59.099 * [progress]: [Phase 1 of 3] Setting up.
0.002 * * * [progress]: [1/2] Preparing points
0.267 * * * [progress]: [2/2] Setting up program.
0.273 * [progress]: [Phase 2 of 3] Improving.
0.274 * * * * [progress]: [ 1 / 1 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
0.274 * [simplify]: Simplifying:
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.274 * * [simplify]: iteration 0: 13 enodes
0.280 * * [simplify]: iteration 1: 31 enodes
0.293 * * [simplify]: iteration 2: 62 enodes
0.317 * * [simplify]: iteration 3: 124 enodes
0.394 * * [simplify]: iteration 4: 327 enodes
0.622 * * [simplify]: iteration 5: 929 enodes
2.081 * * [simplify]: iteration 6: 2719 enodes
2.918 * * [simplify]: iteration complete: 5000 enodes
2.918 * * [simplify]: Extracting #0: cost 1 inf + 0
2.918 * * [simplify]: Extracting #1: cost 61 inf + 0
2.920 * * [simplify]: Extracting #2: cost 488 inf + 1
2.923 * * [simplify]: Extracting #3: cost 953 inf + 92
2.930 * * [simplify]: Extracting #4: cost 921 inf + 18841
2.945 * * [simplify]: Extracting #5: cost 645 inf + 66373
3.028 * * [simplify]: Extracting #6: cost 241 inf + 329522
3.168 * * [simplify]: Extracting #7: cost 5 inf + 560024
3.301 * * [simplify]: Extracting #8: cost 0 inf + 561759
3.465 * * [simplify]: Extracting #9: cost 0 inf + 561250
3.606 * [simplify]: Simplified to:
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
3.611 * * [progress]: iteration 1 / 4
3.611 * * * [progress]: picking best candidate
3.617 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))>
3.617 * * * [progress]: localizing error
3.641 * * * [progress]: generating rewritten candidates
3.641 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
3.658 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1)
3.677 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
3.706 * * * [progress]: generating series expansions
3.706 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
3.707 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
3.707 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
3.707 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
3.707 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
3.707 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
3.707 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
3.707 * [taylor]: Taking taylor expansion of 1/2 in k
3.707 * [backup-simplify]: Simplify 1/2 into 1/2
3.707 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
3.707 * [taylor]: Taking taylor expansion of 1/2 in k
3.707 * [backup-simplify]: Simplify 1/2 into 1/2
3.707 * [taylor]: Taking taylor expansion of k in k
3.707 * [backup-simplify]: Simplify 0 into 0
3.707 * [backup-simplify]: Simplify 1 into 1
3.707 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
3.707 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
3.707 * [taylor]: Taking taylor expansion of 2 in k
3.707 * [backup-simplify]: Simplify 2 into 2
3.707 * [taylor]: Taking taylor expansion of (* n PI) in k
3.707 * [taylor]: Taking taylor expansion of n in k
3.707 * [backup-simplify]: Simplify n into n
3.707 * [taylor]: Taking taylor expansion of PI in k
3.707 * [backup-simplify]: Simplify PI into PI
3.707 * [backup-simplify]: Simplify (* n PI) into (* n PI)
3.707 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
3.707 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
3.708 * [backup-simplify]: Simplify (* 1/2 0) into 0
3.709 * [backup-simplify]: Simplify (- 0) into 0
3.709 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.709 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
3.710 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
3.710 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
3.710 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
3.710 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
3.710 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
3.710 * [taylor]: Taking taylor expansion of 1/2 in n
3.710 * [backup-simplify]: Simplify 1/2 into 1/2
3.710 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
3.710 * [taylor]: Taking taylor expansion of 1/2 in n
3.710 * [backup-simplify]: Simplify 1/2 into 1/2
3.710 * [taylor]: Taking taylor expansion of k in n
3.710 * [backup-simplify]: Simplify k into k
3.710 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
3.710 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.710 * [taylor]: Taking taylor expansion of 2 in n
3.710 * [backup-simplify]: Simplify 2 into 2
3.710 * [taylor]: Taking taylor expansion of (* n PI) in n
3.710 * [taylor]: Taking taylor expansion of n in n
3.710 * [backup-simplify]: Simplify 0 into 0
3.710 * [backup-simplify]: Simplify 1 into 1
3.710 * [taylor]: Taking taylor expansion of PI in n
3.710 * [backup-simplify]: Simplify PI into PI
3.711 * [backup-simplify]: Simplify (* 0 PI) into 0
3.711 * [backup-simplify]: Simplify (* 2 0) into 0
3.713 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.715 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
3.716 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.716 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
3.716 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
3.716 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
3.717 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.718 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
3.719 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
3.719 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
3.719 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
3.719 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
3.719 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
3.719 * [taylor]: Taking taylor expansion of 1/2 in n
3.719 * [backup-simplify]: Simplify 1/2 into 1/2
3.719 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
3.719 * [taylor]: Taking taylor expansion of 1/2 in n
3.719 * [backup-simplify]: Simplify 1/2 into 1/2
3.719 * [taylor]: Taking taylor expansion of k in n
3.719 * [backup-simplify]: Simplify k into k
3.719 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
3.719 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.719 * [taylor]: Taking taylor expansion of 2 in n
3.719 * [backup-simplify]: Simplify 2 into 2
3.719 * [taylor]: Taking taylor expansion of (* n PI) in n
3.719 * [taylor]: Taking taylor expansion of n in n
3.719 * [backup-simplify]: Simplify 0 into 0
3.719 * [backup-simplify]: Simplify 1 into 1
3.719 * [taylor]: Taking taylor expansion of PI in n
3.719 * [backup-simplify]: Simplify PI into PI
3.719 * [backup-simplify]: Simplify (* 0 PI) into 0
3.719 * [backup-simplify]: Simplify (* 2 0) into 0
3.720 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.721 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
3.722 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.722 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
3.722 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
3.722 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
3.723 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.724 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
3.724 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
3.725 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
3.725 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
3.725 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
3.725 * [taylor]: Taking taylor expansion of 1/2 in k
3.725 * [backup-simplify]: Simplify 1/2 into 1/2
3.725 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
3.725 * [taylor]: Taking taylor expansion of 1/2 in k
3.725 * [backup-simplify]: Simplify 1/2 into 1/2
3.725 * [taylor]: Taking taylor expansion of k in k
3.725 * [backup-simplify]: Simplify 0 into 0
3.725 * [backup-simplify]: Simplify 1 into 1
3.725 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
3.725 * [taylor]: Taking taylor expansion of (log n) in k
3.725 * [taylor]: Taking taylor expansion of n in k
3.725 * [backup-simplify]: Simplify n into n
3.725 * [backup-simplify]: Simplify (log n) into (log n)
3.725 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
3.725 * [taylor]: Taking taylor expansion of (* 2 PI) in k
3.725 * [taylor]: Taking taylor expansion of 2 in k
3.725 * [backup-simplify]: Simplify 2 into 2
3.725 * [taylor]: Taking taylor expansion of PI in k
3.725 * [backup-simplify]: Simplify PI into PI
3.725 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.726 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.726 * [backup-simplify]: Simplify (* 1/2 0) into 0
3.726 * [backup-simplify]: Simplify (- 0) into 0
3.727 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.727 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.728 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
3.729 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
3.729 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
3.730 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
3.731 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
3.732 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.732 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
3.732 * [backup-simplify]: Simplify (- 0) into 0
3.733 * [backup-simplify]: Simplify (+ 0 0) into 0
3.734 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.734 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
3.735 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
3.735 * [taylor]: Taking taylor expansion of 0 in k
3.735 * [backup-simplify]: Simplify 0 into 0
3.736 * [backup-simplify]: Simplify 0 into 0
3.736 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
3.736 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
3.737 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.738 * [backup-simplify]: Simplify (+ 0 0) into 0
3.738 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
3.738 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.739 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.740 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
3.741 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
3.743 * [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)))))))
3.745 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
3.746 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
3.749 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
3.750 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
3.751 * [backup-simplify]: Simplify (- 0) into 0
3.751 * [backup-simplify]: Simplify (+ 0 0) into 0
3.752 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.754 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
3.756 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
3.756 * [taylor]: Taking taylor expansion of 0 in k
3.756 * [backup-simplify]: Simplify 0 into 0
3.756 * [backup-simplify]: Simplify 0 into 0
3.756 * [backup-simplify]: Simplify 0 into 0
3.758 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
3.759 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
3.762 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
3.763 * [backup-simplify]: Simplify (+ 0 0) into 0
3.764 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
3.764 * [backup-simplify]: Simplify (- 0) into 0
3.764 * [backup-simplify]: Simplify (+ 0 0) into 0
3.766 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
3.770 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
3.775 * [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)))))
3.785 * [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)))))
3.785 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
3.785 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
3.785 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
3.785 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
3.786 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
3.786 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
3.786 * [taylor]: Taking taylor expansion of 1/2 in k
3.786 * [backup-simplify]: Simplify 1/2 into 1/2
3.786 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.786 * [taylor]: Taking taylor expansion of 1/2 in k
3.786 * [backup-simplify]: Simplify 1/2 into 1/2
3.786 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.786 * [taylor]: Taking taylor expansion of k in k
3.786 * [backup-simplify]: Simplify 0 into 0
3.786 * [backup-simplify]: Simplify 1 into 1
3.786 * [backup-simplify]: Simplify (/ 1 1) into 1
3.786 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
3.786 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
3.786 * [taylor]: Taking taylor expansion of 2 in k
3.786 * [backup-simplify]: Simplify 2 into 2
3.786 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.786 * [taylor]: Taking taylor expansion of PI in k
3.786 * [backup-simplify]: Simplify PI into PI
3.786 * [taylor]: Taking taylor expansion of n in k
3.786 * [backup-simplify]: Simplify n into n
3.786 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.787 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
3.787 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
3.787 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.787 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.788 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.788 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
3.788 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
3.788 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
3.788 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
3.788 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
3.788 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
3.788 * [taylor]: Taking taylor expansion of 1/2 in n
3.788 * [backup-simplify]: Simplify 1/2 into 1/2
3.788 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.788 * [taylor]: Taking taylor expansion of 1/2 in n
3.788 * [backup-simplify]: Simplify 1/2 into 1/2
3.788 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.788 * [taylor]: Taking taylor expansion of k in n
3.788 * [backup-simplify]: Simplify k into k
3.788 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.788 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
3.788 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.788 * [taylor]: Taking taylor expansion of 2 in n
3.788 * [backup-simplify]: Simplify 2 into 2
3.789 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.789 * [taylor]: Taking taylor expansion of PI in n
3.789 * [backup-simplify]: Simplify PI into PI
3.789 * [taylor]: Taking taylor expansion of n in n
3.789 * [backup-simplify]: Simplify 0 into 0
3.789 * [backup-simplify]: Simplify 1 into 1
3.789 * [backup-simplify]: Simplify (/ PI 1) into PI
3.789 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.790 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.790 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.790 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
3.790 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
3.791 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.792 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
3.792 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
3.792 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
3.792 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
3.792 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
3.792 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
3.792 * [taylor]: Taking taylor expansion of 1/2 in n
3.793 * [backup-simplify]: Simplify 1/2 into 1/2
3.793 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.793 * [taylor]: Taking taylor expansion of 1/2 in n
3.793 * [backup-simplify]: Simplify 1/2 into 1/2
3.793 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.793 * [taylor]: Taking taylor expansion of k in n
3.793 * [backup-simplify]: Simplify k into k
3.793 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.793 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
3.793 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.793 * [taylor]: Taking taylor expansion of 2 in n
3.793 * [backup-simplify]: Simplify 2 into 2
3.793 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.793 * [taylor]: Taking taylor expansion of PI in n
3.793 * [backup-simplify]: Simplify PI into PI
3.793 * [taylor]: Taking taylor expansion of n in n
3.793 * [backup-simplify]: Simplify 0 into 0
3.793 * [backup-simplify]: Simplify 1 into 1
3.793 * [backup-simplify]: Simplify (/ PI 1) into PI
3.793 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.794 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.794 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.794 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
3.794 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
3.795 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.796 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
3.796 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
3.797 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
3.797 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
3.797 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
3.797 * [taylor]: Taking taylor expansion of 1/2 in k
3.797 * [backup-simplify]: Simplify 1/2 into 1/2
3.797 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.797 * [taylor]: Taking taylor expansion of 1/2 in k
3.797 * [backup-simplify]: Simplify 1/2 into 1/2
3.797 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.797 * [taylor]: Taking taylor expansion of k in k
3.797 * [backup-simplify]: Simplify 0 into 0
3.797 * [backup-simplify]: Simplify 1 into 1
3.797 * [backup-simplify]: Simplify (/ 1 1) into 1
3.797 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
3.797 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
3.797 * [taylor]: Taking taylor expansion of (* 2 PI) in k
3.797 * [taylor]: Taking taylor expansion of 2 in k
3.797 * [backup-simplify]: Simplify 2 into 2
3.797 * [taylor]: Taking taylor expansion of PI in k
3.797 * [backup-simplify]: Simplify PI into PI
3.797 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.798 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.798 * [taylor]: Taking taylor expansion of (log n) in k
3.798 * [taylor]: Taking taylor expansion of n in k
3.798 * [backup-simplify]: Simplify n into n
3.798 * [backup-simplify]: Simplify (log n) into (log n)
3.798 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.799 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.799 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.799 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
3.800 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
3.801 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
3.801 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
3.802 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
3.803 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.803 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
3.804 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.804 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.805 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
3.805 * [backup-simplify]: Simplify (- 0) into 0
3.805 * [backup-simplify]: Simplify (+ 0 0) into 0
3.806 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.807 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
3.808 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
3.808 * [taylor]: Taking taylor expansion of 0 in k
