrt (/ (/ (- 1 k) 2) 2))))
  (pow (* n (* 2 PI)) (sqrt (/ (/ (- 1 k) 2) 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))) 1))
  (pow (* n (* 2 PI)) (/ (sqrt (/ (- 1 k) 2)) (* (cbrt 2) (cbrt 2))))
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  (* (sqrt (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (* (pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ 1 2) 2)))
  (* (pow (* n (* 2 PI)) (/ (/ 1 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)))
  (real->posit16 (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
  (expm1 (* n (* 2 PI)))
  (log1p (* n (* 2 PI)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
  (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
  (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (- (+ (* 1/8 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/4 (* (pow k 2) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) (log (* 2 PI)))))) (+ (* 1/8 (* (pow k 2) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (pow (log (* 2 PI)) 2)))) (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2)))) (+ (* 1/2 (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (pow (exp (* 1/4 (+ (log n) (log (* 2 PI))))) 2) k)))))
  (pow (exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) 2)
  (pow (exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) 2)
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
12.149 * * [simplify]: iteration 1: (335 enodes)
12.298 * * [simplify]: iteration 2: (1561 enodes)
12.872 * * [simplify]: Extracting #0: cost 103 inf + 0
12.874 * * [simplify]: Extracting #1: cost 747 inf + 1
12.882 * * [simplify]: Extracting #2: cost 1344 inf + 2731
12.899 * * [simplify]: Extracting #3: cost 1468 inf + 35757
12.946 * * [simplify]: Extracting #4: cost 1022 inf + 180113
13.043 * * [simplify]: Extracting #5: cost 350 inf + 472740
13.204 * * [simplify]: Extracting #6: cost 40 inf + 643664
13.357 * * [simplify]: Extracting #7: cost 4 inf + 655886
13.499 * * [simplify]: Extracting #8: cost 0 inf + 657536
13.650 * * [simplify]: Extracting #9: cost 0 inf + 657521
13.809 * [simplify]: Simplified to:
  (expm1 (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (log1p (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (* (/ (- 1 k) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (- 1 k) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (- 1 k) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (- 1 k) (* 2 2)) (log (* (* PI 2) n)))
  (/ (- 1 k) (* 2 2))
  (/ (- 1 k) (* 2 2))
  (/ (- 1 k) (* 2 2))
  (pow (* (* PI 2) n) (/ 1 (* 2 2)))
  (pow (* (* PI 2) n) (/ (/ k 2) 2))
  (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) (* 2 2))) (cbrt (/ (- 1 k) (* 2 2)))))
  (pow (* (* PI 2) n) (sqrt (/ (- 1 k) (* 2 2))))
  (pow (* (* PI 2) n) (* (/ (cbrt (/ (- 1 k) 2)) (cbrt 2)) (/ (cbrt (/ (- 1 k) 2)) (cbrt 2))))
  (pow (* (* PI 2) n) (* (/ (cbrt (/ (- 1 k) 2)) (sqrt 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* PI 2) n) (/ (/ (sqrt (/ (- 1 k) 2)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2)))
  (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (* (/ (/ (cbrt (- 1 k)) (cbrt 2)) (cbrt 2)) (/ (/ (cbrt (- 1 k)) (cbrt 2)) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))) (sqrt 2)))
  (pow (* (* PI 2) n) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 2))
  (pow (* (* PI 2) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* (* PI 2) n) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* (* PI 2) n) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (* (* (cbrt 2) (cbrt 2)) (* (cbrt 2) (cbrt 2)))))
  (pow (* (* PI 2) n) (/ (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) 2))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* PI 2) n) (sqrt (- 1 k)))
  (pow (* (* PI 2) n) (/ 1 (* (* (cbrt 2) (cbrt 2)) (* (cbrt 2) (cbrt 2)))))
  (pow (* (* PI 2) n) (/ (/ (/ 1 (sqrt 2)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (/ (/ 1 (sqrt 2)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 2))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (/ (+ (sqrt k) (sqrt 1)) (* (* (cbrt 2) (cbrt 2)) (* (cbrt 2) (cbrt 2)))))
  (pow (* (* PI 2) n) (/ (/ (/ (+ (sqrt k) (sqrt 1)) (cbrt 2)) (cbrt 2)) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (/ (+ (sqrt k) (sqrt 1)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (/ (/ (+ (sqrt k) (sqrt 1)) (cbrt 2)) (cbrt 2)) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) (sqrt 1)) 2))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) (sqrt 1)) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (/ (+ (sqrt k) (sqrt 1)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) (sqrt 1)) (sqrt 2)))
  (pow (* (* PI 2) n) (+ (sqrt k) (sqrt 1)))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (* (* (cbrt 2) (cbrt 2)) (* (cbrt 2) (cbrt 2)))))
  (pow (* (* PI 2) n) (/ (/ (+ (sqrt k) 1) (sqrt 2)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (/ (+ (sqrt k) 1) (sqrt 2)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) 2))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* (* PI 2) n) (+ (sqrt k) 1))
  (pow (* (* PI 2) n) (/ 1 (* (* (cbrt 2) (cbrt 2)) (* (cbrt 2) (cbrt 2)))))
  (pow (* (* PI 2) n) (/ (/ (/ 1 (sqrt 2)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (/ (/ 1 (sqrt 2)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 2))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (/ (/ (- 1 k) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (- 1 k) (sqrt 2)))
  (pow (* (* PI 2) n) (- 1 k))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (/ (- 1 k) 2))
  (pow n (/ (- 1 k) (* 2 2)))
  (pow (* PI 2) (/ (- 1 k) (* 2 2)))
  (* (/ (- 1 k) (* 2 2)) (log (* (* PI 2) n)))
  (exp (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))))
  (cbrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (* (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (pow (* (* PI 2) n) (/ (- 1 k) (* 2 (* 2 2))))
  (pow (* (* PI 2) n) (/ (- 1 k) (* 2 (* 2 2))))
  (real->posit16 (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (expm1 (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (log1p (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (* (/ (- 1 k) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (- 1 k) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (- 1 k) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (- 1 k) (* 2 2)) (log (* (* PI 2) n)))
  (/ (- 1 k) (* 2 2))
  (/ (- 1 k) (* 2 2))
  (/ (- 1 k) (* 2 2))
  (pow (* (* PI 2) n) (/ 1 (* 2 2)))
  (pow (* (* PI 2) n) (/ (/ k 2) 2))
  (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) (* 2 2))) (cbrt (/ (- 1 k) (* 2 2)))))
  (pow (* (* PI 2) n) (sqrt (/ (- 1 k) (* 2 2))))
  (pow (* (* PI 2) n) (* (/ (cbrt (/ (- 1 k) 2)) (cbrt 2)) (/ (cbrt (/ (- 1 k) 2)) (cbrt 2))))
  (pow (* (* PI 2) n) (* (/ (cbrt (/ (- 1 k) 2)) (sqrt 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* PI 2) n) (/ (/ (sqrt (/ (- 1 k) 2)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (sqrt (/ (- 1 k) 2)) (sqrt 2)))
  (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (* (/ (/ (cbrt (- 1 k)) (cbrt 2)) (cbrt 2)) (/ (/ (cbrt (- 1 k)) (cbrt 2)) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))) (sqrt 2)))
  (pow (* (* PI 2) n) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 2))
  (pow (* (* PI 2) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* (* PI 2) n) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* (* PI 2) n) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (* (* (cbrt 2) (cbrt 2)) (* (cbrt 2) (cbrt 2)))))
  (pow (* (* PI 2) n) (/ (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) 2))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* PI 2) n) (sqrt (- 1 k)))
  (pow (* (* PI 2) n) (/ 1 (* (* (cbrt 2) (cbrt 2)) (* (cbrt 2) (cbrt 2)))))
  (pow (* (* PI 2) n) (/ (/ (/ 1 (sqrt 2)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (/ (/ 1 (sqrt 2)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 2))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (/ (+ (sqrt k) (sqrt 1)) (* (* (cbrt 2) (cbrt 2)) (* (cbrt 2) (cbrt 2)))))
  (pow (* (* PI 2) n) (/ (/ (/ (+ (sqrt k) (sqrt 1)) (cbrt 2)) (cbrt 2)) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (/ (+ (sqrt k) (sqrt 1)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (/ (/ (+ (sqrt k) (sqrt 1)) (cbrt 2)) (cbrt 2)) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) (sqrt 1)) 2))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) (sqrt 1)) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (/ (+ (sqrt k) (sqrt 1)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) (sqrt 1)) (sqrt 2)))
  (pow (* (* PI 2) n) (+ (sqrt k) (sqrt 1)))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (* (* (cbrt 2) (cbrt 2)) (* (cbrt 2) (cbrt 2)))))
  (pow (* (* PI 2) n) (/ (/ (+ (sqrt k) 1) (sqrt 2)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (/ (+ (sqrt k) 1) (sqrt 2)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) 2))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* (* PI 2) n) (+ (sqrt k) 1))
  (pow (* (* PI 2) n) (/ 1 (* (* (cbrt 2) (cbrt 2)) (* (cbrt 2) (cbrt 2)))))
  (pow (* (* PI 2) n) (/ (/ (/ 1 (sqrt 2)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (/ (/ 1 (sqrt 2)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 2))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (/ (/ (- 1 k) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (- 1 k) (sqrt 2)))
  (pow (* (* PI 2) n) (- 1 k))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (/ (- 1 k) 2))
  (pow n (/ (- 1 k) (* 2 2)))
  (pow (* PI 2) (/ (- 1 k) (* 2 2)))
  (* (/ (- 1 k) (* 2 2)) (log (* (* PI 2) n)))
  (exp (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))))
  (cbrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (* (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (pow (* (* PI 2) n) (/ (- 1 k) (* 2 (* 2 2))))
  (pow (* (* PI 2) n) (/ (- 1 k) (* 2 (* 2 2))))
  (real->posit16 (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (expm1 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (log1p (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (+ (/ (- 1 k) (* 2 2)) (/ (- 1 k) (* 2 2)))
  (* (* (* PI 2) n) (* (* PI 2) n))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (* (/ (* 2 (- 1 k)) (* 2 2)) (log (* (* PI 2) n)))
  (exp (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (* (pow (* (* PI 2) n) (/ (- 1 k) 2)) (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (/ 1 2))
  (pow (* (* PI 2) n) (/ (* 2 k) (* 2 2)))
  (pow n (/ (* 2 (- 1 k)) (* 2 2)))
  (pow (* PI 2) (* 2 (/ (- 1 k) (* 2 2))))
  (* (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))) (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))))
  (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))
  (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))
  1
  (pow (* (* PI 2) n) (/ (- 1 k) 2))
  (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))
  (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))
  (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))
  (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))
  (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 (* 2 2)))))
  (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 (* 2 2)))))
  (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 (* 2 2)))))
  (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 (* 2 2)))))
  (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))
  (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))
  (/ (* 2 (- 1 k)) (* 2 2))
  (* (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))) (pow n (/ (- 1 k) (* 2 2))))
  (* (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))) (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))))
  (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))
  (* (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 (* 2 2)))))