3.808 * [backup-simplify]: Simplify 0 into 0
3.808 * [backup-simplify]: Simplify 0 into 0
3.808 * [backup-simplify]: Simplify 0 into 0
3.809 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.809 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
3.811 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
3.811 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.816 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
3.816 * [backup-simplify]: Simplify (- 0) into 0
3.816 * [backup-simplify]: Simplify (+ 0 0) into 0
3.818 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.818 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
3.820 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
3.820 * [taylor]: Taking taylor expansion of 0 in k
3.820 * [backup-simplify]: Simplify 0 into 0
3.820 * [backup-simplify]: Simplify 0 into 0
3.820 * [backup-simplify]: Simplify 0 into 0
3.820 * [backup-simplify]: Simplify 0 into 0
3.821 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.821 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.825 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
3.825 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.826 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
3.826 * [backup-simplify]: Simplify (- 0) into 0
3.826 * [backup-simplify]: Simplify (+ 0 0) into 0
3.827 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
3.828 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
3.830 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
3.830 * [taylor]: Taking taylor expansion of 0 in k
3.830 * [backup-simplify]: Simplify 0 into 0
3.830 * [backup-simplify]: Simplify 0 into 0
3.831 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
3.831 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
3.831 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
3.831 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
3.831 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
3.831 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
3.831 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
3.831 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.831 * [taylor]: Taking taylor expansion of 1/2 in k
3.831 * [backup-simplify]: Simplify 1/2 into 1/2
3.831 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.831 * [taylor]: Taking taylor expansion of k in k
3.831 * [backup-simplify]: Simplify 0 into 0
3.831 * [backup-simplify]: Simplify 1 into 1
3.831 * [backup-simplify]: Simplify (/ 1 1) into 1
3.831 * [taylor]: Taking taylor expansion of 1/2 in k
3.831 * [backup-simplify]: Simplify 1/2 into 1/2
3.831 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
3.831 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
3.831 * [taylor]: Taking taylor expansion of -2 in k
3.831 * [backup-simplify]: Simplify -2 into -2
3.831 * [taylor]: Taking taylor expansion of (/ PI n) in k
3.831 * [taylor]: Taking taylor expansion of PI in k
3.831 * [backup-simplify]: Simplify PI into PI
3.831 * [taylor]: Taking taylor expansion of n in k
3.831 * [backup-simplify]: Simplify n into n
3.831 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
3.832 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
3.832 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
3.832 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.832 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.832 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
3.832 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
3.832 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
3.832 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
3.832 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
3.833 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
3.833 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.833 * [taylor]: Taking taylor expansion of 1/2 in n
3.833 * [backup-simplify]: Simplify 1/2 into 1/2
3.833 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.833 * [taylor]: Taking taylor expansion of k in n
3.833 * [backup-simplify]: Simplify k into k
3.833 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.833 * [taylor]: Taking taylor expansion of 1/2 in n
3.833 * [backup-simplify]: Simplify 1/2 into 1/2
3.833 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
3.833 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.833 * [taylor]: Taking taylor expansion of -2 in n
3.833 * [backup-simplify]: Simplify -2 into -2
3.833 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.833 * [taylor]: Taking taylor expansion of PI in n
3.833 * [backup-simplify]: Simplify PI into PI
3.833 * [taylor]: Taking taylor expansion of n in n
3.833 * [backup-simplify]: Simplify 0 into 0
3.833 * [backup-simplify]: Simplify 1 into 1
3.833 * [backup-simplify]: Simplify (/ PI 1) into PI
3.834 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.834 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
3.834 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.834 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
3.835 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.836 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
3.837 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
3.837 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
3.837 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
3.837 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
3.837 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
3.837 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
3.837 * [taylor]: Taking taylor expansion of 1/2 in n
3.837 * [backup-simplify]: Simplify 1/2 into 1/2
3.837 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.837 * [taylor]: Taking taylor expansion of k in n
3.837 * [backup-simplify]: Simplify k into k
3.837 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.837 * [taylor]: Taking taylor expansion of 1/2 in n
3.837 * [backup-simplify]: Simplify 1/2 into 1/2
3.837 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
3.837 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.837 * [taylor]: Taking taylor expansion of -2 in n
3.837 * [backup-simplify]: Simplify -2 into -2
3.837 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.837 * [taylor]: Taking taylor expansion of PI in n
3.837 * [backup-simplify]: Simplify PI into PI
3.837 * [taylor]: Taking taylor expansion of n in n
3.837 * [backup-simplify]: Simplify 0 into 0
3.837 * [backup-simplify]: Simplify 1 into 1
3.837 * [backup-simplify]: Simplify (/ PI 1) into PI
3.838 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.838 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
3.838 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
3.839 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
3.839 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.840 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
3.841 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
3.841 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
3.841 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
3.841 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
3.841 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
3.841 * [taylor]: Taking taylor expansion of 1/2 in k
3.841 * [backup-simplify]: Simplify 1/2 into 1/2
3.841 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.841 * [taylor]: Taking taylor expansion of k in k
3.841 * [backup-simplify]: Simplify 0 into 0
3.841 * [backup-simplify]: Simplify 1 into 1
3.842 * [backup-simplify]: Simplify (/ 1 1) into 1
3.842 * [taylor]: Taking taylor expansion of 1/2 in k
3.842 * [backup-simplify]: Simplify 1/2 into 1/2
3.842 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
3.842 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
3.842 * [taylor]: Taking taylor expansion of (* -2 PI) in k
3.842 * [taylor]: Taking taylor expansion of -2 in k
3.842 * [backup-simplify]: Simplify -2 into -2
3.842 * [taylor]: Taking taylor expansion of PI in k
3.842 * [backup-simplify]: Simplify PI into PI
3.843 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.844 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
3.844 * [taylor]: Taking taylor expansion of (log n) in k
3.844 * [taylor]: Taking taylor expansion of n in k
3.844 * [backup-simplify]: Simplify n into n
3.844 * [backup-simplify]: Simplify (log n) into (log n)
3.844 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
3.845 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.845 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
3.846 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
3.847 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
3.848 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
3.849 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
3.850 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.851 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
3.853 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
3.853 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.853 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
3.854 * [backup-simplify]: Simplify (+ 0 0) into 0
3.855 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.856 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
3.858 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
3.858 * [taylor]: Taking taylor expansion of 0 in k
3.858 * [backup-simplify]: Simplify 0 into 0
3.858 * [backup-simplify]: Simplify 0 into 0
3.858 * [backup-simplify]: Simplify 0 into 0
3.859 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.860 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
3.863 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
3.863 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.863 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
3.863 * [backup-simplify]: Simplify (+ 0 0) into 0
3.864 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.865 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
3.867 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
3.867 * [taylor]: Taking taylor expansion of 0 in k
3.867 * [backup-simplify]: Simplify 0 into 0
3.867 * [backup-simplify]: Simplify 0 into 0
3.867 * [backup-simplify]: Simplify 0 into 0
3.867 * [backup-simplify]: Simplify 0 into 0
3.867 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.868 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.872 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
3.872 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.873 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
3.873 * [backup-simplify]: Simplify (+ 0 0) into 0
3.874 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
3.875 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
3.877 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
3.877 * [taylor]: Taking taylor expansion of 0 in k
3.877 * [backup-simplify]: Simplify 0 into 0
3.877 * [backup-simplify]: Simplify 0 into 0
3.877 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
3.878 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1)
3.878 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI))
3.878 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
3.878 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.878 * [taylor]: Taking taylor expansion of 2 in n
3.878 * [backup-simplify]: Simplify 2 into 2
3.878 * [taylor]: Taking taylor expansion of (* n PI) in n
3.878 * [taylor]: Taking taylor expansion of n in n
3.878 * [backup-simplify]: Simplify 0 into 0
3.878 * [backup-simplify]: Simplify 1 into 1
3.878 * [taylor]: Taking taylor expansion of PI in n
3.878 * [backup-simplify]: Simplify PI into PI
3.878 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.878 * [taylor]: Taking taylor expansion of 2 in n
3.878 * [backup-simplify]: Simplify 2 into 2
3.878 * [taylor]: Taking taylor expansion of (* n PI) in n
3.878 * [taylor]: Taking taylor expansion of n in n
3.878 * [backup-simplify]: Simplify 0 into 0
3.878 * [backup-simplify]: Simplify 1 into 1
3.878 * [taylor]: Taking taylor expansion of PI in n
3.878 * [backup-simplify]: Simplify PI into PI
3.878 * [backup-simplify]: Simplify (* 0 PI) into 0
3.879 * [backup-simplify]: Simplify (* 2 0) into 0
3.879 * [backup-simplify]: Simplify 0 into 0
3.879 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.880 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
3.881 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.881 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
3.882 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
3.882 * [backup-simplify]: Simplify 0 into 0
3.883 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
3.883 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
3.883 * [backup-simplify]: Simplify 0 into 0
3.884 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.885 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
3.885 * [backup-simplify]: Simplify 0 into 0
3.886 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
3.887 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
3.887 * [backup-simplify]: Simplify 0 into 0
3.888 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
3.889 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
3.889 * [backup-simplify]: Simplify 0 into 0
3.890 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
3.891 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
3.891 * [backup-simplify]: Simplify 0 into 0
3.891 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
3.891 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n))
3.891 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
3.891 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.891 * [taylor]: Taking taylor expansion of 2 in n
3.891 * [backup-simplify]: Simplify 2 into 2
3.891 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.891 * [taylor]: Taking taylor expansion of PI in n
3.891 * [backup-simplify]: Simplify PI into PI
3.891 * [taylor]: Taking taylor expansion of n in n
3.891 * [backup-simplify]: Simplify 0 into 0
3.891 * [backup-simplify]: Simplify 1 into 1
3.892 * [backup-simplify]: Simplify (/ PI 1) into PI
3.892 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
3.892 * [taylor]: Taking taylor expansion of 2 in n
3.892 * [backup-simplify]: Simplify 2 into 2
3.892 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.892 * [taylor]: Taking taylor expansion of PI in n
3.892 * [backup-simplify]: Simplify PI into PI
3.892 * [taylor]: Taking taylor expansion of n in n
3.892 * [backup-simplify]: Simplify 0 into 0
3.892 * [backup-simplify]: Simplify 1 into 1
3.892 * [backup-simplify]: Simplify (/ PI 1) into PI
3.893 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.893 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.894 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.895 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
3.895 * [backup-simplify]: Simplify 0 into 0
3.896 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.897 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
3.897 * [backup-simplify]: Simplify 0 into 0
3.898 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.899 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.899 * [backup-simplify]: Simplify 0 into 0
3.901 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.902 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.902 * [backup-simplify]: Simplify 0 into 0
3.903 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.905 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
3.905 * [backup-simplify]: Simplify 0 into 0
3.906 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.908 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
3.908 * [backup-simplify]: Simplify 0 into 0
3.908 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
3.909 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n))
3.909 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
3.909 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.909 * [taylor]: Taking taylor expansion of -2 in n
3.909 * [backup-simplify]: Simplify -2 into -2
3.909 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.909 * [taylor]: Taking taylor expansion of PI in n
3.909 * [backup-simplify]: Simplify PI into PI
3.909 * [taylor]: Taking taylor expansion of n in n
3.909 * [backup-simplify]: Simplify 0 into 0
3.909 * [backup-simplify]: Simplify 1 into 1
3.909 * [backup-simplify]: Simplify (/ PI 1) into PI
3.909 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
3.909 * [taylor]: Taking taylor expansion of -2 in n
3.909 * [backup-simplify]: Simplify -2 into -2
3.909 * [taylor]: Taking taylor expansion of (/ PI n) in n
3.910 * [taylor]: Taking taylor expansion of PI in n
3.910 * [backup-simplify]: Simplify PI into PI
3.910 * [taylor]: Taking taylor expansion of n in n
3.910 * [backup-simplify]: Simplify 0 into 0
3.910 * [backup-simplify]: Simplify 1 into 1
3.910 * [backup-simplify]: Simplify (/ PI 1) into PI
3.911 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.911 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
3.912 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
3.913 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
3.913 * [backup-simplify]: Simplify 0 into 0
3.914 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.915 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
3.915 * [backup-simplify]: Simplify 0 into 0
3.916 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.917 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
3.918 * [backup-simplify]: Simplify 0 into 0
3.919 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.920 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
3.920 * [backup-simplify]: Simplify 0 into 0
3.921 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.925 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
3.926 * [backup-simplify]: Simplify 0 into 0
3.927 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
3.929 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
3.929 * [backup-simplify]: Simplify 0 into 0
3.930 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
3.930 * * * * [progress]: [ 3 / 3 ] generating series at (2)
3.930 * [backup-simplify]: Simplify (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))))
3.930 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0
3.930 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
3.930 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
3.930 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.930 * [taylor]: Taking taylor expansion of k in k
3.930 * [backup-simplify]: Simplify 0 into 0
3.930 * [backup-simplify]: Simplify 1 into 1
3.931 * [backup-simplify]: Simplify (/ 1 1) into 1
3.931 * [backup-simplify]: Simplify (sqrt 0) into 0
3.933 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.933 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
3.933 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
3.933 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
3.933 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
3.933 * [taylor]: Taking taylor expansion of 1/2 in k
3.933 * [backup-simplify]: Simplify 1/2 into 1/2
3.933 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
3.933 * [taylor]: Taking taylor expansion of 1/2 in k
3.933 * [backup-simplify]: Simplify 1/2 into 1/2
3.933 * [taylor]: Taking taylor expansion of k in k
3.933 * [backup-simplify]: Simplify 0 into 0
3.933 * [backup-simplify]: Simplify 1 into 1
3.933 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
3.933 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
3.933 * [taylor]: Taking taylor expansion of 2 in k
3.933 * [backup-simplify]: Simplify 2 into 2
3.933 * [taylor]: Taking taylor expansion of (* n PI) in k
3.933 * [taylor]: Taking taylor expansion of n in k
3.933 * [backup-simplify]: Simplify n into n
3.933 * [taylor]: Taking taylor expansion of PI in k
3.933 * [backup-simplify]: Simplify PI into PI
3.933 * [backup-simplify]: Simplify (* n PI) into (* n PI)
3.933 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
3.934 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
3.934 * [backup-simplify]: Simplify (* 1/2 0) into 0
3.934 * [backup-simplify]: Simplify (- 0) into 0
3.935 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.935 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
3.935 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
3.935 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
3.935 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
3.935 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.935 * [taylor]: Taking taylor expansion of k in n
3.935 * [backup-simplify]: Simplify k into k
3.935 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.935 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
3.935 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.936 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
3.936 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
3.936 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
3.936 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
3.936 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
3.936 * [taylor]: Taking taylor expansion of 1/2 in n
3.936 * [backup-simplify]: Simplify 1/2 into 1/2
3.936 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
3.936 * [taylor]: Taking taylor expansion of 1/2 in n
3.936 * [backup-simplify]: Simplify 1/2 into 1/2
3.936 * [taylor]: Taking taylor expansion of k in n
3.936 * [backup-simplify]: Simplify k into k
3.936 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
3.936 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.936 * [taylor]: Taking taylor expansion of 2 in n
3.936 * [backup-simplify]: Simplify 2 into 2
3.936 * [taylor]: Taking taylor expansion of (* n PI) in n
3.936 * [taylor]: Taking taylor expansion of n in n
3.936 * [backup-simplify]: Simplify 0 into 0
3.936 * [backup-simplify]: Simplify 1 into 1
3.936 * [taylor]: Taking taylor expansion of PI in n
3.936 * [backup-simplify]: Simplify PI into PI
3.937 * [backup-simplify]: Simplify (* 0 PI) into 0
3.937 * [backup-simplify]: Simplify (* 2 0) into 0
3.939 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.941 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
3.942 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.942 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
3.942 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
3.942 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
3.944 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.945 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
3.946 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
3.946 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
3.946 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
3.946 * [taylor]: Taking taylor expansion of (/ 1 k) in n
3.946 * [taylor]: Taking taylor expansion of k in n
3.946 * [backup-simplify]: Simplify k into k
3.946 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
3.946 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
3.946 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
3.947 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
3.947 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
3.947 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
3.947 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
3.947 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
3.947 * [taylor]: Taking taylor expansion of 1/2 in n
3.947 * [backup-simplify]: Simplify 1/2 into 1/2
3.947 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
3.947 * [taylor]: Taking taylor expansion of 1/2 in n
3.947 * [backup-simplify]: Simplify 1/2 into 1/2
3.947 * [taylor]: Taking taylor expansion of k in n
3.947 * [backup-simplify]: Simplify k into k
3.947 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
3.947 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
3.947 * [taylor]: Taking taylor expansion of 2 in n
3.947 * [backup-simplify]: Simplify 2 into 2
3.947 * [taylor]: Taking taylor expansion of (* n PI) in n
3.947 * [taylor]: Taking taylor expansion of n in n
3.947 * [backup-simplify]: Simplify 0 into 0
3.947 * [backup-simplify]: Simplify 1 into 1
3.947 * [taylor]: Taking taylor expansion of PI in n
3.947 * [backup-simplify]: Simplify PI into PI
3.948 * [backup-simplify]: Simplify (* 0 PI) into 0
3.948 * [backup-simplify]: Simplify (* 2 0) into 0
3.949 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
3.950 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
3.951 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.951 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
3.951 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
3.951 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
3.952 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.953 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
3.953 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
3.954 * [backup-simplify]: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k)))
3.954 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k
3.954 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
3.954 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
3.954 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
3.954 * [taylor]: Taking taylor expansion of 1/2 in k
3.954 * [backup-simplify]: Simplify 1/2 into 1/2
3.954 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
3.954 * [taylor]: Taking taylor expansion of 1/2 in k
3.954 * [backup-simplify]: Simplify 1/2 into 1/2
3.954 * [taylor]: Taking taylor expansion of k in k
3.954 * [backup-simplify]: Simplify 0 into 0
3.954 * [backup-simplify]: Simplify 1 into 1
3.954 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
3.954 * [taylor]: Taking taylor expansion of (log n) in k
3.954 * [taylor]: Taking taylor expansion of n in k
3.954 * [backup-simplify]: Simplify n into n
3.954 * [backup-simplify]: Simplify (log n) into (log n)
3.954 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
3.954 * [taylor]: Taking taylor expansion of (* 2 PI) in k
3.954 * [taylor]: Taking taylor expansion of 2 in k
3.955 * [backup-simplify]: Simplify 2 into 2
3.955 * [taylor]: Taking taylor expansion of PI in k
3.955 * [backup-simplify]: Simplify PI into PI
3.955 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
3.955 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
3.956 * [backup-simplify]: Simplify (* 1/2 0) into 0
3.956 * [backup-simplify]: Simplify (- 0) into 0
3.956 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
3.957 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.958 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
3.958 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
3.958 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
3.958 * [taylor]: Taking taylor expansion of (/ 1 k) in k
3.958 * [taylor]: Taking taylor expansion of k in k
3.958 * [backup-simplify]: Simplify 0 into 0
3.958 * [backup-simplify]: Simplify 1 into 1
3.959 * [backup-simplify]: Simplify (/ 1 1) into 1
3.959 * [backup-simplify]: Simplify (sqrt 0) into 0
3.960 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
3.960 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
3.960 * [backup-simplify]: Simplify 0 into 0
3.961 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
3.962 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
3.963 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.963 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
3.964 * [backup-simplify]: Simplify (- 0) into 0
3.964 * [backup-simplify]: Simplify (+ 0 0) into 0
3.965 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.965 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
3.967 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
3.967 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0
3.967 * [taylor]: Taking taylor expansion of 0 in k
3.967 * [backup-simplify]: Simplify 0 into 0
3.968 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
3.968 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
3.969 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
3.970 * [backup-simplify]: Simplify (+ 0 0) into 0
3.970 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
3.970 * [backup-simplify]: Simplify (- 1/2) into -1/2
3.971 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
3.972 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
3.974 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
3.976 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
3.977 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
3.978 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
3.978 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
3.980 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
3.981 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
3.981 * [backup-simplify]: Simplify (- 0) into 0
3.981 * [backup-simplify]: Simplify (+ 0 0) into 0
3.982 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
3.983 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
3.985 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
3.985 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
3.985 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
3.986 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0
3.986 * [taylor]: Taking taylor expansion of 0 in k
3.986 * [backup-simplify]: Simplify 0 into 0
3.986 * [backup-simplify]: Simplify 0 into 0
3.987 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
3.989 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
3.990 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
3.990 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
3.992 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
3.992 * [backup-simplify]: Simplify (+ 0 0) into 0
3.993 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
3.993 * [backup-simplify]: Simplify (- 0) into 0
3.994 * [backup-simplify]: Simplify (+ 0 0) into 0
3.995 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
3.998 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
4.004 * [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))))))))
4.007 * [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))))))))
4.007 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
4.008 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
4.011 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
4.012 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
4.013 * [backup-simplify]: Simplify (- 0) into 0
4.013 * [backup-simplify]: Simplify (+ 0 0) into 0
4.014 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
4.015 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
4.017 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
4.017 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.017 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
4.019 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0
4.019 * [taylor]: Taking taylor expansion of 0 in k
4.019 * [backup-simplify]: Simplify 0 into 0
4.019 * [backup-simplify]: Simplify 0 into 0
4.019 * [backup-simplify]: Simplify 0 into 0
4.019 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.024 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
4.026 * [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
4.027 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
4.031 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
4.032 * [backup-simplify]: Simplify (+ 0 0) into 0
4.033 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
4.033 * [backup-simplify]: Simplify (- 0) into 0
4.034 * [backup-simplify]: Simplify (+ 0 0) into 0
4.036 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
4.043 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
4.060 * [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))))))))))))))
4.073 * [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))))))))))))))
4.093 * [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))))))))))))))))))))))
4.093 * [backup-simplify]: Simplify (/ (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))
4.093 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
4.093 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
4.093 * [taylor]: Taking taylor expansion of (sqrt k) in k
4.094 * [taylor]: Taking taylor expansion of k in k
4.094 * [backup-simplify]: Simplify 0 into 0
4.094 * [backup-simplify]: Simplify 1 into 1
4.094 * [backup-simplify]: Simplify (sqrt 0) into 0
4.096 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
4.096 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
4.096 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
4.096 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
4.096 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
4.096 * [taylor]: Taking taylor expansion of 1/2 in k
4.096 * [backup-simplify]: Simplify 1/2 into 1/2
4.096 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
4.096 * [taylor]: Taking taylor expansion of 1/2 in k
4.096 * [backup-simplify]: Simplify 1/2 into 1/2
4.096 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.096 * [taylor]: Taking taylor expansion of k in k
4.096 * [backup-simplify]: Simplify 0 into 0
4.096 * [backup-simplify]: Simplify 1 into 1
4.096 * [backup-simplify]: Simplify (/ 1 1) into 1
4.096 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
4.096 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
4.097 * [taylor]: Taking taylor expansion of 2 in k
4.097 * [backup-simplify]: Simplify 2 into 2
4.097 * [taylor]: Taking taylor expansion of (/ PI n) in k
4.097 * [taylor]: Taking taylor expansion of PI in k
4.097 * [backup-simplify]: Simplify PI into PI
4.097 * [taylor]: Taking taylor expansion of n in k
4.097 * [backup-simplify]: Simplify n into n
4.097 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
4.097 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
4.097 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
4.097 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
4.098 * [backup-simplify]: Simplify (- 1/2) into -1/2
4.098 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
4.098 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
4.099 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
4.099 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
4.099 * [taylor]: Taking taylor expansion of (sqrt k) in n
4.099 * [taylor]: Taking taylor expansion of k in n
4.099 * [backup-simplify]: Simplify k into k
4.099 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
4.099 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
4.099 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
4.099 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
4.099 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
4.099 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
4.099 * [taylor]: Taking taylor expansion of 1/2 in n
4.099 * [backup-simplify]: Simplify 1/2 into 1/2
4.099 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
4.099 * [taylor]: Taking taylor expansion of 1/2 in n
4.099 * [backup-simplify]: Simplify 1/2 into 1/2
4.099 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.099 * [taylor]: Taking taylor expansion of k in n
4.099 * [backup-simplify]: Simplify k into k
4.099 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.099 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
4.099 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
4.099 * [taylor]: Taking taylor expansion of 2 in n
4.099 * [backup-simplify]: Simplify 2 into 2
4.099 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.099 * [taylor]: Taking taylor expansion of PI in n
4.099 * [backup-simplify]: Simplify PI into PI
4.099 * [taylor]: Taking taylor expansion of n in n
4.099 * [backup-simplify]: Simplify 0 into 0
4.099 * [backup-simplify]: Simplify 1 into 1
4.100 * [backup-simplify]: Simplify (/ PI 1) into PI
4.100 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
4.102 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.102 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
4.102 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
4.102 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
4.103 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
4.105 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
4.106 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
4.106 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
4.106 * [taylor]: Taking taylor expansion of (sqrt k) in n
4.106 * [taylor]: Taking taylor expansion of k in n
4.106 * [backup-simplify]: Simplify k into k
4.106 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
4.106 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
4.106 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
4.106 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
4.106 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
4.106 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
4.106 * [taylor]: Taking taylor expansion of 1/2 in n
4.106 * [backup-simplify]: Simplify 1/2 into 1/2
4.106 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
4.106 * [taylor]: Taking taylor expansion of 1/2 in n
4.107 * [backup-simplify]: Simplify 1/2 into 1/2
4.107 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.107 * [taylor]: Taking taylor expansion of k in n
4.107 * [backup-simplify]: Simplify k into k
4.107 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.107 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
4.107 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
4.107 * [taylor]: Taking taylor expansion of 2 in n
4.107 * [backup-simplify]: Simplify 2 into 2
4.107 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.107 * [taylor]: Taking taylor expansion of PI in n
4.107 * [backup-simplify]: Simplify PI into PI
4.107 * [taylor]: Taking taylor expansion of n in n
4.107 * [backup-simplify]: Simplify 0 into 0
4.107 * [backup-simplify]: Simplify 1 into 1
4.107 * [backup-simplify]: Simplify (/ PI 1) into PI
4.108 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
4.109 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.109 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
4.109 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
4.109 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
4.111 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
4.113 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
4.114 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
4.115 * [backup-simplify]: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k))
4.115 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k
4.115 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
4.116 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