  (* (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))) (pow (* PI 2) (/ (- 1 k) (* 2 2))))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (* (sqrt (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2)))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (pow (* (* PI 2) n) (/ (- 1 k) 2))
  (* (* (pow (* (* PI 2) n) (/ (- 1 k) (* 2 (* 2 2)))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 (* 2 2))))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 (* 2 2)))))
  (* (pow (* (* PI 2) n) (/ 1 (* 2 2))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (* (pow (* (* PI 2) n) (/ 1 (* 2 2))) (pow (* (* PI 2) n) (/ (- 1 k) (* 2 2))))
  (real->posit16 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (expm1 (* (* PI 2) n))
  (log1p (* (* PI 2) n))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (* (exp (* n PI)) (exp (* n PI)))
  (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n))
  (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n))
  (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n)))
  (cbrt (* (* PI 2) n))
  (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (* n 2)
  (* 2 (* PI (cbrt n)))
  (* (* 2 (sqrt n)) PI)
  (* (* PI 2) n)
  (real->posit16 (* (* PI 2) n))
  (- (fma (* (exp (* 1/4 (log (* (* PI 2) n)))) (* (log (* PI 2)) (* (log n) (* k k)))) 1/16 (fma 1/32 (* (* k k) (+ (* (* (log n) (log n)) (exp (* 1/4 (log (* (* PI 2) n))))) (* (* (log (* PI 2)) (log (* PI 2))) (exp (* 1/4 (log (* (* PI 2) n))))))) (exp (* 1/4 (log (* (* PI 2) n)))))) (* 1/4 (* k (+ (* (log n) (exp (* 1/4 (log (* (* PI 2) n))))) (* (log (* PI 2)) (exp (* 1/4 (log (* (* PI 2) n)))))))))
  (exp (* (* (log (* (* PI 2) n)) (- 1 k)) 1/4))
  (exp (* (- 1 k) (* (- (log (* PI -2)) (log (/ -1 n))) 1/4)))
  (- (fma (* (exp (* 1/4 (log (* (* PI 2) n)))) (* (log (* PI 2)) (* (log n) (* k k)))) 1/16 (fma 1/32 (* (* k k) (+ (* (* (log n) (log n)) (exp (* 1/4 (log (* (* PI 2) n))))) (* (* (log (* PI 2)) (log (* PI 2))) (exp (* 1/4 (log (* (* PI 2) n))))))) (exp (* 1/4 (log (* (* PI 2) n)))))) (* 1/4 (* k (+ (* (log n) (exp (* 1/4 (log (* (* PI 2) n))))) (* (log (* PI 2)) (exp (* 1/4 (log (* (* PI 2) n)))))))))
  (exp (* (* (log (* (* PI 2) n)) (- 1 k)) 1/4))
  (exp (* (- 1 k) (* (- (log (* PI -2)) (log (/ -1 n))) 1/4)))
  (fma (* 1/8 (* (exp (* 1/4 (log (* (* PI 2) n)))) (exp (* 1/4 (log (* (* PI 2) n)))))) (* (* (log n) k) (* (log n) k)) (- (fma (* 1/4 (* k k)) (* (* (exp (* 1/4 (log (* (* PI 2) n)))) (exp (* 1/4 (log (* (* PI 2) n))))) (* (log n) (log (* PI 2)))) (fma (* 1/8 (* k k)) (* (* (log (* PI 2)) (exp (* 1/4 (log (* (* PI 2) n))))) (* (log (* PI 2)) (exp (* 1/4 (log (* (* PI 2) n)))))) (* (exp (* 1/4 (log (* (* PI 2) n)))) (exp (* 1/4 (log (* (* PI 2) n))))))) (* 1/2 (* k (+ (* (log n) (* (exp (* 1/4 (log (* (* PI 2) n)))) (exp (* 1/4 (log (* (* PI 2) n)))))) (* (* (log (* PI 2)) (exp (* 1/4 (log (* (* PI 2) n))))) (exp (* 1/4 (log (* (* PI 2) n))))))))))
  (exp (+ (* (* (log (* (* PI 2) n)) (- 1 k)) 1/4) (* (* (log (* (* PI 2) n)) (- 1 k)) 1/4)))
  (exp (+ (* (- 1 k) (* (- (log (* PI -2)) (log (/ -1 n))) 1/4)) (* (- 1 k) (* (- (log (* PI -2)) (log (/ -1 n))) 1/4))))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (* (* PI 2) n)
13.839 * * * [progress]: adding candidates to table
17.891 * * [progress]: iteration 4 / 4
17.891 * * * [progress]: picking best candidate
18.304 * * * * [pick]: Picked  #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.304 * * * [progress]: localizing error
18.345 * * * [progress]: generating rewritten candidates
18.345 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 1)
18.372 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1)
18.382 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 2 1)
18.399 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1)
18.430 * * * [progress]: generating series expansions
18.430 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 1)
18.431 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
18.431 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
18.431 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
18.431 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
18.431 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
18.431 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
18.431 * [taylor]: Taking taylor expansion of 1/2 in k
18.431 * [backup-simplify]: Simplify 1/2 into 1/2
18.431 * [taylor]: Taking taylor expansion of (- 1 k) in k
18.431 * [taylor]: Taking taylor expansion of 1 in k
18.431 * [backup-simplify]: Simplify 1 into 1
18.431 * [taylor]: Taking taylor expansion of k in k
18.431 * [backup-simplify]: Simplify 0 into 0
18.431 * [backup-simplify]: Simplify 1 into 1
18.431 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
18.431 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
18.431 * [taylor]: Taking taylor expansion of 2 in k
18.431 * [backup-simplify]: Simplify 2 into 2
18.431 * [taylor]: Taking taylor expansion of (* n PI) in k
18.431 * [taylor]: Taking taylor expansion of n in k
18.431 * [backup-simplify]: Simplify n into n
18.431 * [taylor]: Taking taylor expansion of PI in k
18.431 * [backup-simplify]: Simplify PI into PI
18.431 * [backup-simplify]: Simplify (* n PI) into (* n PI)
18.431 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
18.431 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
18.431 * [backup-simplify]: Simplify (- 0) into 0
18.432 * [backup-simplify]: Simplify (+ 1 0) into 1
18.432 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
18.432 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
18.432 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
18.432 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
18.432 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
18.432 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
18.432 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
18.432 * [taylor]: Taking taylor expansion of 1/2 in n
18.432 * [backup-simplify]: Simplify 1/2 into 1/2
18.432 * [taylor]: Taking taylor expansion of (- 1 k) in n
18.432 * [taylor]: Taking taylor expansion of 1 in n
18.432 * [backup-simplify]: Simplify 1 into 1
18.432 * [taylor]: Taking taylor expansion of k in n
18.432 * [backup-simplify]: Simplify k into k
18.432 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
18.432 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
18.432 * [taylor]: Taking taylor expansion of 2 in n
18.432 * [backup-simplify]: Simplify 2 into 2
18.432 * [taylor]: Taking taylor expansion of (* n PI) in n
18.432 * [taylor]: Taking taylor expansion of n in n
18.432 * [backup-simplify]: Simplify 0 into 0
18.432 * [backup-simplify]: Simplify 1 into 1
18.432 * [taylor]: Taking taylor expansion of PI in n
18.432 * [backup-simplify]: Simplify PI into PI
18.433 * [backup-simplify]: Simplify (* 0 PI) into 0
18.433 * [backup-simplify]: Simplify (* 2 0) into 0
18.434 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
18.435 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
18.436 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
18.436 * [backup-simplify]: Simplify (- k) into (- k)
18.436 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
18.436 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
18.437 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
18.437 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
18.438 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
18.438 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
18.438 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
18.438 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
18.438 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
18.438 * [taylor]: Taking taylor expansion of 1/2 in n
18.438 * [backup-simplify]: Simplify 1/2 into 1/2
18.438 * [taylor]: Taking taylor expansion of (- 1 k) in n
18.438 * [taylor]: Taking taylor expansion of 1 in n
18.438 * [backup-simplify]: Simplify 1 into 1
18.438 * [taylor]: Taking taylor expansion of k in n
18.438 * [backup-simplify]: Simplify k into k
18.438 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
18.438 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
18.438 * [taylor]: Taking taylor expansion of 2 in n
18.438 * [backup-simplify]: Simplify 2 into 2
18.438 * [taylor]: Taking taylor expansion of (* n PI) in n
18.438 * [taylor]: Taking taylor expansion of n in n
18.438 * [backup-simplify]: Simplify 0 into 0
18.438 * [backup-simplify]: Simplify 1 into 1
18.438 * [taylor]: Taking taylor expansion of PI in n
18.438 * [backup-simplify]: Simplify PI into PI
18.439 * [backup-simplify]: Simplify (* 0 PI) into 0
18.439 * [backup-simplify]: Simplify (* 2 0) into 0
18.440 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
18.441 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
18.442 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
18.442 * [backup-simplify]: Simplify (- k) into (- k)
18.442 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
18.442 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
18.443 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
18.444 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
18.444 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
18.445 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
18.445 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
18.445 * [taylor]: Taking taylor expansion of 1/2 in k
18.445 * [backup-simplify]: Simplify 1/2 into 1/2
18.445 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
18.445 * [taylor]: Taking taylor expansion of (- 1 k) in k
18.445 * [taylor]: Taking taylor expansion of 1 in k
18.445 * [backup-simplify]: Simplify 1 into 1
18.445 * [taylor]: Taking taylor expansion of k in k
18.445 * [backup-simplify]: Simplify 0 into 0
18.445 * [backup-simplify]: Simplify 1 into 1
18.445 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
18.445 * [taylor]: Taking taylor expansion of (log n) in k
18.445 * [taylor]: Taking taylor expansion of n in k
18.445 * [backup-simplify]: Simplify n into n
18.445 * [backup-simplify]: Simplify (log n) into (log n)
18.445 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
18.445 * [taylor]: Taking taylor expansion of (* 2 PI) in k
18.445 * [taylor]: Taking taylor expansion of 2 in k
18.445 * [backup-simplify]: Simplify 2 into 2
18.445 * [taylor]: Taking taylor expansion of PI in k
18.445 * [backup-simplify]: Simplify PI into PI
18.445 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
18.446 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
18.446 * [backup-simplify]: Simplify (- 0) into 0
18.446 * [backup-simplify]: Simplify (+ 1 0) into 1
18.447 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
18.448 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
18.448 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
18.449 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
18.450 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
18.450 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
18.451 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
18.452 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
18.452 * [backup-simplify]: Simplify (- 0) into 0
18.452 * [backup-simplify]: Simplify (+ 0 0) into 0
18.453 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
18.454 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
18.454 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
18.455 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
18.455 * [taylor]: Taking taylor expansion of 0 in k
18.456 * [backup-simplify]: Simplify 0 into 0
18.456 * [backup-simplify]: Simplify 0 into 0
18.456 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
18.457 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