4.116 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
4.116 * [taylor]: Taking taylor expansion of 1/2 in k
4.116 * [backup-simplify]: Simplify 1/2 into 1/2
4.116 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
4.116 * [taylor]: Taking taylor expansion of 1/2 in k
4.116 * [backup-simplify]: Simplify 1/2 into 1/2
4.116 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.116 * [taylor]: Taking taylor expansion of k in k
4.116 * [backup-simplify]: Simplify 0 into 0
4.116 * [backup-simplify]: Simplify 1 into 1
4.116 * [backup-simplify]: Simplify (/ 1 1) into 1
4.116 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
4.116 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
4.116 * [taylor]: Taking taylor expansion of (* 2 PI) in k
4.116 * [taylor]: Taking taylor expansion of 2 in k
4.116 * [backup-simplify]: Simplify 2 into 2
4.116 * [taylor]: Taking taylor expansion of PI in k
4.116 * [backup-simplify]: Simplify PI into PI
4.117 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
4.118 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.118 * [taylor]: Taking taylor expansion of (log n) in k
4.118 * [taylor]: Taking taylor expansion of n in k
4.118 * [backup-simplify]: Simplify n into n
4.118 * [backup-simplify]: Simplify (log n) into (log n)
4.118 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
4.119 * [backup-simplify]: Simplify (- 1/2) into -1/2
4.119 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
4.119 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
4.120 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
4.122 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
4.123 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
4.123 * [taylor]: Taking taylor expansion of (sqrt k) in k
4.123 * [taylor]: Taking taylor expansion of k in k
4.123 * [backup-simplify]: Simplify 0 into 0
4.123 * [backup-simplify]: Simplify 1 into 1
4.123 * [backup-simplify]: Simplify (sqrt 0) into 0
4.125 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
4.126 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0
4.126 * [backup-simplify]: Simplify 0 into 0
4.127 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
4.128 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
4.130 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
4.130 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
4.131 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
4.131 * [backup-simplify]: Simplify (- 0) into 0
4.131 * [backup-simplify]: Simplify (+ 0 0) into 0
4.133 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
4.134 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
4.136 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
4.138 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0
4.138 * [taylor]: Taking taylor expansion of 0 in k
4.138 * [backup-simplify]: Simplify 0 into 0
4.138 * [backup-simplify]: Simplify 0 into 0
4.139 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
4.141 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
4.142 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.143 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
4.146 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
4.147 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.147 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
4.148 * [backup-simplify]: Simplify (- 0) into 0
4.148 * [backup-simplify]: Simplify (+ 0 0) into 0
4.150 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
4.151 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
4.154 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
4.154 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
4.156 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0
4.156 * [taylor]: Taking taylor expansion of 0 in k
4.156 * [backup-simplify]: Simplify 0 into 0
4.156 * [backup-simplify]: Simplify 0 into 0
4.156 * [backup-simplify]: Simplify 0 into 0
4.162 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
4.164 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
4.165 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
4.166 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.168 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
4.174 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
4.174 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.176 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
4.176 * [backup-simplify]: Simplify (- 0) into 0
4.176 * [backup-simplify]: Simplify (+ 0 0) into 0
4.178 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
4.180 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
4.182 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
4.183 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
4.185 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0
4.185 * [taylor]: Taking taylor expansion of 0 in k
4.185 * [backup-simplify]: Simplify 0 into 0
4.185 * [backup-simplify]: Simplify 0 into 0
4.186 * [backup-simplify]: Simplify 0 into 0
4.186 * [backup-simplify]: Simplify 0 into 0
4.190 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
4.192 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
4.193 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
4.198 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
4.199 * [backup-simplify]: Simplify (/ (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k)))
4.199 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0
4.199 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
4.199 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
4.199 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
4.199 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
4.199 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
4.199 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
4.199 * [taylor]: Taking taylor expansion of 1/2 in k
4.199 * [backup-simplify]: Simplify 1/2 into 1/2
4.199 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.199 * [taylor]: Taking taylor expansion of k in k
4.199 * [backup-simplify]: Simplify 0 into 0
4.199 * [backup-simplify]: Simplify 1 into 1
4.199 * [backup-simplify]: Simplify (/ 1 1) into 1
4.199 * [taylor]: Taking taylor expansion of 1/2 in k
4.199 * [backup-simplify]: Simplify 1/2 into 1/2
4.200 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
4.200 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
4.200 * [taylor]: Taking taylor expansion of -2 in k
4.200 * [backup-simplify]: Simplify -2 into -2
4.200 * [taylor]: Taking taylor expansion of (/ PI n) in k
4.200 * [taylor]: Taking taylor expansion of PI in k
4.200 * [backup-simplify]: Simplify PI into PI
4.200 * [taylor]: Taking taylor expansion of n in k
4.200 * [backup-simplify]: Simplify n into n
4.200 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
4.200 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
4.200 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
4.200 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
4.201 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
4.201 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
4.201 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
4.201 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
4.201 * [taylor]: Taking taylor expansion of (/ -1 k) in k
4.201 * [taylor]: Taking taylor expansion of -1 in k
4.201 * [backup-simplify]: Simplify -1 into -1
4.201 * [taylor]: Taking taylor expansion of k in k
4.201 * [backup-simplify]: Simplify 0 into 0
4.201 * [backup-simplify]: Simplify 1 into 1
4.202 * [backup-simplify]: Simplify (/ -1 1) into -1
4.202 * [backup-simplify]: Simplify (sqrt 0) into 0
4.203 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
4.204 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
4.204 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
4.204 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
4.204 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
4.204 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
4.204 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
4.204 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
4.204 * [taylor]: Taking taylor expansion of 1/2 in n
4.204 * [backup-simplify]: Simplify 1/2 into 1/2
4.204 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.204 * [taylor]: Taking taylor expansion of k in n
4.204 * [backup-simplify]: Simplify k into k
4.204 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.204 * [taylor]: Taking taylor expansion of 1/2 in n
4.204 * [backup-simplify]: Simplify 1/2 into 1/2
4.204 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
4.204 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
4.204 * [taylor]: Taking taylor expansion of -2 in n
4.204 * [backup-simplify]: Simplify -2 into -2
4.204 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.204 * [taylor]: Taking taylor expansion of PI in n
4.204 * [backup-simplify]: Simplify PI into PI
4.204 * [taylor]: Taking taylor expansion of n in n
4.204 * [backup-simplify]: Simplify 0 into 0
4.204 * [backup-simplify]: Simplify 1 into 1
4.205 * [backup-simplify]: Simplify (/ PI 1) into PI
4.205 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
4.207 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
4.207 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
4.207 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
4.208 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
4.210 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
4.212 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
4.212 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
4.212 * [taylor]: Taking taylor expansion of (/ -1 k) in n
4.212 * [taylor]: Taking taylor expansion of -1 in n
4.212 * [backup-simplify]: Simplify -1 into -1
4.212 * [taylor]: Taking taylor expansion of k in n
4.212 * [backup-simplify]: Simplify k into k
4.212 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
4.212 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
4.212 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
4.213 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
4.214 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
4.214 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
4.214 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
4.214 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
4.214 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
4.214 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
4.214 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
4.214 * [taylor]: Taking taylor expansion of 1/2 in n
4.214 * [backup-simplify]: Simplify 1/2 into 1/2
4.214 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.214 * [taylor]: Taking taylor expansion of k in n
4.214 * [backup-simplify]: Simplify k into k
4.214 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.214 * [taylor]: Taking taylor expansion of 1/2 in n
4.214 * [backup-simplify]: Simplify 1/2 into 1/2
4.214 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
4.214 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
4.214 * [taylor]: Taking taylor expansion of -2 in n
4.214 * [backup-simplify]: Simplify -2 into -2
4.214 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.214 * [taylor]: Taking taylor expansion of PI in n
4.215 * [backup-simplify]: Simplify PI into PI
4.215 * [taylor]: Taking taylor expansion of n in n
4.215 * [backup-simplify]: Simplify 0 into 0
4.215 * [backup-simplify]: Simplify 1 into 1
4.215 * [backup-simplify]: Simplify (/ PI 1) into PI
4.216 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
4.217 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
4.217 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
4.217 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
4.218 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
4.219 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
4.221 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
4.221 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
4.221 * [taylor]: Taking taylor expansion of (/ -1 k) in n
4.221 * [taylor]: Taking taylor expansion of -1 in n
4.221 * [backup-simplify]: Simplify -1 into -1
4.221 * [taylor]: Taking taylor expansion of k in n
4.221 * [backup-simplify]: Simplify k into k
4.221 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
4.221 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
4.221 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
4.221 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
4.222 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
4.223 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k
4.223 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
4.223 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
4.223 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
4.223 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
4.223 * [taylor]: Taking taylor expansion of 1/2 in k
4.223 * [backup-simplify]: Simplify 1/2 into 1/2
4.223 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.223 * [taylor]: Taking taylor expansion of k in k
4.223 * [backup-simplify]: Simplify 0 into 0
4.223 * [backup-simplify]: Simplify 1 into 1
4.223 * [backup-simplify]: Simplify (/ 1 1) into 1
4.223 * [taylor]: Taking taylor expansion of 1/2 in k
4.223 * [backup-simplify]: Simplify 1/2 into 1/2
4.223 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
4.223 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
4.223 * [taylor]: Taking taylor expansion of (* -2 PI) in k
4.223 * [taylor]: Taking taylor expansion of -2 in k
4.223 * [backup-simplify]: Simplify -2 into -2
4.223 * [taylor]: Taking taylor expansion of PI in k
4.223 * [backup-simplify]: Simplify PI into PI
4.224 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
4.225 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
4.225 * [taylor]: Taking taylor expansion of (log n) in k
4.225 * [taylor]: Taking taylor expansion of n in k
4.225 * [backup-simplify]: Simplify n into n
4.225 * [backup-simplify]: Simplify (log n) into (log n)
4.225 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
4.226 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
4.226 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
4.227 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
4.228 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
4.229 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
4.229 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
4.229 * [taylor]: Taking taylor expansion of (/ -1 k) in k
4.229 * [taylor]: Taking taylor expansion of -1 in k
4.229 * [backup-simplify]: Simplify -1 into -1
4.229 * [taylor]: Taking taylor expansion of k in k
4.229 * [backup-simplify]: Simplify 0 into 0
4.229 * [backup-simplify]: Simplify 1 into 1
4.230 * [backup-simplify]: Simplify (/ -1 1) into -1
4.230 * [backup-simplify]: Simplify (sqrt 0) into 0
4.232 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
4.233 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
4.234 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
4.235 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
4.236 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
4.238 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
4.238 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
4.238 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
4.239 * [backup-simplify]: Simplify (+ 0 0) into 0
4.240 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
4.241 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
4.243 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
4.245 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
4.245 * [taylor]: Taking taylor expansion of 0 in k
4.245 * [backup-simplify]: Simplify 0 into 0
4.245 * [backup-simplify]: Simplify 0 into 0
4.246 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
4.249 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
4.251 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
4.252 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
4.253 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.254 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
4.257 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
4.258 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.259 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
4.259 * [backup-simplify]: Simplify (+ 0 0) into 0
4.260 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
4.262 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
4.264 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
4.265 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.265 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
4.267 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
4.267 * [taylor]: Taking taylor expansion of 0 in k
4.267 * [backup-simplify]: Simplify 0 into 0
4.267 * [backup-simplify]: Simplify 0 into 0
4.267 * [backup-simplify]: Simplify 0 into 0
4.268 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.272 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
4.275 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
4.277 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
4.281 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
4.281 * * * [progress]: simplifying candidates
4.281 * * * * [progress]: [ 1 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
4.281 * * * * [progress]: [ 2 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
4.281 * * * * [progress]: [ 3 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
4.281 * * * * [progress]: [ 4 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
4.281 * * * * [progress]: [ 5 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
4.282 * * * * [progress]: [ 6 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
4.282 * * * * [progress]: [ 7 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
4.282 * * * * [progress]: [ 8 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
4.282 * * * * [progress]: [ 9 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))>
4.282 * * * * [progress]: [ 10 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))>
4.282 * * * * [progress]: [ 11 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
4.282 * * * * [progress]: [ 12 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k)))>
4.282 * * * * [progress]: [ 13 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt k)))>
4.282 * * * * [progress]: [ 14 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
4.282 * * * * [progress]: [ 15 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k)))>
4.282 * * * * [progress]: [ 16 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k)))>
4.282 * * * * [progress]: [ 17 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k)))>
4.282 * * * * [progress]: [ 18 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (sqrt k)))>
4.282 * * * * [progress]: [ 19 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
4.282 * * * * [progress]: [ 20 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
4.282 * * * * [progress]: [ 21 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
4.283 * * * * [progress]: [ 22 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
4.283 * * * * [progress]: [ 23 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
4.283 * * * * [progress]: [ 24 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)))>