18.458 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
18.458 * [backup-simplify]: Simplify (+ 0 0) into 0
18.458 * [backup-simplify]: Simplify (- 1) into -1
18.458 * [backup-simplify]: Simplify (+ 0 -1) into -1
18.459 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
18.461 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
18.463 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
18.466 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
18.467 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
18.469 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
18.472 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
18.473 * [backup-simplify]: Simplify (- 0) into 0
18.473 * [backup-simplify]: Simplify (+ 0 0) into 0
18.474 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
18.476 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
18.477 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
18.480 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
18.480 * [taylor]: Taking taylor expansion of 0 in k
18.480 * [backup-simplify]: Simplify 0 into 0
18.480 * [backup-simplify]: Simplify 0 into 0
18.480 * [backup-simplify]: Simplify 0 into 0
18.482 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
18.483 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
18.486 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
18.487 * [backup-simplify]: Simplify (+ 0 0) into 0
18.487 * [backup-simplify]: Simplify (- 0) into 0
18.488 * [backup-simplify]: Simplify (+ 0 0) into 0
18.490 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
18.492 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
18.496 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
18.500 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
18.505 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
18.506 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
18.506 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
18.506 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
18.506 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
18.506 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
18.506 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
18.506 * [taylor]: Taking taylor expansion of 1/2 in k
18.506 * [backup-simplify]: Simplify 1/2 into 1/2
18.506 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
18.506 * [taylor]: Taking taylor expansion of 1 in k
18.506 * [backup-simplify]: Simplify 1 into 1
18.506 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.506 * [taylor]: Taking taylor expansion of k in k
18.506 * [backup-simplify]: Simplify 0 into 0
18.506 * [backup-simplify]: Simplify 1 into 1
18.509 * [backup-simplify]: Simplify (/ 1 1) into 1
18.510 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
18.510 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
18.510 * [taylor]: Taking taylor expansion of 2 in k
18.510 * [backup-simplify]: Simplify 2 into 2
18.510 * [taylor]: Taking taylor expansion of (/ PI n) in k
18.510 * [taylor]: Taking taylor expansion of PI in k
18.510 * [backup-simplify]: Simplify PI into PI
18.510 * [taylor]: Taking taylor expansion of n in k
18.510 * [backup-simplify]: Simplify n into n
18.510 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
18.510 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
18.510 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
18.510 * [backup-simplify]: Simplify (- 1) into -1
18.511 * [backup-simplify]: Simplify (+ 0 -1) into -1
18.511 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
18.511 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
18.511 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
18.511 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
18.511 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
18.512 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
18.512 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
18.512 * [taylor]: Taking taylor expansion of 1/2 in n
18.512 * [backup-simplify]: Simplify 1/2 into 1/2
18.512 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
18.512 * [taylor]: Taking taylor expansion of 1 in n
18.512 * [backup-simplify]: Simplify 1 into 1
18.512 * [taylor]: Taking taylor expansion of (/ 1 k) in n
18.512 * [taylor]: Taking taylor expansion of k in n
18.512 * [backup-simplify]: Simplify k into k
18.512 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
18.512 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
18.512 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
18.512 * [taylor]: Taking taylor expansion of 2 in n
18.512 * [backup-simplify]: Simplify 2 into 2
18.512 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.512 * [taylor]: Taking taylor expansion of PI in n
18.512 * [backup-simplify]: Simplify PI into PI
18.512 * [taylor]: Taking taylor expansion of n in n
18.512 * [backup-simplify]: Simplify 0 into 0
18.512 * [backup-simplify]: Simplify 1 into 1
18.512 * [backup-simplify]: Simplify (/ PI 1) into PI
18.512 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
18.513 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
18.513 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
18.513 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
18.513 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
18.514 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
18.515 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
18.516 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
18.516 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
18.516 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
18.516 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
18.516 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
18.516 * [taylor]: Taking taylor expansion of 1/2 in n
18.516 * [backup-simplify]: Simplify 1/2 into 1/2
18.516 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
18.516 * [taylor]: Taking taylor expansion of 1 in n
18.516 * [backup-simplify]: Simplify 1 into 1
18.516 * [taylor]: Taking taylor expansion of (/ 1 k) in n
18.516 * [taylor]: Taking taylor expansion of k in n
18.516 * [backup-simplify]: Simplify k into k
18.516 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
18.516 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
18.516 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
18.516 * [taylor]: Taking taylor expansion of 2 in n
18.516 * [backup-simplify]: Simplify 2 into 2
18.516 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.516 * [taylor]: Taking taylor expansion of PI in n
18.516 * [backup-simplify]: Simplify PI into PI
18.516 * [taylor]: Taking taylor expansion of n in n
18.516 * [backup-simplify]: Simplify 0 into 0
18.516 * [backup-simplify]: Simplify 1 into 1
18.517 * [backup-simplify]: Simplify (/ PI 1) into PI
18.517 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
18.517 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
18.517 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
18.518 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
18.518 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
18.518 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
18.519 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
18.520 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
18.520 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
18.520 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
18.520 * [taylor]: Taking taylor expansion of 1/2 in k
18.520 * [backup-simplify]: Simplify 1/2 into 1/2
18.520 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
18.520 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
18.520 * [taylor]: Taking taylor expansion of 1 in k
18.520 * [backup-simplify]: Simplify 1 into 1
18.520 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.520 * [taylor]: Taking taylor expansion of k in k
18.520 * [backup-simplify]: Simplify 0 into 0
18.520 * [backup-simplify]: Simplify 1 into 1
18.520 * [backup-simplify]: Simplify (/ 1 1) into 1
18.520 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
18.521 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
18.521 * [taylor]: Taking taylor expansion of (* 2 PI) in k
18.521 * [taylor]: Taking taylor expansion of 2 in k
18.521 * [backup-simplify]: Simplify 2 into 2
18.521 * [taylor]: Taking taylor expansion of PI in k
18.521 * [backup-simplify]: Simplify PI into PI
18.521 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
18.522 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
18.522 * [taylor]: Taking taylor expansion of (log n) in k
18.522 * [taylor]: Taking taylor expansion of n in k
18.522 * [backup-simplify]: Simplify n into n
18.522 * [backup-simplify]: Simplify (log n) into (log n)
18.522 * [backup-simplify]: Simplify (- 1) into -1
18.522 * [backup-simplify]: Simplify (+ 0 -1) into -1
18.522 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
18.523 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
18.523 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
18.524 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
18.525 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
18.526 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
18.526 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
18.527 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
18.528 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
18.528 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
18.528 * [backup-simplify]: Simplify (- 0) into 0
18.529 * [backup-simplify]: Simplify (+ 0 0) into 0
18.529 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
18.530 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
18.531 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
18.532 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
18.532 * [taylor]: Taking taylor expansion of 0 in k
18.532 * [backup-simplify]: Simplify 0 into 0
18.532 * [backup-simplify]: Simplify 0 into 0
18.532 * [backup-simplify]: Simplify 0 into 0
18.532 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.533 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
18.535 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
18.535 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
18.535 * [backup-simplify]: Simplify (- 0) into 0
18.536 * [backup-simplify]: Simplify (+ 0 0) into 0
18.536 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
18.537 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
18.538 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
18.539 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
18.540 * [taylor]: Taking taylor expansion of 0 in k
18.540 * [backup-simplify]: Simplify 0 into 0
18.540 * [backup-simplify]: Simplify 0 into 0
18.540 * [backup-simplify]: Simplify 0 into 0
18.540 * [backup-simplify]: Simplify 0 into 0
18.540 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.541 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
18.544 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
18.545 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
18.545 * [backup-simplify]: Simplify (- 0) into 0
18.545 * [backup-simplify]: Simplify (+ 0 0) into 0
18.546 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
18.547 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
18.548 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
18.550 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
18.550 * [taylor]: Taking taylor expansion of 0 in k
18.550 * [backup-simplify]: Simplify 0 into 0
18.550 * [backup-simplify]: Simplify 0 into 0
18.551 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
18.552 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
18.552 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
18.552 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
18.552 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
18.552 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
18.552 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
18.552 * [taylor]: Taking taylor expansion of 1/2 in k
18.552 * [backup-simplify]: Simplify 1/2 into 1/2
18.552 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
18.552 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.552 * [taylor]: Taking taylor expansion of k in k
18.552 * [backup-simplify]: Simplify 0 into 0
18.552 * [backup-simplify]: Simplify 1 into 1
18.553 * [backup-simplify]: Simplify (/ 1 1) into 1
18.553 * [taylor]: Taking taylor expansion of 1 in k
18.553 * [backup-simplify]: Simplify 1 into 1
18.553 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
18.553 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
18.553 * [taylor]: Taking taylor expansion of -2 in k
18.553 * [backup-simplify]: Simplify -2 into -2
18.553 * [taylor]: Taking taylor expansion of (/ PI n) in k
18.553 * [taylor]: Taking taylor expansion of PI in k
18.553 * [backup-simplify]: Simplify PI into PI
18.553 * [taylor]: Taking taylor expansion of n in k
18.553 * [backup-simplify]: Simplify n into n
18.553 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
18.553 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
18.553 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
18.554 * [backup-simplify]: Simplify (+ 1 0) into 1
18.554 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
18.554 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
18.555 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
18.555 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
18.555 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
18.555 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
18.555 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
18.555 * [taylor]: Taking taylor expansion of 1/2 in n
18.555 * [backup-simplify]: Simplify 1/2 into 1/2
18.555 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
18.555 * [taylor]: Taking taylor expansion of (/ 1 k) in n
18.555 * [taylor]: Taking taylor expansion of k in n
18.555 * [backup-simplify]: Simplify k into k
18.555 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
18.555 * [taylor]: Taking taylor expansion of 1 in n
18.555 * [backup-simplify]: Simplify 1 into 1
18.555 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
18.555 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
18.555 * [taylor]: Taking taylor expansion of -2 in n
18.555 * [backup-simplify]: Simplify -2 into -2
18.555 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.555 * [taylor]: Taking taylor expansion of PI in n
18.555 * [backup-simplify]: Simplify PI into PI
18.555 * [taylor]: Taking taylor expansion of n in n
18.555 * [backup-simplify]: Simplify 0 into 0
18.555 * [backup-simplify]: Simplify 1 into 1
18.556 * [backup-simplify]: Simplify (/ PI 1) into PI
18.556 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
18.557 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
18.557 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
18.558 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
18.559 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
18.560 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
18.562 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
18.562 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
18.562 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
18.562 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
18.562 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
18.562 * [taylor]: Taking taylor expansion of 1/2 in n
18.562 * [backup-simplify]: Simplify 1/2 into 1/2
18.562 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
18.562 * [taylor]: Taking taylor expansion of (/ 1 k) in n
18.562 * [taylor]: Taking taylor expansion of k in n
18.562 * [backup-simplify]: Simplify k into k
18.562 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
18.562 * [taylor]: Taking taylor expansion of 1 in n
18.562 * [backup-simplify]: Simplify 1 into 1
18.562 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
18.562 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
18.562 * [taylor]: Taking taylor expansion of -2 in n
18.562 * [backup-simplify]: Simplify -2 into -2
18.562 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.562 * [taylor]: Taking taylor expansion of PI in n
18.562 * [backup-simplify]: Simplify PI into PI
18.562 * [taylor]: Taking taylor expansion of n in n
18.562 * [backup-simplify]: Simplify 0 into 0
18.562 * [backup-simplify]: Simplify 1 into 1
18.563 * [backup-simplify]: Simplify (/ PI 1) into PI
18.563 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
18.564 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
18.564 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
18.564 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
18.566 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
18.567 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
18.568 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
18.568 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
18.568 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
18.568 * [taylor]: Taking taylor expansion of 1/2 in k
18.568 * [backup-simplify]: Simplify 1/2 into 1/2
18.568 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
18.569 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
18.569 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.569 * [taylor]: Taking taylor expansion of k in k
18.569 * [backup-simplify]: Simplify 0 into 0
18.569 * [backup-simplify]: Simplify 1 into 1
18.569 * [backup-simplify]: Simplify (/ 1 1) into 1
18.569 * [taylor]: Taking taylor expansion of 1 in k
18.569 * [backup-simplify]: Simplify 1 into 1
18.569 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
18.569 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
18.569 * [taylor]: Taking taylor expansion of (* -2 PI) in k
18.569 * [taylor]: Taking taylor expansion of -2 in k
18.569 * [backup-simplify]: Simplify -2 into -2
18.569 * [taylor]: Taking taylor expansion of PI in k
18.569 * [backup-simplify]: Simplify PI into PI
18.570 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
18.571 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
18.571 * [taylor]: Taking taylor expansion of (log n) in k
18.571 * [taylor]: Taking taylor expansion of n in k
18.571 * [backup-simplify]: Simplify n into n
18.571 * [backup-simplify]: Simplify (log n) into (log n)
18.571 * [backup-simplify]: Simplify (+ 1 0) into 1
18.571 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
18.573 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
18.574 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
18.575 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
18.576 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
18.577 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
18.578 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
18.579 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
18.581 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
18.581 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
18.582 * [backup-simplify]: Simplify (+ 0 0) into 0
18.582 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
18.584 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
18.585 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
18.587 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
18.587 * [taylor]: Taking taylor expansion of 0 in k
18.587 * [backup-simplify]: Simplify 0 into 0
18.587 * [backup-simplify]: Simplify 0 into 0
18.587 * [backup-simplify]: Simplify 0 into 0
18.588 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.590 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
18.593 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
18.594 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
18.594 * [backup-simplify]: Simplify (+ 0 0) into 0
18.595 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
18.597 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
18.599 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
18.602 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
18.602 * [taylor]: Taking taylor expansion of 0 in k
18.602 * [backup-simplify]: Simplify 0 into 0
18.602 * [backup-simplify]: Simplify 0 into 0
18.602 * [backup-simplify]: Simplify 0 into 0
18.602 * [backup-simplify]: Simplify 0 into 0
18.603 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.604 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
18.611 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
18.611 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
18.612 * [backup-simplify]: Simplify (+ 0 0) into 0
18.613 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
18.615 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
18.617 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
18.620 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
18.620 * [taylor]: Taking taylor expansion of 0 in k
18.620 * [backup-simplify]: Simplify 0 into 0
18.620 * [backup-simplify]: Simplify 0 into 0
18.622 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
18.622 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1)
18.622 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k))
18.622 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0
18.622 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
18.622 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.622 * [taylor]: Taking taylor expansion of k in k
18.622 * [backup-simplify]: Simplify 0 into 0
18.622 * [backup-simplify]: Simplify 1 into 1
18.623 * [backup-simplify]: Simplify (/ 1 1) into 1
18.623 * [backup-simplify]: Simplify (sqrt 0) into 0
18.625 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
18.625 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
18.625 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.625 * [taylor]: Taking taylor expansion of k in k
18.625 * [backup-simplify]: Simplify 0 into 0
18.625 * [backup-simplify]: Simplify 1 into 1
18.625 * [backup-simplify]: Simplify (/ 1 1) into 1
18.626 * [backup-simplify]: Simplify (sqrt 0) into 0
18.627 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
18.627 * [backup-simplify]: Simplify 0 into 0
18.627 * [backup-simplify]: Simplify +nan.0 into +nan.0
18.628 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
18.632 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
18.632 * [backup-simplify]: Simplify +nan.0 into +nan.0
18.633 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.640 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
18.640 * [backup-simplify]: Simplify +nan.0 into +nan.0
18.640 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
18.640 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k)
18.640 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0
18.640 * [taylor]: Taking taylor expansion of (sqrt k) in k
18.640 * [taylor]: Taking taylor expansion of k in k
18.640 * [backup-simplify]: Simplify 0 into 0
18.640 * [backup-simplify]: Simplify 1 into 1
18.641 * [backup-simplify]: Simplify (sqrt 0) into 0
18.642 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
18.642 * [taylor]: Taking taylor expansion of (sqrt k) in k
18.642 * [taylor]: Taking taylor expansion of k in k
18.642 * [backup-simplify]: Simplify 0 into 0
18.642 * [backup-simplify]: Simplify 1 into 1
18.643 * [backup-simplify]: Simplify (sqrt 0) into 0
18.644 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
18.644 * [backup-simplify]: Simplify 0 into 0
18.644 * [backup-simplify]: Simplify +nan.0 into +nan.0
18.648 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
18.648 * [backup-simplify]: Simplify +nan.0 into +nan.0
18.652 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