4.283 * * * * [progress]: [ 25 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
4.283 * * * * [progress]: [ 26 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
4.283 * * * * [progress]: [ 27 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
4.283 * * * * [progress]: [ 28 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
4.283 * * * * [progress]: [ 29 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
4.283 * * * * [progress]: [ 30 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (+ (log n) (log 2)) (log PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.283 * * * * [progress]: [ 31 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log (* n 2)) (log PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.283 * * * * [progress]: [ 32 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.283 * * * * [progress]: [ 33 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.283 * * * * [progress]: [ 34 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.283 * * * * [progress]: [ 35 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.283 * * * * [progress]: [ 36 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.283 * * * * [progress]: [ 37 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.283 * * * * [progress]: [ 38 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.284 * * * * [progress]: [ 39 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* (* n 2) PI)) (- 1/2 (/ k 2))) (sqrt k)))>
4.284 * * * * [progress]: [ 40 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (* (cbrt PI) (cbrt PI))) (cbrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
4.284 * * * * [progress]: [ 41 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
4.284 * * * * [progress]: [ 42 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) 1) PI) (- 1/2 (/ k 2))) (sqrt k)))>
4.284 * * * * [progress]: [ 43 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))>
4.284 * * * * [progress]: [ 44 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
4.284 * * * * [progress]: [ 45 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))>
4.284 * * * * [progress]: [ 46 / 127 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) 1))>
4.284 * * * * [progress]: [ 47 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
4.284 * * * * [progress]: [ 48 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
4.284 * * * * [progress]: [ 49 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
4.284 * * * * [progress]: [ 50 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
4.285 * * * * [progress]: [ 51 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
4.285 * * * * [progress]: [ 52 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
4.285 * * * * [progress]: [ 53 / 127 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
4.285 * * * * [progress]: [ 54 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
4.285 * * * * [progress]: [ 55 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
4.285 * * * * [progress]: [ 56 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
4.285 * * * * [progress]: [ 57 / 127 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
4.285 * * * * [progress]: [ 58 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (- (sqrt k))))>
4.285 * * * * [progress]: [ 59 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))))>
4.285 * * * * [progress]: [ 60 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))))>
4.285 * * * * [progress]: [ 61 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))>
4.285 * * * * [progress]: [ 62 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt 1)) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))>
4.285 * * * * [progress]: [ 63 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))>
4.285 * * * * [progress]: [ 64 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) 1) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))>
4.286 * * * * [progress]: [ 65 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))))>
4.286 * * * * [progress]: [ 66 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))))>
4.286 * * * * [progress]: [ 67 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))>
4.286 * * * * [progress]: [ 68 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt 1)) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))>
4.286 * * * * [progress]: [ 69 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))>
4.286 * * * * [progress]: [ 70 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) 1) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))>
4.286 * * * * [progress]: [ 71 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
4.286 * * * * [progress]: [ 72 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
4.286 * * * * [progress]: [ 73 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
4.286 * * * * [progress]: [ 74 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))>
4.286 * * * * [progress]: [ 75 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
4.286 * * * * [progress]: [ 76 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n 2) (- 1/2 (/ k 2))) 1) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))>
4.286 * * * * [progress]: [ 77 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
4.286 * * * * [progress]: [ 78 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
4.287 * * * * [progress]: [ 79 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
4.287 * * * * [progress]: [ 80 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt 1)) (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))>
4.287 * * * * [progress]: [ 81 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
4.287 * * * * [progress]: [ 82 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) 1) (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))>
4.287 * * * * [progress]: [ 83 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
4.287 * * * * [progress]: [ 84 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
4.287 * * * * [progress]: [ 85 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
4.287 * * * * [progress]: [ 86 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt 1)) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))>
4.287 * * * * [progress]: [ 87 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
4.287 * * * * [progress]: [ 88 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))>
4.287 * * * * [progress]: [ 89 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
4.287 * * * * [progress]: [ 90 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
4.287 * * * * [progress]: [ 91 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
4.287 * * * * [progress]: [ 92 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))>
4.287 * * * * [progress]: [ 93 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
4.288 * * * * [progress]: [ 94 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))>
4.288 * * * * [progress]: [ 95 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))))>
4.288 * * * * [progress]: [ 96 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))))>
4.288 * * * * [progress]: [ 97 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
4.288 * * * * [progress]: [ 98 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
4.288 * * * * [progress]: [ 99 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
4.288 * * * * [progress]: [ 100 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
4.288 * * * * [progress]: [ 101 / 127 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))>
4.288 * * * * [progress]: [ 102 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (/ 1 (sqrt k))))>
4.288 * * * * [progress]: [ 103 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))>
4.288 * * * * [progress]: [ 104 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
4.288 * * * * [progress]: [ 105 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))>
4.288 * * * * [progress]: [ 106 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
4.288 * * * * [progress]: [ 107 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt 1)) (sqrt k)))>
4.288 * * * * [progress]: [ 108 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
4.289 * * * * [progress]: [ 109 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (sqrt k)))>
4.289 * * * * [progress]: [ 110 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) 1/2) (/ (sqrt k) (pow (* (* n 2) PI) (- (/ k 2))))))>
4.289 * * * * [progress]: [ 111 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) 1/2) (/ (sqrt k) (pow (* (* n 2) PI) (- (/ k 2))))))>
4.289 * * * * [progress]: [ 112 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n 2) (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))))>
4.289 * * * * [progress]: [ 113 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))))>
4.289 * * * * [progress]: [ 114 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))))>
4.289 * * * * [progress]: [ 115 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))>
4.289 * * * * [progress]: [ 116 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))))>
4.289 * * * * [progress]: [ 117 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) 1/2) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))))>
4.289 * * * * [progress]: [ 118 / 127 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
4.289 * * * * [progress]: [ 119 / 127 ] 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)))>
4.289 * * * * [progress]: [ 120 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k)))>
4.289 * * * * [progress]: [ 121 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k)))>
4.289 * * * * [progress]: [ 122 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
4.289 * * * * [progress]: [ 123 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
4.290 * * * * [progress]: [ 124 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
4.290 * * * * [progress]: [ 125 / 127 ] 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)))))))))))))))))))))))>
4.290 * * * * [progress]: [ 126 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))))>
4.290 * * * * [progress]: [ 127 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))))>
4.293 * [simplify]: Simplifying:
  (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (/ k 2))
  (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (+ (+ (log n) (log 2)) (log PI))
  (+ (log (* n 2)) (log PI))
  (log (* (* n 2) PI))
  (exp (* (* n 2) PI))
  (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI))
  (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI))
  (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI)))
  (cbrt (* (* n 2) PI))
  (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))
  (sqrt (* (* n 2) PI))
  (sqrt (* (* n 2) PI))
  (* (* n 2) (* (cbrt PI) (cbrt PI)))
  (* (* n 2) (sqrt PI))
  (* (* n 2) 1)
  (* 2 PI)
  (real->posit16 (* (* n 2) PI))
  (- (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (log (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (log (sqrt k)))
  (log (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (exp (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (/ (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (* (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (- (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (- (sqrt k))
  (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt 1))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) 1/2) 1)
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))
  (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt 1))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))
  (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) 1/2) 1)
  (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt 1))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n 2) (- 1/2 (/ k 2))) 1)
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt 1))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) 1)
  (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt 1))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1)
  (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ 1 1)
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1)
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt 1))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1)
  (/ (sqrt k) (pow (* (* n 2) PI) (- (/ k 2))))
  (/ (sqrt k) (pow (* (* n 2) PI) (- (/ k 2))))
  (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))
  (/ (sqrt k) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))
  (real->posit16 (/ (pow (* (* n 2) PI) (- 1/2 (/ 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 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 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 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
4.298 * * [simplify]: iteration 0: 271 enodes
4.401 * * [simplify]: iteration 1: 662 enodes
4.649 * * [simplify]: iteration 2: 2241 enodes
5.375 * * [simplify]: iteration complete: 5008 enodes
5.375 * * [simplify]: Extracting #0: cost 96 inf + 0
5.377 * * [simplify]: Extracting #1: cost 556 inf + 1
5.383 * * [simplify]: Extracting #2: cost 1197 inf + 932
5.402 * * [simplify]: Extracting #3: cost 1527 inf + 33350
5.441 * * [simplify]: Extracting #4: cost 1063 inf + 205576
5.524 * * [simplify]: Extracting #5: cost 381 inf + 501395
5.695 * * [simplify]: Extracting #6: cost 148 inf + 646155
5.860 * * [simplify]: Extracting #7: cost 56 inf + 693103
6.067 * * [simplify]: Extracting #8: cost 3 inf + 723366
6.313 * * [simplify]: Extracting #9: cost 0 inf + 713906
6.546 * * [simplify]: Extracting #10: cost 0 inf + 709106
6.800 * * [simplify]: Extracting #11: cost 0 inf + 708436
6.982 * [simplify]: Simplified to:
  (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))
  (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))
  (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))
  (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))
  (- 1/2 (* 1/2 k))
  (- 1/2 (* 1/2 k))
  (- 1/2 (* 1/2 k))
  (sqrt (* (* 2 PI) n))
  (pow (* (* 2 PI) n) (/ k 2))
  (pow (* (* 2 PI) n) (* (cbrt (- 1/2 (* 1/2 k))) (cbrt (- 1/2 (* 1/2 k)))))
  (pow (* (* 2 PI) n) (sqrt (- 1/2 (* 1/2 k))))
  (* (* 2 PI) n)
  (pow (* (* 2 PI) n) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* 2 PI) n) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* (* 2 PI) n)
  (sqrt (* (* 2 PI) n))
  (pow (* (* 2 PI) n) (* -1/2 k))
  (sqrt (* (* 2 PI) n))
  (pow (* (* 2 PI) n) (* -1/2 k))
  (pow (* n 2) (- 1/2 (* 1/2 k)))
  (pow PI (- 1/2 (* 1/2 k)))
  (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))
  (exp (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (* (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (* (* (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (pow (* (* 2 PI) n) (- 1/4 (/ k 4)))
  (pow (* (* 2 PI) n) (- 1/4 (/ k 4)))
  (real->posit16 (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (log (* (* 2 PI) n))
  (log (* (* 2 PI) n))
  (log (* (* 2 PI) n))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* (* 2 PI) n) (* (* (* 2 PI) n) (* (* 2 PI) n)))
  (* (* (* 2 PI) n) (* (* (* 2 PI) n) (* (* 2 PI) n)))
  (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n)))
  (cbrt (* (* 2 PI) n))
  (* (* (* 2 PI) n) (* (* (* 2 PI) n) (* (* 2 PI) n)))
  (sqrt (* (* 2 PI) n))
  (sqrt (* (* 2 PI) n))
  (* (* (cbrt PI) (* n 2)) (cbrt PI))
  (* 2 (* n (sqrt PI)))
  (* n 2)
  (* 2 PI)
  (real->posit16 (* (* 2 PI) n))
  (- (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))) (log (sqrt k)))
  (- (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))) (log (sqrt k)))
  (- (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))) (log (sqrt k)))
  (- (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))) (log (sqrt k)))
  (- (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))) (log (sqrt k)))
  (- (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))) (log (sqrt k)))
  (exp (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)))
  (* (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) k) (* (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k))))
  (* (cbrt (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k))) (cbrt (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k))))
  (cbrt (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)))
  (* (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)) (* (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)) (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k))))
  (sqrt (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)))
  (sqrt (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)))
  (- (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (- (sqrt k))
  (/ (/ (sqrt (* (* 2 PI) n)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (cbrt (sqrt k)))
  (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (cbrt k)))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt k))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt k))
  (/ (/ (sqrt (* (* 2 PI) n)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (cbrt (sqrt k)))
  (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (cbrt k)))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt k))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt k))
  (/ (/ (pow (* n 2) (- 1/2 (* 1/2 k))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow PI (- 1/2 (* 1/2 k))) (cbrt (sqrt k)))
  (/ (pow (* n 2) (- 1/2 (* 1/2 k))) (fabs (cbrt k)))
  (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt (cbrt k)))
  (/ (pow (* n 2) (- 1/2 (* 1/2 k))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt (sqrt k)))
  (pow (* n 2) (- 1/2 (* 1/2 k)))
  (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k))
  (/ (pow (* n 2) (- 1/2 (* 1/2 k))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt (sqrt k)))
  (pow (* n 2) (- 1/2 (* 1/2 k)))
  (/ (pow PI (- 1/2 (* 1/2 k))) (sqrt k))
  (* (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (sqrt k))) (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (sqrt k))))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (sqrt k)))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (/ (fabs (cbrt k)) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (cbrt k)))
  (* (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k))) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))
  (* (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt k))
  (* (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k))) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))
  (* (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (/ (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt k))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (cbrt (sqrt k)))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (fabs (cbrt k)))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (cbrt k)))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))
  (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt k))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt (sqrt k)))
  (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (/ (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt (sqrt k)))
  1
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt (sqrt k)))
  1