18.652 * [backup-simplify]: Simplify +nan.0 into +nan.0
18.653 * [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))))))))
18.653 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k)))
18.653 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0
18.653 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
18.653 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
18.653 * [taylor]: Taking taylor expansion of (/ -1 k) in k
18.653 * [taylor]: Taking taylor expansion of -1 in k
18.653 * [backup-simplify]: Simplify -1 into -1
18.653 * [taylor]: Taking taylor expansion of k in k
18.653 * [backup-simplify]: Simplify 0 into 0
18.653 * [backup-simplify]: Simplify 1 into 1
18.654 * [backup-simplify]: Simplify (/ -1 1) into -1
18.654 * [backup-simplify]: Simplify (sqrt 0) into 0
18.656 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
18.656 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
18.656 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
18.656 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
18.656 * [taylor]: Taking taylor expansion of (/ -1 k) in k
18.656 * [taylor]: Taking taylor expansion of -1 in k
18.656 * [backup-simplify]: Simplify -1 into -1
18.656 * [taylor]: Taking taylor expansion of k in k
18.656 * [backup-simplify]: Simplify 0 into 0
18.656 * [backup-simplify]: Simplify 1 into 1
18.657 * [backup-simplify]: Simplify (/ -1 1) into -1
18.657 * [backup-simplify]: Simplify (sqrt 0) into 0
18.659 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
18.659 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
18.659 * [backup-simplify]: Simplify +nan.0 into +nan.0
18.660 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
18.664 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
18.666 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
18.666 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
18.667 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.672 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
18.676 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
18.676 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
18.677 * [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)))))
18.678 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 2 1)
18.678 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k))
18.678 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0
18.678 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
18.678 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.678 * [taylor]: Taking taylor expansion of k in k
18.678 * [backup-simplify]: Simplify 0 into 0
18.678 * [backup-simplify]: Simplify 1 into 1
18.678 * [backup-simplify]: Simplify (/ 1 1) into 1
18.679 * [backup-simplify]: Simplify (sqrt 0) into 0
18.680 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
18.680 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
18.680 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.680 * [taylor]: Taking taylor expansion of k in k
18.680 * [backup-simplify]: Simplify 0 into 0
18.680 * [backup-simplify]: Simplify 1 into 1
18.681 * [backup-simplify]: Simplify (/ 1 1) into 1
18.681 * [backup-simplify]: Simplify (sqrt 0) into 0
18.682 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
18.683 * [backup-simplify]: Simplify 0 into 0
18.683 * [backup-simplify]: Simplify +nan.0 into +nan.0
18.684 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
18.687 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
18.687 * [backup-simplify]: Simplify +nan.0 into +nan.0
18.688 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.693 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
18.693 * [backup-simplify]: Simplify +nan.0 into +nan.0
18.693 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
18.693 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k)
18.693 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0
18.693 * [taylor]: Taking taylor expansion of (sqrt k) in k
18.693 * [taylor]: Taking taylor expansion of k in k
18.693 * [backup-simplify]: Simplify 0 into 0
18.693 * [backup-simplify]: Simplify 1 into 1
18.694 * [backup-simplify]: Simplify (sqrt 0) into 0
18.695 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
18.695 * [taylor]: Taking taylor expansion of (sqrt k) in k
18.695 * [taylor]: Taking taylor expansion of k in k
18.695 * [backup-simplify]: Simplify 0 into 0
18.695 * [backup-simplify]: Simplify 1 into 1
18.696 * [backup-simplify]: Simplify (sqrt 0) into 0
18.697 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
18.697 * [backup-simplify]: Simplify 0 into 0
18.697 * [backup-simplify]: Simplify +nan.0 into +nan.0
18.701 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
18.701 * [backup-simplify]: Simplify +nan.0 into +nan.0
18.705 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
18.705 * [backup-simplify]: Simplify +nan.0 into +nan.0
18.706 * [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))))))))
18.706 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k)))
18.706 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0
18.706 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
18.706 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
18.706 * [taylor]: Taking taylor expansion of (/ -1 k) in k
18.706 * [taylor]: Taking taylor expansion of -1 in k
18.706 * [backup-simplify]: Simplify -1 into -1
18.706 * [taylor]: Taking taylor expansion of k in k
18.706 * [backup-simplify]: Simplify 0 into 0
18.706 * [backup-simplify]: Simplify 1 into 1
18.707 * [backup-simplify]: Simplify (/ -1 1) into -1
18.707 * [backup-simplify]: Simplify (sqrt 0) into 0
18.709 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
18.709 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
18.709 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
18.709 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
18.709 * [taylor]: Taking taylor expansion of (/ -1 k) in k
18.709 * [taylor]: Taking taylor expansion of -1 in k
18.709 * [backup-simplify]: Simplify -1 into -1
18.709 * [taylor]: Taking taylor expansion of k in k
18.709 * [backup-simplify]: Simplify 0 into 0
18.709 * [backup-simplify]: Simplify 1 into 1
18.710 * [backup-simplify]: Simplify (/ -1 1) into -1
18.710 * [backup-simplify]: Simplify (sqrt 0) into 0
18.712 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
18.712 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
18.712 * [backup-simplify]: Simplify +nan.0 into +nan.0
18.713 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
18.716 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
18.718 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
18.718 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
18.719 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.722 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
18.725 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
18.725 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
18.725 * [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)))))
18.726 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1)
18.726 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
18.726 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
18.726 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
18.726 * [taylor]: Taking taylor expansion of 2 in n
18.726 * [backup-simplify]: Simplify 2 into 2
18.726 * [taylor]: Taking taylor expansion of (* n PI) in n
18.726 * [taylor]: Taking taylor expansion of n in n
18.726 * [backup-simplify]: Simplify 0 into 0
18.726 * [backup-simplify]: Simplify 1 into 1
18.726 * [taylor]: Taking taylor expansion of PI in n
18.726 * [backup-simplify]: Simplify PI into PI
18.726 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
18.726 * [taylor]: Taking taylor expansion of 2 in n
18.726 * [backup-simplify]: Simplify 2 into 2
18.726 * [taylor]: Taking taylor expansion of (* n PI) in n
18.726 * [taylor]: Taking taylor expansion of n in n
18.726 * [backup-simplify]: Simplify 0 into 0
18.726 * [backup-simplify]: Simplify 1 into 1
18.726 * [taylor]: Taking taylor expansion of PI in n
18.726 * [backup-simplify]: Simplify PI into PI
18.726 * [backup-simplify]: Simplify (* 0 PI) into 0
18.727 * [backup-simplify]: Simplify (* 2 0) into 0
18.727 * [backup-simplify]: Simplify 0 into 0
18.728 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
18.729 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
18.729 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
18.730 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
18.730 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
18.730 * [backup-simplify]: Simplify 0 into 0
18.731 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
18.732 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
18.732 * [backup-simplify]: Simplify 0 into 0
18.732 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
18.733 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
18.733 * [backup-simplify]: Simplify 0 into 0
18.734 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
18.735 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
18.735 * [backup-simplify]: Simplify 0 into 0
18.736 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
18.737 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
18.737 * [backup-simplify]: Simplify 0 into 0
18.738 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
18.739 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
18.739 * [backup-simplify]: Simplify 0 into 0
18.740 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
18.740 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
18.740 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
18.740 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
18.740 * [taylor]: Taking taylor expansion of 2 in n
18.740 * [backup-simplify]: Simplify 2 into 2
18.740 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.740 * [taylor]: Taking taylor expansion of PI in n
18.740 * [backup-simplify]: Simplify PI into PI
18.740 * [taylor]: Taking taylor expansion of n in n
18.740 * [backup-simplify]: Simplify 0 into 0
18.740 * [backup-simplify]: Simplify 1 into 1
18.741 * [backup-simplify]: Simplify (/ PI 1) into PI
18.741 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
18.741 * [taylor]: Taking taylor expansion of 2 in n
18.741 * [backup-simplify]: Simplify 2 into 2
18.741 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.741 * [taylor]: Taking taylor expansion of PI in n
18.741 * [backup-simplify]: Simplify PI into PI
18.741 * [taylor]: Taking taylor expansion of n in n
18.741 * [backup-simplify]: Simplify 0 into 0
18.741 * [backup-simplify]: Simplify 1 into 1
18.741 * [backup-simplify]: Simplify (/ PI 1) into PI
18.741 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
18.742 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
18.742 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
18.743 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
18.743 * [backup-simplify]: Simplify 0 into 0
18.743 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.744 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
18.744 * [backup-simplify]: Simplify 0 into 0
18.745 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.745 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
18.745 * [backup-simplify]: Simplify 0 into 0
18.746 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.748 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
18.748 * [backup-simplify]: Simplify 0 into 0
18.749 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.751 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
18.751 * [backup-simplify]: Simplify 0 into 0
18.752 * [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
18.754 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
18.754 * [backup-simplify]: Simplify 0 into 0
18.754 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
18.755 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
18.755 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
18.755 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
18.755 * [taylor]: Taking taylor expansion of -2 in n
18.755 * [backup-simplify]: Simplify -2 into -2
18.755 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.755 * [taylor]: Taking taylor expansion of PI in n
18.755 * [backup-simplify]: Simplify PI into PI
18.755 * [taylor]: Taking taylor expansion of n in n
18.755 * [backup-simplify]: Simplify 0 into 0
18.755 * [backup-simplify]: Simplify 1 into 1
18.756 * [backup-simplify]: Simplify (/ PI 1) into PI
18.756 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
18.756 * [taylor]: Taking taylor expansion of -2 in n
18.756 * [backup-simplify]: Simplify -2 into -2
18.756 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.756 * [taylor]: Taking taylor expansion of PI in n
18.756 * [backup-simplify]: Simplify PI into PI
18.756 * [taylor]: Taking taylor expansion of n in n
18.756 * [backup-simplify]: Simplify 0 into 0
18.756 * [backup-simplify]: Simplify 1 into 1
18.757 * [backup-simplify]: Simplify (/ PI 1) into PI
18.757 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
18.758 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
18.759 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
18.760 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
18.760 * [backup-simplify]: Simplify 0 into 0
18.761 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.762 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
18.762 * [backup-simplify]: Simplify 0 into 0
18.763 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.765 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
18.765 * [backup-simplify]: Simplify 0 into 0
18.766 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.767 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
18.767 * [backup-simplify]: Simplify 0 into 0
18.769 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.773 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
18.773 * [backup-simplify]: Simplify 0 into 0
18.775 * [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
18.777 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
18.777 * [backup-simplify]: Simplify 0 into 0
18.778 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
18.778 * * * [progress]: simplifying candidates
18.778 * * * * [progress]: [ 1 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (log1p (expm1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.778 * * * * [progress]: [ 2 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (expm1 (log1p (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.778 * * * * [progress]: [ 3 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (exp (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.778 * * * * [progress]: [ 4 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (exp (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.778 * * * * [progress]: [ 5 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (exp (* (log (* n (* 2 PI))) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.778 * * * * [progress]: [ 6 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (exp (* (log (* n (* 2 PI))) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.778 * * * * [progress]: [ 7 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.778 * * * * [progress]: [ 8 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.778 * * * * [progress]: [ 9 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (* 1 (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.778 * * * * [progress]: [ 10 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (pow (* n (* 2 PI)) (/ 1 2)) (pow (* n (* 2 PI)) (/ k 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.779 * * * * [progress]: [ 11 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.779 * * * * [progress]: [ 12 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.779 * * * * [progress]: [ 13 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.779 * * * * [progress]: [ 14 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.779 * * * * [progress]: [ 15 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.779 * * * * [progress]: [ 16 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.779 * * * * [progress]: [ 17 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.779 * * * * [progress]: [ 18 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.779 * * * * [progress]: [ 19 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.779 * * * * [progress]: [ 20 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.780 * * * * [progress]: [ 21 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.780 * * * * [progress]: [ 22 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.780 * * * * [progress]: [ 23 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.780 * * * * [progress]: [ 24 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.780 * * * * [progress]: [ 25 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.780 * * * * [progress]: [ 26 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.780 * * * * [progress]: [ 27 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.780 * * * * [progress]: [ 28 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.780 * * * * [progress]: [ 29 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.780 * * * * [progress]: [ 30 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ 1 1)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.780 * * * * [progress]: [ 31 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.780 * * * * [progress]: [ 32 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (- 1 k)) (/ 1 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.780 * * * * [progress]: [ 33 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (* (pow n (/ (- 1 k) 2)) (pow (* 2 PI) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.781 * * * * [progress]: [ 34 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 1) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.781 * * * * [progress]: [ 35 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (exp (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.781 * * * * [progress]: [ 36 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (log (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.781 * * * * [progress]: [ 37 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (* (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.781 * * * * [progress]: [ 38 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.781 * * * * [progress]: [ 39 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.781 * * * * [progress]: [ 40 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (* 1 (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.781 * * * * [progress]: [ 41 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.781 * * * * [progress]: [ 42 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (posit16->real (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.781 * * * * [progress]: [ 43 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (log1p (expm1 (/ 1 (sqrt k)))))))>
18.781 * * * * [progress]: [ 44 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (expm1 (log1p (/ 1 (sqrt k)))))))>
18.781 * * * * [progress]: [ 45 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (pow (sqrt k) -1))))>
18.781 * * * * [progress]: [ 46 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (pow k (- 1/2)))))>
18.781 * * * * [progress]: [ 47 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (pow (sqrt k) (- 1)))))>
18.781 * * * * [progress]: [ 48 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (pow k (- (/ 1 2))))))>
18.782 * * * * [progress]: [ 49 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (pow (/ 1 (sqrt k)) 1))))>
18.782 * * * * [progress]: [ 50 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (exp (- (log (sqrt k)))))))>
18.782 * * * * [progress]: [ 51 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (exp (- 0 (log (sqrt k)))))))>
18.782 * * * * [progress]: [ 52 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (exp (- (log 1) (log (sqrt k)))))))>
18.782 * * * * [progress]: [ 53 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (exp (log (/ 1 (sqrt k)))))))>
18.782 * * * * [progress]: [ 54 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (log (exp (/ 1 (sqrt k)))))))>
18.782 * * * * [progress]: [ 55 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (cbrt (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k)))))))>
18.782 * * * * [progress]: [ 56 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k)))))))>
18.782 * * * * [progress]: [ 57 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (cbrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))))))>
18.782 * * * * [progress]: [ 58 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))))))>
18.782 * * * * [progress]: [ 59 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ (- 1) (- (sqrt k))))))>
18.782 * * * * [progress]: [ 60 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1) (cbrt (sqrt k)))))))>
18.782 * * * * [progress]: [ 61 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1) (sqrt (cbrt k)))))))>
18.783 * * * * [progress]: [ 62 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k)))))))>
18.783 * * * * [progress]: [ 63 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (/ (cbrt 1) (sqrt k))))))>
18.783 * * * * [progress]: [ 64 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k)))))))>
18.783 * * * * [progress]: [ 65 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sqrt k))))))>
18.783 * * * * [progress]: [ 66 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1) (cbrt (sqrt k)))))))>
18.783 * * * * [progress]: [ 67 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1) (sqrt (cbrt k)))))))>
18.783 * * * * [progress]: [ 68 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))))))>
18.783 * * * * [progress]: [ 69 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ (sqrt 1) (sqrt 1)) (/ (sqrt 1) (sqrt k))))))>
18.783 * * * * [progress]: [ 70 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))))))>
18.783 * * * * [progress]: [ 71 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ (sqrt 1) 1) (/ (sqrt 1) (sqrt k))))))>
18.783 * * * * [progress]: [ 72 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1 (cbrt (sqrt k)))))))>
18.783 * * * * [progress]: [ 73 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1 (sqrt (cbrt k)))))))>
18.783 * * * * [progress]: [ 74 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))))))>
18.784 * * * * [progress]: [ 75 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ 1 (sqrt 1)) (/ 1 (sqrt k))))))>
18.784 * * * * [progress]: [ 76 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))))))>
18.784 * * * * [progress]: [ 77 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ 1 1) (/ 1 (sqrt k))))))>
18.784 * * * * [progress]: [ 78 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* 1 (/ 1 (sqrt k))))))>
18.784 * * * * [progress]: [ 79 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* 1 (/ 1 (sqrt k))))))>
18.784 * * * * [progress]: [ 80 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (/ (sqrt k) 1)))))>
18.784 * * * * [progress]: [ 81 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))))>
18.784 * * * * [progress]: [ 82 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))))>
18.784 * * * * [progress]: [ 83 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))))))>
18.784 * * * * [progress]: [ 84 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ (/ 1 (sqrt 1)) (sqrt k)))))>
18.784 * * * * [progress]: [ 85 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))))))>