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (cbrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt (cbrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* (* 2 PI) n) (- 1/4 (/ k 4)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt k))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* (* 2 PI) n) (- 1/4 (/ k 4)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ k 4))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (/ (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (fabs (cbrt k)))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt (sqrt k)))
  (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))
  (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt (sqrt k)))
  (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))
  (/ (sqrt k) (pow (* (* 2 PI) n) (* -1/2 k)))
  (/ (sqrt k) (pow (* (* 2 PI) n) (* -1/2 k)))
  (/ (sqrt k) (pow PI (- 1/2 (* 1/2 k))))
  (/ (sqrt k) (cbrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (/ (sqrt k) (sqrt (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))))
  (/ (sqrt k) (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))))
  (/ (sqrt k) (pow (* (* 2 PI) n) (- 1/4 (/ k 4))))
  (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
  (real->posit16 (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (sqrt k)))
  (- (+ (+ (* (log (* 2 PI)) (* (* (* (* k k) (log n)) (sqrt (* (* 2 PI) n))) 1/4)) (sqrt (* (* 2 PI) n))) (* (* (* k k) 1/8) (+ (* (sqrt (* (* 2 PI) n)) (* (log (* 2 PI)) (log (* 2 PI)))) (* (sqrt (* (* 2 PI) n)) (* (log n) (log n)))))) (/ (* (* k (sqrt (* (* 2 PI) n))) (log (* (* 2 PI) n))) 2))
  (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n)))))
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (+ (+ (* (- (log (* 2 PI))) (* (* (* k k) (* +nan.0 (sqrt (* (* 2 PI) n)))) (log n))) (* (* (* k k) (* +nan.0 (sqrt (* (* 2 PI) n)))) (- (log (* 2 PI)) (* (log n) (log n))))) (+ (+ (- (* k (* +nan.0 (sqrt (* (* 2 PI) n)))) (* +nan.0 (sqrt (* (* 2 PI) n)))) (* (* (* k k) (* +nan.0 (sqrt (* (* 2 PI) n)))) (- (* (log (* 2 PI)) (log (* 2 PI))) (log n)))) (- (* (* k k) (* +nan.0 (sqrt (* (* 2 PI) n)))) (* +nan.0 (* (* k (sqrt (* (* 2 PI) n))) (- (log (* 2 PI)) (log n)))))))
  (+ (/ (* (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (- +nan.0)) (* (* k k) k)) (* +nan.0 (- (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) k) (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* 1/2 k)))) (* k k)))))
  (+ (- (* (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))) k) +nan.0)) (* +nan.0 (- (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))) (* k k)) (exp (* (- 1/2 (* 1/2 k)) (- (log (* PI -2)) (log (/ -1 n))))))))
7.003 * * * [progress]: adding candidates to table
7.628 * * [progress]: iteration 2 / 4
7.628 * * * [progress]: picking best candidate
7.670 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
7.670 * * * [progress]: localizing error
7.706 * * * [progress]: generating rewritten candidates
7.706 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2)
7.729 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1)
7.735 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1)
7.758 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
7.799 * * * [progress]: generating series expansions
7.799 * * * * [progress]: [ 1 / 4 ] generating series at (2 2)
7.800 * [backup-simplify]: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
7.800 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
7.800 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
7.800 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
7.800 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
7.800 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
7.800 * [taylor]: Taking taylor expansion of 1/2 in k
7.800 * [backup-simplify]: Simplify 1/2 into 1/2
7.800 * [taylor]: Taking taylor expansion of (- 1 k) in k
7.800 * [taylor]: Taking taylor expansion of 1 in k
7.800 * [backup-simplify]: Simplify 1 into 1
7.800 * [taylor]: Taking taylor expansion of k in k
7.800 * [backup-simplify]: Simplify 0 into 0
7.800 * [backup-simplify]: Simplify 1 into 1
7.800 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
7.800 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
7.800 * [taylor]: Taking taylor expansion of 2 in k
7.800 * [backup-simplify]: Simplify 2 into 2
7.800 * [taylor]: Taking taylor expansion of (* n PI) in k
7.800 * [taylor]: Taking taylor expansion of n in k
7.800 * [backup-simplify]: Simplify n into n
7.800 * [taylor]: Taking taylor expansion of PI in k
7.800 * [backup-simplify]: Simplify PI into PI
7.800 * [backup-simplify]: Simplify (* n PI) into (* n PI)
7.800 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
7.800 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
7.801 * [backup-simplify]: Simplify (- 0) into 0
7.801 * [backup-simplify]: Simplify (+ 1 0) into 1
7.801 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.801 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
7.804 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
7.804 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
7.804 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
7.804 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
7.804 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
7.804 * [taylor]: Taking taylor expansion of 1/2 in n
7.804 * [backup-simplify]: Simplify 1/2 into 1/2
7.804 * [taylor]: Taking taylor expansion of (- 1 k) in n
7.804 * [taylor]: Taking taylor expansion of 1 in n
7.804 * [backup-simplify]: Simplify 1 into 1
7.804 * [taylor]: Taking taylor expansion of k in n
7.804 * [backup-simplify]: Simplify k into k
7.804 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
7.804 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
7.804 * [taylor]: Taking taylor expansion of 2 in n
7.804 * [backup-simplify]: Simplify 2 into 2
7.804 * [taylor]: Taking taylor expansion of (* n PI) in n
7.804 * [taylor]: Taking taylor expansion of n in n
7.804 * [backup-simplify]: Simplify 0 into 0
7.804 * [backup-simplify]: Simplify 1 into 1
7.804 * [taylor]: Taking taylor expansion of PI in n
7.804 * [backup-simplify]: Simplify PI into PI
7.805 * [backup-simplify]: Simplify (* 0 PI) into 0
7.805 * [backup-simplify]: Simplify (* 2 0) into 0
7.806 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.807 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
7.807 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.808 * [backup-simplify]: Simplify (- k) into (- k)
7.808 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
7.808 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
7.808 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.809 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
7.810 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
7.810 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
7.810 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
7.810 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
7.810 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
7.810 * [taylor]: Taking taylor expansion of 1/2 in n
7.810 * [backup-simplify]: Simplify 1/2 into 1/2
7.810 * [taylor]: Taking taylor expansion of (- 1 k) in n
7.810 * [taylor]: Taking taylor expansion of 1 in n
7.810 * [backup-simplify]: Simplify 1 into 1
7.810 * [taylor]: Taking taylor expansion of k in n
7.810 * [backup-simplify]: Simplify k into k
7.810 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
7.810 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
7.810 * [taylor]: Taking taylor expansion of 2 in n
7.810 * [backup-simplify]: Simplify 2 into 2
7.810 * [taylor]: Taking taylor expansion of (* n PI) in n
7.810 * [taylor]: Taking taylor expansion of n in n
7.810 * [backup-simplify]: Simplify 0 into 0
7.810 * [backup-simplify]: Simplify 1 into 1
7.810 * [taylor]: Taking taylor expansion of PI in n
7.810 * [backup-simplify]: Simplify PI into PI
7.811 * [backup-simplify]: Simplify (* 0 PI) into 0
7.811 * [backup-simplify]: Simplify (* 2 0) into 0
7.812 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.813 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
7.813 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.813 * [backup-simplify]: Simplify (- k) into (- k)
7.813 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
7.814 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
7.814 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.815 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
7.816 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
7.816 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
7.816 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
7.816 * [taylor]: Taking taylor expansion of 1/2 in k
7.816 * [backup-simplify]: Simplify 1/2 into 1/2
7.816 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
7.816 * [taylor]: Taking taylor expansion of (- 1 k) in k
7.816 * [taylor]: Taking taylor expansion of 1 in k
7.816 * [backup-simplify]: Simplify 1 into 1
7.816 * [taylor]: Taking taylor expansion of k in k
7.816 * [backup-simplify]: Simplify 0 into 0
7.816 * [backup-simplify]: Simplify 1 into 1
7.816 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
7.816 * [taylor]: Taking taylor expansion of (log n) in k
7.816 * [taylor]: Taking taylor expansion of n in k
7.816 * [backup-simplify]: Simplify n into n
7.816 * [backup-simplify]: Simplify (log n) into (log n)
7.816 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
7.816 * [taylor]: Taking taylor expansion of (* 2 PI) in k
7.816 * [taylor]: Taking taylor expansion of 2 in k
7.817 * [backup-simplify]: Simplify 2 into 2
7.817 * [taylor]: Taking taylor expansion of PI in k
7.817 * [backup-simplify]: Simplify PI into PI
7.817 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.817 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.818 * [backup-simplify]: Simplify (- 0) into 0
7.818 * [backup-simplify]: Simplify (+ 1 0) into 1
7.819 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.819 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
7.820 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
7.821 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
7.821 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
7.822 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
7.823 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
7.824 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.824 * [backup-simplify]: Simplify (- 0) into 0
7.825 * [backup-simplify]: Simplify (+ 0 0) into 0
7.825 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
7.826 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.827 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
7.828 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.828 * [taylor]: Taking taylor expansion of 0 in k
7.828 * [backup-simplify]: Simplify 0 into 0
7.828 * [backup-simplify]: Simplify 0 into 0
7.828 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
7.829 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
7.831 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.831 * [backup-simplify]: Simplify (+ 0 0) into 0
7.832 * [backup-simplify]: Simplify (- 1) into -1
7.832 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.834 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
7.836 * [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)))))
7.840 * [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)))))))
7.843 * [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)))))))
7.844 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
7.845 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
7.847 * [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
7.847 * [backup-simplify]: Simplify (- 0) into 0
7.847 * [backup-simplify]: Simplify (+ 0 0) into 0
7.848 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
7.849 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.850 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
7.851 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.851 * [taylor]: Taking taylor expansion of 0 in k
7.851 * [backup-simplify]: Simplify 0 into 0
7.851 * [backup-simplify]: Simplify 0 into 0
7.851 * [backup-simplify]: Simplify 0 into 0
7.852 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
7.853 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
7.855 * [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
7.855 * [backup-simplify]: Simplify (+ 0 0) into 0
7.855 * [backup-simplify]: Simplify (- 0) into 0
7.855 * [backup-simplify]: Simplify (+ 0 0) into 0
7.857 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
7.858 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
7.860 * [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)))))
7.863 * [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)))))
7.869 * [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)))))
7.870 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
7.870 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
7.870 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
7.870 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
7.870 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
7.870 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
7.870 * [taylor]: Taking taylor expansion of 1/2 in k
7.870 * [backup-simplify]: Simplify 1/2 into 1/2
7.870 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
7.870 * [taylor]: Taking taylor expansion of 1 in k
7.870 * [backup-simplify]: Simplify 1 into 1
7.870 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.870 * [taylor]: Taking taylor expansion of k in k
7.870 * [backup-simplify]: Simplify 0 into 0
7.870 * [backup-simplify]: Simplify 1 into 1
7.871 * [backup-simplify]: Simplify (/ 1 1) into 1
7.871 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
7.871 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
7.871 * [taylor]: Taking taylor expansion of 2 in k
7.871 * [backup-simplify]: Simplify 2 into 2
7.871 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.871 * [taylor]: Taking taylor expansion of PI in k
7.871 * [backup-simplify]: Simplify PI into PI
7.871 * [taylor]: Taking taylor expansion of n in k
7.871 * [backup-simplify]: Simplify n into n
7.871 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.871 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
7.871 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
7.871 * [backup-simplify]: Simplify (- 1) into -1
7.871 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.872 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
7.872 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
7.872 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
7.872 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
7.872 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
7.872 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
7.872 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
7.872 * [taylor]: Taking taylor expansion of 1/2 in n
7.872 * [backup-simplify]: Simplify 1/2 into 1/2
7.872 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
7.872 * [taylor]: Taking taylor expansion of 1 in n
7.872 * [backup-simplify]: Simplify 1 into 1
7.872 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.872 * [taylor]: Taking taylor expansion of k in n
7.872 * [backup-simplify]: Simplify k into k
7.872 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.872 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
7.872 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
7.872 * [taylor]: Taking taylor expansion of 2 in n
7.872 * [backup-simplify]: Simplify 2 into 2
7.872 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.872 * [taylor]: Taking taylor expansion of PI in n
7.872 * [backup-simplify]: Simplify PI into PI
7.872 * [taylor]: Taking taylor expansion of n in n
7.872 * [backup-simplify]: Simplify 0 into 0
7.872 * [backup-simplify]: Simplify 1 into 1
7.873 * [backup-simplify]: Simplify (/ PI 1) into PI
7.873 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.874 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.875 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
7.875 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
7.875 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
7.876 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.877 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
7.879 * [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)))))
7.879 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
7.879 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
7.879 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
7.879 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
7.879 * [taylor]: Taking taylor expansion of 1/2 in n
7.879 * [backup-simplify]: Simplify 1/2 into 1/2
7.879 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
7.879 * [taylor]: Taking taylor expansion of 1 in n
7.879 * [backup-simplify]: Simplify 1 into 1
7.879 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.879 * [taylor]: Taking taylor expansion of k in n
7.879 * [backup-simplify]: Simplify k into k
7.879 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.879 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
7.879 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
7.879 * [taylor]: Taking taylor expansion of 2 in n
7.879 * [backup-simplify]: Simplify 2 into 2
7.879 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.879 * [taylor]: Taking taylor expansion of PI in n
7.879 * [backup-simplify]: Simplify PI into PI
7.879 * [taylor]: Taking taylor expansion of n in n
7.879 * [backup-simplify]: Simplify 0 into 0
7.879 * [backup-simplify]: Simplify 1 into 1
7.880 * [backup-simplify]: Simplify (/ PI 1) into PI
7.880 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.882 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.882 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
7.882 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
7.882 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
7.883 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.885 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
7.886 * [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)))))
7.886 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
7.886 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
7.886 * [taylor]: Taking taylor expansion of 1/2 in k
7.886 * [backup-simplify]: Simplify 1/2 into 1/2
7.886 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
7.886 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
7.886 * [taylor]: Taking taylor expansion of 1 in k
7.886 * [backup-simplify]: Simplify 1 into 1
7.886 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.886 * [taylor]: Taking taylor expansion of k in k
7.886 * [backup-simplify]: Simplify 0 into 0
7.886 * [backup-simplify]: Simplify 1 into 1
7.887 * [backup-simplify]: Simplify (/ 1 1) into 1
7.887 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
7.887 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
7.887 * [taylor]: Taking taylor expansion of (* 2 PI) in k
7.887 * [taylor]: Taking taylor expansion of 2 in k
7.887 * [backup-simplify]: Simplify 2 into 2
7.887 * [taylor]: Taking taylor expansion of PI in k
7.887 * [backup-simplify]: Simplify PI into PI
7.887 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.888 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.889 * [taylor]: Taking taylor expansion of (log n) in k