18.784 * * * * [progress]: [ 86 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ (/ 1 1) (sqrt k)))))>
18.784 * * * * [progress]: [ 87 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt k) (cbrt 1))))))>
18.784 * * * * [progress]: [ 88 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ (sqrt 1) (/ (sqrt k) (sqrt 1))))))>
18.785 * * * * [progress]: [ 89 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (/ (sqrt k) 1)))))>
18.785 * * * * [progress]: [ 90 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (posit16->real (real->posit16 (/ 1 (sqrt k)))))))>
18.785 * * * * [progress]: [ 91 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (log1p (expm1 (/ 1 (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.785 * * * * [progress]: [ 92 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (expm1 (log1p (/ 1 (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.785 * * * * [progress]: [ 93 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (pow (sqrt k) -1))) (sqrt (/ 1 (sqrt k)))))>
18.785 * * * * [progress]: [ 94 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (pow k (- 1/2)))) (sqrt (/ 1 (sqrt k)))))>
18.785 * * * * [progress]: [ 95 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (pow (sqrt k) (- 1)))) (sqrt (/ 1 (sqrt k)))))>
18.785 * * * * [progress]: [ 96 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (pow k (- (/ 1 2))))) (sqrt (/ 1 (sqrt k)))))>
18.785 * * * * [progress]: [ 97 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (pow (/ 1 (sqrt k)) 1))) (sqrt (/ 1 (sqrt k)))))>
18.785 * * * * [progress]: [ 98 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (exp (- (log (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.785 * * * * [progress]: [ 99 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (exp (- 0 (log (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.785 * * * * [progress]: [ 100 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (exp (- (log 1) (log (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.785 * * * * [progress]: [ 101 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (exp (log (/ 1 (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.785 * * * * [progress]: [ 102 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (log (exp (/ 1 (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.786 * * * * [progress]: [ 103 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.786 * * * * [progress]: [ 104 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.786 * * * * [progress]: [ 105 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.786 * * * * [progress]: [ 106 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.786 * * * * [progress]: [ 107 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ (- 1) (- (sqrt k))))) (sqrt (/ 1 (sqrt k)))))>
18.786 * * * * [progress]: [ 108 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1) (cbrt (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.786 * * * * [progress]: [ 109 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1) (sqrt (cbrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.786 * * * * [progress]: [ 110 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.786 * * * * [progress]: [ 111 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (/ (cbrt 1) (sqrt k))))) (sqrt (/ 1 (sqrt k)))))>
18.786 * * * * [progress]: [ 112 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.786 * * * * [progress]: [ 113 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sqrt k))))) (sqrt (/ 1 (sqrt k)))))>
18.786 * * * * [progress]: [ 114 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1) (cbrt (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.786 * * * * [progress]: [ 115 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1) (sqrt (cbrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.787 * * * * [progress]: [ 116 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.787 * * * * [progress]: [ 117 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (/ (sqrt 1) (sqrt 1)) (/ (sqrt 1) (sqrt k))))) (sqrt (/ 1 (sqrt k)))))>
18.787 * * * * [progress]: [ 118 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.787 * * * * [progress]: [ 119 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (/ (sqrt 1) 1) (/ (sqrt 1) (sqrt k))))) (sqrt (/ 1 (sqrt k)))))>
18.787 * * * * [progress]: [ 120 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1 (cbrt (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.787 * * * * [progress]: [ 121 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1 (sqrt (cbrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.787 * * * * [progress]: [ 122 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.787 * * * * [progress]: [ 123 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (/ 1 (sqrt 1)) (/ 1 (sqrt k))))) (sqrt (/ 1 (sqrt k)))))>
18.787 * * * * [progress]: [ 124 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.787 * * * * [progress]: [ 125 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* (/ 1 1) (/ 1 (sqrt k))))) (sqrt (/ 1 (sqrt k)))))>
18.787 * * * * [progress]: [ 126 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* 1 (/ 1 (sqrt k))))) (sqrt (/ 1 (sqrt k)))))>
18.787 * * * * [progress]: [ 127 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (* 1 (/ 1 (sqrt k))))) (sqrt (/ 1 (sqrt k)))))>
18.787 * * * * [progress]: [ 128 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (/ (sqrt k) 1)))) (sqrt (/ 1 (sqrt k)))))>
18.788 * * * * [progress]: [ 129 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))) (sqrt (/ 1 (sqrt k)))))>
18.788 * * * * [progress]: [ 130 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))) (sqrt (/ 1 (sqrt k)))))>
18.788 * * * * [progress]: [ 131 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))))) (sqrt (/ 1 (sqrt k)))))>
18.788 * * * * [progress]: [ 132 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ (/ 1 (sqrt 1)) (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.788 * * * * [progress]: [ 133 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))))) (sqrt (/ 1 (sqrt k)))))>
18.788 * * * * [progress]: [ 134 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ (/ 1 1) (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.788 * * * * [progress]: [ 135 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt k) (cbrt 1))))) (sqrt (/ 1 (sqrt k)))))>
18.788 * * * * [progress]: [ 136 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ (sqrt 1) (/ (sqrt k) (sqrt 1))))) (sqrt (/ 1 (sqrt k)))))>
18.788 * * * * [progress]: [ 137 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (/ (sqrt k) 1)))) (sqrt (/ 1 (sqrt k)))))>
18.788 * * * * [progress]: [ 138 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (posit16->real (real->posit16 (/ 1 (sqrt k)))))) (sqrt (/ 1 (sqrt k)))))>
18.788 * * * * [progress]: [ 139 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (log1p (expm1 (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.788 * * * * [progress]: [ 140 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (expm1 (log1p (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.788 * * * * [progress]: [ 141 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.788 * * * * [progress]: [ 142 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.789 * * * * [progress]: [ 143 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (pow (* n (* 2 PI)) 1) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.789 * * * * [progress]: [ 144 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (exp (+ (log n) (+ (log 2) (log PI)))) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.789 * * * * [progress]: [ 145 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (exp (+ (log n) (log (* 2 PI)))) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.789 * * * * [progress]: [ 146 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (exp (log (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.789 * * * * [progress]: [ 147 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (log (exp (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.789 * * * * [progress]: [ 148 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.789 * * * * [progress]: [ 149 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.789 * * * * [progress]: [ 150 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.789 * * * * [progress]: [ 151 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.789 * * * * [progress]: [ 152 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.789 * * * * [progress]: [ 153 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* 1 (* n (* 2 PI))) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.789 * * * * [progress]: [ 154 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.789 * * * * [progress]: [ 155 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.790 * * * * [progress]: [ 156 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.790 * * * * [progress]: [ 157 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* 1 (* n (* 2 PI))) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.790 * * * * [progress]: [ 158 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.790 * * * * [progress]: [ 159 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.790 * * * * [progress]: [ 160 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.790 * * * * [progress]: [ 161 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.790 * * * * [progress]: [ 162 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.790 * * * * [progress]: [ 163 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))))))>
18.790 * * * * [progress]: [ 164 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))))))>
18.790 * * * * [progress]: [ 165 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))))))>
18.790 * * * * [progress]: [ 166 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))))) (sqrt (/ 1 (sqrt k)))))>
18.790 * * * * [progress]: [ 167 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))))) (sqrt (/ 1 (sqrt k)))))>
18.790 * * * * [progress]: [ 168 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))))) (sqrt (/ 1 (sqrt k)))))>
18.790 * * * * [progress]: [ 169 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.791 * * * * [progress]: [ 170 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.791 * * * * [progress]: [ 171 / 171 ] simplifiying candidate #<alt (λ (k n) (* (* (pow (* 2 (* n PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (/ 1 (sqrt k)))))>
18.793 * [simplify]: Simplifying:
  (expm1 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (log1p (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2))
  (* (+ (log n) (log (* 2 PI))) (/ (- 1 k) 2))
  (* (log (* n (* 2 PI))) (/ (- 1 k) 2))
  (* (log (* n (* 2 PI))) (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (pow (* n (* 2 PI)) (/ 1 2))
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) 1))
  (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (pow (* n (* 2 PI)) (/ 1 1))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (+ (sqrt 1) (sqrt k)) 1))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (/ (+ 1 (sqrt k)) 1))
  (pow (* n (* 2 PI)) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (pow (* n (* 2 PI)) (/ 1 1))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (- 1 k))
  (pow n (/ (- 1 k) 2))
  (pow (* 2 PI) (/ (- 1 k) 2))
  (log (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
  (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
  (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (expm1 (/ 1 (sqrt k)))
  (log1p (/ 1 (sqrt k)))
  (- 1/2)
  (- 1)
  (- (/ 1 2))
  (- (log (sqrt k)))
  (- 0 (log (sqrt k)))
  (- (log 1) (log (sqrt k)))
  (log (/ 1 (sqrt k)))
  (exp (/ 1 (sqrt k)))
  (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
  (cbrt (/ 1 (sqrt k)))
  (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (- 1)
  (- (sqrt k))
  (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt 1) (cbrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt 1) (sqrt (cbrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt 1))
  (/ (cbrt 1) (sqrt k))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) 1)
  (/ (cbrt 1) (sqrt k))
  (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1) (cbrt (sqrt k)))
  (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt 1) (sqrt (cbrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt 1))
  (/ (sqrt 1) (sqrt k))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) 1)
  (/ (sqrt 1) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 1)
  (/ 1 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1)
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 1)
  (/ (sqrt k) (cbrt 1))
  (/ (sqrt k) (sqrt 1))
  (/ (sqrt k) 1)
  (real->posit16 (/ 1 (sqrt k)))
  (expm1 (/ 1 (sqrt k)))
  (log1p (/ 1 (sqrt k)))
  (- 1/2)
  (- 1)
  (- (/ 1 2))
  (- (log (sqrt k)))
  (- 0 (log (sqrt k)))
  (- (log 1) (log (sqrt k)))
  (log (/ 1 (sqrt k)))
  (exp (/ 1 (sqrt k)))
  (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
  (cbrt (/ 1 (sqrt k)))
  (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (- 1)
  (- (sqrt k))
  (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt 1) (cbrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt 1) (sqrt (cbrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt 1))
  (/ (cbrt 1) (sqrt k))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) 1)
  (/ (cbrt 1) (sqrt k))
  (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1) (cbrt (sqrt k)))
  (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt 1) (sqrt (cbrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt 1))
  (/ (sqrt 1) (sqrt k))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) 1)
  (/ (sqrt 1) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 1)
  (/ 1 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1)
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 1)
  (/ (sqrt k) (cbrt 1))
  (/ (sqrt k) (sqrt 1))
  (/ (sqrt k) 1)
  (real->posit16 (/ 1 (sqrt k)))
  (expm1 (* n (* 2 PI)))
  (log1p (* n (* 2 PI)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
  (- (+ (* +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)) (- (+ +nan.0 (- (* +nan.0 k))))))
  (- (+ (* +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 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
18.798 * * [simplify]: iteration 1: (246 enodes)
18.930 * * [simplify]: iteration 2: (1043 enodes)
19.244 * * [simplify]: Extracting #0: cost 92 inf + 0
19.245 * * [simplify]: Extracting #1: cost 477 inf + 42
19.248 * * [simplify]: Extracting #2: cost 745 inf + 16290
19.259 * * [simplify]: Extracting #3: cost 638 inf + 68353
19.287 * * [simplify]: Extracting #4: cost 295 inf + 176337
19.343 * * [simplify]: Extracting #5: cost 88 inf + 257146
19.403 * * [simplify]: Extracting #6: cost 28 inf + 285121
19.461 * * [simplify]: Extracting #7: cost 1 inf + 293131
19.546 * * [simplify]: Extracting #8: cost 0 inf + 292718
19.627 * [simplify]: Simplified to:
  (expm1 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (log1p (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (pow (* (* PI 2) n) (/ 1 2))
  (pow (* (* PI 2) n) (/ k 2))
  (pow (* (* PI 2) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* PI 2) n) (sqrt (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* (* PI 2) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* (* PI 2) n) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* (* PI 2) n) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* PI 2) n) (sqrt (- 1 k)))
  (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (/ (/ (+ (sqrt 1) (sqrt k)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)))
  (pow (* (* PI 2) n) (+ (sqrt 1) (sqrt k)))
  (pow (* (* PI 2) n) (/ (/ (+ 1 (sqrt k)) (cbrt 2)) (cbrt 2)))
  (pow (* (* PI 2) n) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* (* PI 2) n) (+ 1 (sqrt k)))
  (pow (* (* PI 2) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* PI 2) n) (/ 1 (sqrt 2)))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (- 1 k))
  (pow n (/ (- 1 k) 2))
  (pow (* PI 2) (/ (- 1 k) 2))
  (* (/ (- 1 k) 2) (log (* (* PI 2) n)))
  (exp (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (* (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))) (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2))))
  (cbrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (pow (pow (* (* PI 2) n) (/ (- 1 k) 2)) 3)
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2))
  (pow (* (* PI 2) n) (/ (/ (- 1 k) 2) 2))
  (real->posit16 (pow (* (* PI 2) n) (/ (- 1 k) 2)))
  (expm1 (/ 1 (sqrt k)))
  (log1p (/ 1 (sqrt k)))
  (- 1/2)
  (- 1)
  (/ (- 1) 2)
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (exp (/ 1 (sqrt k)))
  (/ (/ 1 k) (sqrt k))
  (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
  (cbrt (/ 1 (sqrt k)))
  (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (- 1)
  (- (sqrt k))
  (* (/ (cbrt 1) (cbrt (sqrt k))) (/ (cbrt 1) (cbrt (sqrt k))))
  (/ (cbrt 1) (cbrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (fabs (cbrt k)))
  (/ (cbrt 1) (sqrt (cbrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt 1))
  (/ (cbrt 1) (sqrt k))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (* (cbrt 1) (cbrt 1))
  (/ (cbrt 1) (sqrt k))
  (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1) (cbrt (sqrt k)))
  (/ (sqrt 1) (fabs (cbrt k)))
  (/ (sqrt 1) (sqrt (cbrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  1
  (/ (sqrt 1) (sqrt k))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (sqrt 1)
  (/ (sqrt 1) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt k))
  (sqrt k)
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ (sqrt k) (cbrt 1))
  (/ (sqrt k) (sqrt 1))
  (sqrt k)
  (real->posit16 (/ 1 (sqrt k)))
  (expm1 (/ 1 (sqrt k)))
  (log1p (/ 1 (sqrt k)))
  (- 1/2)
  (- 1)
  (/ (- 1) 2)
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (exp (/ 1 (sqrt k)))
  (/ (/ 1 k) (sqrt k))
  (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
  (cbrt (/ 1 (sqrt k)))
  (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (- 1)
  (- (sqrt k))
  (* (/ (cbrt 1) (cbrt (sqrt k))) (/ (cbrt 1) (cbrt (sqrt k))))
  (/ (cbrt 1) (cbrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (fabs (cbrt k)))
  (/ (cbrt 1) (sqrt (cbrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt 1))
  (/ (cbrt 1) (sqrt k))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (* (cbrt 1) (cbrt 1))
  (/ (cbrt 1) (sqrt k))
  (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1) (cbrt (sqrt k)))
  (/ (sqrt 1) (fabs (cbrt k)))
  (/ (sqrt 1) (sqrt (cbrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  1
  (/ (sqrt 1) (sqrt k))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (sqrt 1)
  (/ (sqrt 1) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt k))
  (sqrt k)
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ (sqrt k) (cbrt 1))
  (/ (sqrt k) (sqrt 1))
  (sqrt k)
  (real->posit16 (/ 1 (sqrt k)))
  (expm1 (* (* PI 2) n))
  (log1p (* (* PI 2) n))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (* (exp (* n PI)) (exp (* n PI)))
  (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n))
  (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n))
  (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n)))
  (cbrt (* (* PI 2) n))
  (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (* n 2)
  (* PI (* (cbrt n) 2))
  (* (sqrt n) (* PI 2))
  (* (* PI 2) n)
  (real->posit16 (* (* PI 2) n))
  (fma (* 1/4 (log (* PI 2))) (* (exp (* 1/2 (log (* (* PI 2) n)))) (* (log n) (* k k))) (- (fma 1/8 (* (* (* (log n) k) (* (log n) k)) (exp (* 1/2 (log (* (* PI 2) n))))) (fma (* 1/8 (* (log (* PI 2)) (log (* PI 2)))) (* (* k k) (exp (* 1/2 (log (* (* PI 2) n))))) (exp (* 1/2 (log (* (* PI 2) n)))))) (* 1/2 (* k (+ (* (log n) (exp (* 1/2 (log (* (* PI 2) n))))) (* (log (* PI 2)) (exp (* 1/2 (log (* (* PI 2) n))))))))))
  (exp (* 1/2 (* (log (* (* PI 2) n)) (- 1 k))))
  (exp (* (* (- 1 k) (- (log (* PI -2)) (log (/ -1 n)))) 1/2))
  (- (+ (- (* (* k k) +nan.0) +nan.0) (* k +nan.0)))
  (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ +nan.0 (* k (* k k)))))
  (+ (- (/ +nan.0 k) +nan.0) (- (/ +nan.0 (* k k))))
  (- (+ (- (* (* k k) +nan.0) +nan.0) (* k +nan.0)))
  (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ +nan.0 (* k (* k k)))))
  (+ (- (/ +nan.0 k) +nan.0) (- (/ +nan.0 (* k k))))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (* (* PI 2) n)
19.641 * * * [progress]: adding candidates to table
22.303 * [progress]: [Phase 3 of 3] Extracting.
22.303 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ 1 2)) (pow (* n (* 2 PI)) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))> #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (+ (sqrt k) 1)) (/ (- 1 (sqrt k)) 2)) (sqrt k)))> #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ 1 (fabs (cbrt k))) (/ 1 (sqrt (cbrt k)))))))> #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (fabs (cbrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))> #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))))))> #<alt (λ (k n) (/ (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (fabs (cbrt k))) (sqrt (cbrt k))))>)
22.305 * * * [regime-changes]: Trying 2 branch expressions: (n k)
22.305 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ 1 2)) (pow (* n (* 2 PI)) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))> #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (+ (sqrt k) 1)) (/ (- 1 (sqrt k)) 2)) (sqrt k)))> #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ 1 (fabs (cbrt k))) (/ 1 (sqrt (cbrt k)))))))> #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (fabs (cbrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))> #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))))))> #<alt (λ (k n) (/ (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (fabs (cbrt k))) (sqrt (cbrt k))))>)
22.386 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (/ 1 2)) (pow (* n (* 2 PI)) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))) (sqrt k)))> #<alt (λ (k n) (/ (pow (pow (* (* PI 2) n) (+ (sqrt k) 1)) (/ (- 1 (sqrt k)) 2)) (sqrt k)))> #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ 1 (fabs (cbrt k))) (/ 1 (sqrt (cbrt k)))))))> #<alt (λ (k n) (* (/ (pow n (/ (- 1 k) 2)) (fabs (cbrt k))) (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))))> #<alt (λ (k n) (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k)))) (sqrt (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))))))> #<alt (λ (k n) (/ (/ (pow (* (* PI 2) n) (/ (- 1 k) 2)) (fabs (cbrt k))) (sqrt (cbrt k))))>)
22.484 * * * [regime]: Found split indices: #<option (#s(si 5 255))>
22.485 * [simplify]: Simplifying:
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
22.485 * * [simplify]: iteration 1: (13 enodes)
22.488 * * [simplify]: iteration 2: (18 enodes)
22.490 * * [simplify]: Extracting #0: cost 1 inf + 0
22.490 * * [simplify]: Extracting #1: cost 3 inf + 0
22.490 * * [simplify]: Extracting #2: cost 7 inf + 0
22.490 * * [simplify]: Extracting #3: cost 11 inf + 1
22.490 * * [simplify]: Extracting #4: cost 5 inf + 252
22.490 * * [simplify]: Extracting #5: cost 3 inf + 295
22.490 * * [simplify]: Extracting #6: cost 1 inf + 753
22.491 * * [simplify]: Extracting #7: cost 0 inf + 1248
22.491 * [simplify]: Simplified to:
  (* (/ 1 (sqrt k)) (pow (* (* PI 2) n) (/ (- 1 k) 2)))
31.876 * [regime-testing]: Baseline error score: 0.3551739828205917
31.880 * [regime-testing]: Oracle error score: 0.04248427342157948
31.889 * [regime-testing]: End program error score: 0.3551739828205917