7.889 * [taylor]: Taking taylor expansion of n in k
7.889 * [backup-simplify]: Simplify n into n
7.889 * [backup-simplify]: Simplify (log n) into (log n)
7.889 * [backup-simplify]: Simplify (- 1) into -1
7.889 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.889 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.891 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
7.892 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
7.893 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
7.894 * [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)))))
7.895 * [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)))))
7.896 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.897 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
7.898 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.899 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.899 * [backup-simplify]: Simplify (- 0) into 0
7.899 * [backup-simplify]: Simplify (+ 0 0) into 0
7.900 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
7.901 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.902 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
7.904 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.904 * [taylor]: Taking taylor expansion of 0 in k
7.904 * [backup-simplify]: Simplify 0 into 0
7.904 * [backup-simplify]: Simplify 0 into 0
7.904 * [backup-simplify]: Simplify 0 into 0
7.905 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.906 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
7.908 * [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
7.908 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.908 * [backup-simplify]: Simplify (- 0) into 0
7.908 * [backup-simplify]: Simplify (+ 0 0) into 0
7.913 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
7.914 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.915 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
7.917 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.917 * [taylor]: Taking taylor expansion of 0 in k
7.917 * [backup-simplify]: Simplify 0 into 0
7.917 * [backup-simplify]: Simplify 0 into 0
7.917 * [backup-simplify]: Simplify 0 into 0
7.917 * [backup-simplify]: Simplify 0 into 0
7.918 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.918 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.922 * [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
7.922 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.922 * [backup-simplify]: Simplify (- 0) into 0
7.922 * [backup-simplify]: Simplify (+ 0 0) into 0
7.923 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
7.924 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.925 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
7.927 * [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
7.927 * [taylor]: Taking taylor expansion of 0 in k
7.927 * [backup-simplify]: Simplify 0 into 0
7.927 * [backup-simplify]: Simplify 0 into 0
7.927 * [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))))))
7.928 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
7.928 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
7.928 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
7.928 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
7.928 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
7.928 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
7.928 * [taylor]: Taking taylor expansion of 1/2 in k
7.928 * [backup-simplify]: Simplify 1/2 into 1/2
7.928 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
7.928 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.928 * [taylor]: Taking taylor expansion of k in k
7.928 * [backup-simplify]: Simplify 0 into 0
7.928 * [backup-simplify]: Simplify 1 into 1
7.928 * [backup-simplify]: Simplify (/ 1 1) into 1
7.928 * [taylor]: Taking taylor expansion of 1 in k
7.928 * [backup-simplify]: Simplify 1 into 1
7.928 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
7.928 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
7.928 * [taylor]: Taking taylor expansion of -2 in k
7.928 * [backup-simplify]: Simplify -2 into -2
7.928 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.928 * [taylor]: Taking taylor expansion of PI in k
7.929 * [backup-simplify]: Simplify PI into PI
7.929 * [taylor]: Taking taylor expansion of n in k
7.929 * [backup-simplify]: Simplify n into n
7.929 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.929 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
7.929 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
7.929 * [backup-simplify]: Simplify (+ 1 0) into 1
7.929 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.929 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
7.929 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
7.929 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
7.929 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
7.929 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
7.929 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
7.930 * [taylor]: Taking taylor expansion of 1/2 in n
7.930 * [backup-simplify]: Simplify 1/2 into 1/2
7.930 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
7.930 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.930 * [taylor]: Taking taylor expansion of k in n
7.930 * [backup-simplify]: Simplify k into k
7.930 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.930 * [taylor]: Taking taylor expansion of 1 in n
7.930 * [backup-simplify]: Simplify 1 into 1
7.930 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
7.930 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
7.930 * [taylor]: Taking taylor expansion of -2 in n
7.930 * [backup-simplify]: Simplify -2 into -2
7.930 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.930 * [taylor]: Taking taylor expansion of PI in n
7.930 * [backup-simplify]: Simplify PI into PI
7.930 * [taylor]: Taking taylor expansion of n in n
7.930 * [backup-simplify]: Simplify 0 into 0
7.930 * [backup-simplify]: Simplify 1 into 1
7.930 * [backup-simplify]: Simplify (/ PI 1) into PI
7.930 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.931 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
7.931 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
7.931 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
7.932 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.933 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
7.934 * [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)))))
7.934 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
7.934 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
7.934 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
7.934 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
7.934 * [taylor]: Taking taylor expansion of 1/2 in n
7.934 * [backup-simplify]: Simplify 1/2 into 1/2
7.934 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
7.934 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.934 * [taylor]: Taking taylor expansion of k in n
7.934 * [backup-simplify]: Simplify k into k
7.934 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.934 * [taylor]: Taking taylor expansion of 1 in n
7.934 * [backup-simplify]: Simplify 1 into 1
7.934 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
7.934 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
7.934 * [taylor]: Taking taylor expansion of -2 in n
7.934 * [backup-simplify]: Simplify -2 into -2
7.934 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.934 * [taylor]: Taking taylor expansion of PI in n
7.934 * [backup-simplify]: Simplify PI into PI
7.934 * [taylor]: Taking taylor expansion of n in n
7.934 * [backup-simplify]: Simplify 0 into 0
7.934 * [backup-simplify]: Simplify 1 into 1
7.934 * [backup-simplify]: Simplify (/ PI 1) into PI
7.935 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.935 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
7.935 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
7.935 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
7.936 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.937 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
7.938 * [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)))))
7.938 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
7.938 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
7.938 * [taylor]: Taking taylor expansion of 1/2 in k
7.938 * [backup-simplify]: Simplify 1/2 into 1/2
7.938 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
7.938 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
7.938 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.938 * [taylor]: Taking taylor expansion of k in k
7.938 * [backup-simplify]: Simplify 0 into 0
7.938 * [backup-simplify]: Simplify 1 into 1
7.938 * [backup-simplify]: Simplify (/ 1 1) into 1
7.938 * [taylor]: Taking taylor expansion of 1 in k
7.938 * [backup-simplify]: Simplify 1 into 1
7.938 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
7.938 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
7.938 * [taylor]: Taking taylor expansion of (* -2 PI) in k
7.938 * [taylor]: Taking taylor expansion of -2 in k
7.938 * [backup-simplify]: Simplify -2 into -2
7.938 * [taylor]: Taking taylor expansion of PI in k
7.938 * [backup-simplify]: Simplify PI into PI
7.939 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.939 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
7.939 * [taylor]: Taking taylor expansion of (log n) in k
7.939 * [taylor]: Taking taylor expansion of n in k
7.939 * [backup-simplify]: Simplify n into n
7.939 * [backup-simplify]: Simplify (log n) into (log n)
7.940 * [backup-simplify]: Simplify (+ 1 0) into 1
7.940 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.940 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
7.941 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
7.942 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
7.943 * [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)))))
7.944 * [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)))))
7.945 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.946 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
7.947 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
7.948 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.948 * [backup-simplify]: Simplify (+ 0 0) into 0
7.948 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
7.950 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.951 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
7.953 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.953 * [taylor]: Taking taylor expansion of 0 in k
7.953 * [backup-simplify]: Simplify 0 into 0
7.953 * [backup-simplify]: Simplify 0 into 0
7.953 * [backup-simplify]: Simplify 0 into 0
7.954 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.955 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
7.957 * [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
7.957 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.958 * [backup-simplify]: Simplify (+ 0 0) into 0
7.958 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
7.959 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.960 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
7.962 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.962 * [taylor]: Taking taylor expansion of 0 in k
7.962 * [backup-simplify]: Simplify 0 into 0
7.962 * [backup-simplify]: Simplify 0 into 0
7.962 * [backup-simplify]: Simplify 0 into 0
7.962 * [backup-simplify]: Simplify 0 into 0
7.962 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.963 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.967 * [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
7.967 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.967 * [backup-simplify]: Simplify (+ 0 0) into 0
7.968 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
7.969 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.970 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
7.972 * [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
7.972 * [taylor]: Taking taylor expansion of 0 in k
7.972 * [backup-simplify]: Simplify 0 into 0
7.972 * [backup-simplify]: Simplify 0 into 0
7.973 * [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))))))
7.973 * * * * [progress]: [ 2 / 4 ] generating series at (2 1)
7.973 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k))
7.973 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0
7.973 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
7.973 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.973 * [taylor]: Taking taylor expansion of k in k
7.973 * [backup-simplify]: Simplify 0 into 0
7.973 * [backup-simplify]: Simplify 1 into 1
7.973 * [backup-simplify]: Simplify (/ 1 1) into 1
7.973 * [backup-simplify]: Simplify (sqrt 0) into 0
7.974 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.974 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
7.974 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.974 * [taylor]: Taking taylor expansion of k in k
7.974 * [backup-simplify]: Simplify 0 into 0
7.974 * [backup-simplify]: Simplify 1 into 1
7.974 * [backup-simplify]: Simplify (/ 1 1) into 1
7.975 * [backup-simplify]: Simplify (sqrt 0) into 0
7.976 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.976 * [backup-simplify]: Simplify 0 into 0
7.976 * [backup-simplify]: Simplify +nan.0 into +nan.0
7.976 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
7.978 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
7.978 * [backup-simplify]: Simplify +nan.0 into +nan.0
7.979 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.981 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
7.981 * [backup-simplify]: Simplify +nan.0 into +nan.0
7.981 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
7.981 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k)
7.981 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0
7.981 * [taylor]: Taking taylor expansion of (sqrt k) in k
7.981 * [taylor]: Taking taylor expansion of k in k
7.981 * [backup-simplify]: Simplify 0 into 0
7.981 * [backup-simplify]: Simplify 1 into 1
7.982 * [backup-simplify]: Simplify (sqrt 0) into 0
7.982 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.982 * [taylor]: Taking taylor expansion of (sqrt k) in k
7.982 * [taylor]: Taking taylor expansion of k in k
7.982 * [backup-simplify]: Simplify 0 into 0
7.982 * [backup-simplify]: Simplify 1 into 1
7.983 * [backup-simplify]: Simplify (sqrt 0) into 0
7.983 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.983 * [backup-simplify]: Simplify 0 into 0
7.984 * [backup-simplify]: Simplify +nan.0 into +nan.0
7.985 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
7.985 * [backup-simplify]: Simplify +nan.0 into +nan.0
7.988 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
7.988 * [backup-simplify]: Simplify +nan.0 into +nan.0
7.988 * [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))))))))
7.988 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k)))
7.988 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0
7.988 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
7.988 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
7.988 * [taylor]: Taking taylor expansion of (/ -1 k) in k
7.988 * [taylor]: Taking taylor expansion of -1 in k
7.988 * [backup-simplify]: Simplify -1 into -1
7.988 * [taylor]: Taking taylor expansion of k in k
7.988 * [backup-simplify]: Simplify 0 into 0
7.988 * [backup-simplify]: Simplify 1 into 1
7.988 * [backup-simplify]: Simplify (/ -1 1) into -1
7.989 * [backup-simplify]: Simplify (sqrt 0) into 0
7.989 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
7.990 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
7.990 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
7.990 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
7.990 * [taylor]: Taking taylor expansion of (/ -1 k) in k
7.990 * [taylor]: Taking taylor expansion of -1 in k
7.990 * [backup-simplify]: Simplify -1 into -1
7.990 * [taylor]: Taking taylor expansion of k in k
7.990 * [backup-simplify]: Simplify 0 into 0
7.990 * [backup-simplify]: Simplify 1 into 1
7.990 * [backup-simplify]: Simplify (/ -1 1) into -1
7.990 * [backup-simplify]: Simplify (sqrt 0) into 0
7.991 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
7.991 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
7.991 * [backup-simplify]: Simplify +nan.0 into +nan.0
7.992 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
7.994 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
7.995 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
7.995 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
7.996 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.998 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
8.000 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
8.000 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
8.001 * [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)))))
8.001 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1)
8.002 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
8.002 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
8.002 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
8.002 * [taylor]: Taking taylor expansion of 2 in n
8.002 * [backup-simplify]: Simplify 2 into 2
8.002 * [taylor]: Taking taylor expansion of (* n PI) in n
8.002 * [taylor]: Taking taylor expansion of n in n
8.002 * [backup-simplify]: Simplify 0 into 0
8.002 * [backup-simplify]: Simplify 1 into 1
8.002 * [taylor]: Taking taylor expansion of PI in n
8.002 * [backup-simplify]: Simplify PI into PI
8.002 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
8.002 * [taylor]: Taking taylor expansion of 2 in n
8.002 * [backup-simplify]: Simplify 2 into 2
8.002 * [taylor]: Taking taylor expansion of (* n PI) in n
8.002 * [taylor]: Taking taylor expansion of n in n
8.002 * [backup-simplify]: Simplify 0 into 0
8.002 * [backup-simplify]: Simplify 1 into 1
8.002 * [taylor]: Taking taylor expansion of PI in n
8.002 * [backup-simplify]: Simplify PI into PI
8.002 * [backup-simplify]: Simplify (* 0 PI) into 0
8.003 * [backup-simplify]: Simplify (* 2 0) into 0
8.003 * [backup-simplify]: Simplify 0 into 0
8.009 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.010 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
8.011 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.012 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
8.013 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
8.013 * [backup-simplify]: Simplify 0 into 0
8.014 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
8.015 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
8.015 * [backup-simplify]: Simplify 0 into 0
8.017 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.018 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
8.018 * [backup-simplify]: Simplify 0 into 0
8.020 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
8.021 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
8.021 * [backup-simplify]: Simplify 0 into 0
8.022 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
8.023 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
8.023 * [backup-simplify]: Simplify 0 into 0
8.024 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
8.025 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
8.025 * [backup-simplify]: Simplify 0 into 0
8.025 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
8.026 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n))
8.026 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
8.026 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
8.026 * [taylor]: Taking taylor expansion of 2 in n
8.026 * [backup-simplify]: Simplify 2 into 2
8.026 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.026 * [taylor]: Taking taylor expansion of PI in n
8.026 * [backup-simplify]: Simplify PI into PI
8.026 * [taylor]: Taking taylor expansion of n in n
8.026 * [backup-simplify]: Simplify 0 into 0
8.026 * [backup-simplify]: Simplify 1 into 1
8.026 * [backup-simplify]: Simplify (/ PI 1) into PI
8.026 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
8.026 * [taylor]: Taking taylor expansion of 2 in n
8.026 * [backup-simplify]: Simplify 2 into 2
8.026 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.026 * [taylor]: Taking taylor expansion of PI in n
8.026 * [backup-simplify]: Simplify PI into PI
8.026 * [taylor]: Taking taylor expansion of n in n
8.026 * [backup-simplify]: Simplify 0 into 0
8.026 * [backup-simplify]: Simplify 1 into 1
8.027 * [backup-simplify]: Simplify (/ PI 1) into PI
8.027 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.027 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.028 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.028 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
8.028 * [backup-simplify]: Simplify 0 into 0
8.029 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.029 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
8.029 * [backup-simplify]: Simplify 0 into 0
8.030 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.031 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.031 * [backup-simplify]: Simplify 0 into 0
8.031 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.032 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.032 * [backup-simplify]: Simplify 0 into 0
8.033 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.034 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
8.034 * [backup-simplify]: Simplify 0 into 0
8.035 * [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
8.036 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
8.036 * [backup-simplify]: Simplify 0 into 0
8.036 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
8.037 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n))
8.037 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
8.037 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
8.037 * [taylor]: Taking taylor expansion of -2 in n
8.037 * [backup-simplify]: Simplify -2 into -2
8.037 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.037 * [taylor]: Taking taylor expansion of PI in n
8.037 * [backup-simplify]: Simplify PI into PI
8.037 * [taylor]: Taking taylor expansion of n in n
8.037 * [backup-simplify]: Simplify 0 into 0
8.037 * [backup-simplify]: Simplify 1 into 1
8.037 * [backup-simplify]: Simplify (/ PI 1) into PI
8.037 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
8.037 * [taylor]: Taking taylor expansion of -2 in n
8.037 * [backup-simplify]: Simplify -2 into -2
8.037 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.037 * [taylor]: Taking taylor expansion of PI in n
8.037 * [backup-simplify]: Simplify PI into PI
8.037 * [taylor]: Taking taylor expansion of n in n
8.037 * [backup-simplify]: Simplify 0 into 0
8.037 * [backup-simplify]: Simplify 1 into 1
8.038 * [backup-simplify]: Simplify (/ PI 1) into PI
8.038 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
8.038 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
8.039 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.039 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
8.039 * [backup-simplify]: Simplify 0 into 0
8.040 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.041 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
8.041 * [backup-simplify]: Simplify 0 into 0
8.041 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.042 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.042 * [backup-simplify]: Simplify 0 into 0
8.043 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.043 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.043 * [backup-simplify]: Simplify 0 into 0
8.044 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.045 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
8.045 * [backup-simplify]: Simplify 0 into 0
8.046 * [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
8.047 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
8.047 * [backup-simplify]: Simplify 0 into 0
8.047 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
8.047 * * * * [progress]: [ 4 / 4 ] generating series at (2)
8.048 * [backup-simplify]: Simplify (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
8.048 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0
8.048 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
8.048 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
8.048 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
8.048 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
8.048 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
8.048 * [taylor]: Taking taylor expansion of 1/2 in n
8.048 * [backup-simplify]: Simplify 1/2 into 1/2
8.048 * [taylor]: Taking taylor expansion of (- 1 k) in n
8.048 * [taylor]: Taking taylor expansion of 1 in n
8.048 * [backup-simplify]: Simplify 1 into 1
8.048 * [taylor]: Taking taylor expansion of k in n
8.048 * [backup-simplify]: Simplify k into k
8.048 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
8.048 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
8.048 * [taylor]: Taking taylor expansion of 2 in n
8.048 * [backup-simplify]: Simplify 2 into 2
8.048 * [taylor]: Taking taylor expansion of (* n PI) in n
8.048 * [taylor]: Taking taylor expansion of n in n
8.048 * [backup-simplify]: Simplify 0 into 0
8.048 * [backup-simplify]: Simplify 1 into 1
8.048 * [taylor]: Taking taylor expansion of PI in n
8.048 * [backup-simplify]: Simplify PI into PI
8.048 * [backup-simplify]: Simplify (* 0 PI) into 0
8.049 * [backup-simplify]: Simplify (* 2 0) into 0
8.050 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.052 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
8.053 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.053 * [backup-simplify]: Simplify (- k) into (- k)
8.053 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
8.053 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
8.055 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.056 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
8.057 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
8.057 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
8.057 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.057 * [taylor]: Taking taylor expansion of k in n
8.057 * [backup-simplify]: Simplify k into k
8.057 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.057 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
8.057 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
8.057 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
8.057 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
8.058 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
8.058 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
8.058 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
8.058 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
8.058 * [taylor]: Taking taylor expansion of 1/2 in k
8.058 * [backup-simplify]: Simplify 1/2 into 1/2
8.058 * [taylor]: Taking taylor expansion of (- 1 k) in k
8.058 * [taylor]: Taking taylor expansion of 1 in k
8.058 * [backup-simplify]: Simplify 1 into 1
8.058 * [taylor]: Taking taylor expansion of k in k
8.058 * [backup-simplify]: Simplify 0 into 0
8.058 * [backup-simplify]: Simplify 1 into 1
8.058 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
8.058 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
8.058 * [taylor]: Taking taylor expansion of 2 in k
8.058 * [backup-simplify]: Simplify 2 into 2
8.058 * [taylor]: Taking taylor expansion of (* n PI) in k
8.058 * [taylor]: Taking taylor expansion of n in k
8.058 * [backup-simplify]: Simplify n into n
8.058 * [taylor]: Taking taylor expansion of PI in k
8.058 * [backup-simplify]: Simplify PI into PI
8.058 * [backup-simplify]: Simplify (* n PI) into (* n PI)
8.058 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
8.058 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
8.059 * [backup-simplify]: Simplify (- 0) into 0
8.059 * [backup-simplify]: Simplify (+ 1 0) into 1
8.060 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
8.060 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
8.060 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
8.060 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
8.060 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.060 * [taylor]: Taking taylor expansion of k in k
8.060 * [backup-simplify]: Simplify 0 into 0
8.060 * [backup-simplify]: Simplify 1 into 1
8.060 * [backup-simplify]: Simplify (/ 1 1) into 1
8.061 * [backup-simplify]: Simplify (sqrt 0) into 0
8.062 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
8.062 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
8.062 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
8.062 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
8.062 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
8.062 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
8.062 * [taylor]: Taking taylor expansion of 1/2 in k
8.062 * [backup-simplify]: Simplify 1/2 into 1/2
8.062 * [taylor]: Taking taylor expansion of (- 1 k) in k
8.063 * [taylor]: Taking taylor expansion of 1 in k
8.063 * [backup-simplify]: Simplify 1 into 1
8.063 * [taylor]: Taking taylor expansion of k in k
8.063 * [backup-simplify]: Simplify 0 into 0
8.063 * [backup-simplify]: Simplify 1 into 1
8.063 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
8.063 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
8.063 * [taylor]: Taking taylor expansion of 2 in k
8.063 * [backup-simplify]: Simplify 2 into 2
8.063 * [taylor]: Taking taylor expansion of (* n PI) in k
8.063 * [taylor]: Taking taylor expansion of n in k
8.063 * [backup-simplify]: Simplify n into n
8.063 * [taylor]: Taking taylor expansion of PI in k
8.063 * [backup-simplify]: Simplify PI into PI
8.063 * [backup-simplify]: Simplify (* n PI) into (* n PI)
8.063 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
8.063 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
8.064 * [backup-simplify]: Simplify (- 0) into 0
8.064 * [backup-simplify]: Simplify (+ 1 0) into 1
8.064 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
8.065 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
8.065 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
8.065 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
8.065 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.065 * [taylor]: Taking taylor expansion of k in k
8.065 * [backup-simplify]: Simplify 0 into 0
8.065 * [backup-simplify]: Simplify 1 into 1
8.065 * [backup-simplify]: Simplify (/ 1 1) into 1
8.066 * [backup-simplify]: Simplify (sqrt 0) into 0
8.067 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
8.067 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0
8.067 * [taylor]: Taking taylor expansion of 0 in n
8.067 * [backup-simplify]: Simplify 0 into 0
8.067 * [backup-simplify]: Simplify 0 into 0
8.068 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
8.069 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
8.069 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
8.070 * [backup-simplify]: Simplify (- 1) into -1
8.070 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.071 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
8.071 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
8.072 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))
8.072 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))
8.072 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
8.072 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
8.072 * [taylor]: Taking taylor expansion of +nan.0 in n
8.072 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.072 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
8.072 * [taylor]: Taking taylor expansion of (sqrt 2) in n
8.072 * [taylor]: Taking taylor expansion of 2 in n
8.072 * [backup-simplify]: Simplify 2 into 2
8.073 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
8.073 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
8.073 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
8.074 * [taylor]: Taking taylor expansion of (* n PI) in n
8.074 * [taylor]: Taking taylor expansion of n in n
8.074 * [backup-simplify]: Simplify 0 into 0
8.074 * [backup-simplify]: Simplify 1 into 1
8.074 * [taylor]: Taking taylor expansion of PI in n
8.074 * [backup-simplify]: Simplify PI into PI
8.074 * [backup-simplify]: Simplify (* 0 PI) into 0
8.076 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.076 * [backup-simplify]: Simplify (sqrt 0) into 0
8.077 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
8.078 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
8.078 * [backup-simplify]: Simplify (* +nan.0 0) into 0
8.079 * [backup-simplify]: Simplify (- 0) into 0
8.079 * [backup-simplify]: Simplify 0 into 0
8.079 * [backup-simplify]: Simplify 0 into 0
8.080 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
8.083 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
8.083 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
8.084 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
8.086 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0
8.086 * [backup-simplify]: Simplify (- 0) into 0
8.087 * [backup-simplify]: Simplify (+ 0 0) into 0
8.088 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
8.089 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
8.090 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))
8.091 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))
8.091 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n
8.091 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n
8.091 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
8.091 * [taylor]: Taking taylor expansion of +nan.0 in n
8.091 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.091 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
8.091 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
8.091 * [taylor]: Taking taylor expansion of (sqrt 2) in n
8.091 * [taylor]: Taking taylor expansion of 2 in n
8.091 * [backup-simplify]: Simplify 2 into 2
8.091 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
8.092 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
8.092 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
8.092 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
8.092 * [taylor]: Taking taylor expansion of 2 in n
8.092 * [backup-simplify]: Simplify 2 into 2
8.092 * [taylor]: Taking taylor expansion of (* n PI) in n
8.092 * [taylor]: Taking taylor expansion of n in n
8.092 * [backup-simplify]: Simplify 0 into 0
8.092 * [backup-simplify]: Simplify 1 into 1
8.092 * [taylor]: Taking taylor expansion of PI in n
8.092 * [backup-simplify]: Simplify PI into PI
8.093 * [backup-simplify]: Simplify (* 0 PI) into 0
8.093 * [backup-simplify]: Simplify (* 2 0) into 0
8.095 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.096 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
8.097 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.097 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
8.097 * [taylor]: Taking taylor expansion of (* n PI) in n
8.097 * [taylor]: Taking taylor expansion of n in n
8.097 * [backup-simplify]: Simplify 0 into 0
8.098 * [backup-simplify]: Simplify 1 into 1
8.098 * [taylor]: Taking taylor expansion of PI in n
8.098 * [backup-simplify]: Simplify PI into PI
8.098 * [backup-simplify]: Simplify (* 0 PI) into 0
8.100 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.100 * [backup-simplify]: Simplify (sqrt 0) into 0
8.101 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
8.101 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
8.101 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
8.102 * [taylor]: Taking taylor expansion of +nan.0 in n
8.102 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.102 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
8.102 * [taylor]: Taking taylor expansion of (sqrt 2) in n
8.102 * [taylor]: Taking taylor expansion of 2 in n
8.102 * [backup-simplify]: Simplify 2 into 2
8.102 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
8.103 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
8.103 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
8.103 * [taylor]: Taking taylor expansion of (* n PI) in n
8.103 * [taylor]: Taking taylor expansion of n in n
8.103 * [backup-simplify]: Simplify 0 into 0
8.103 * [backup-simplify]: Simplify 1 into 1
8.103 * [taylor]: Taking taylor expansion of PI in n
8.103 * [backup-simplify]: Simplify PI into PI
8.104 * [backup-simplify]: Simplify (* 0 PI) into 0
8.105 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.106 * [backup-simplify]: Simplify (sqrt 0) into 0
8.107 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
8.109 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.110 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
8.112 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
8.112 * [backup-simplify]: Simplify (* +nan.0 0) into 0
8.113 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
8.113 * [backup-simplify]: Simplify (* +nan.0 0) into 0
8.114 * [backup-simplify]: Simplify (- 0) into 0
8.114 * [backup-simplify]: Simplify (+ 0 0) into 0
8.115 * [backup-simplify]: Simplify (- 0) into 0
8.115 * [backup-simplify]: Simplify 0 into 0
8.118 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
8.124 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
8.128 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
8.130 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI)))
8.131 * [backup-simplify]: Simplify 0 into 0
8.131 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.142 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
8.143 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.144 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
8.147 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0
8.147 * [backup-simplify]: Simplify (- 0) into 0
8.147 * [backup-simplify]: Simplify (+ 0 0) into 0
8.149 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
8.149 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0
8.150 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))
8.151 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))))
8.151 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n
8.151 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n
8.151 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
8.151 * [taylor]: Taking taylor expansion of +nan.0 in n
8.151 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.151 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
8.151 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
8.151 * [taylor]: Taking taylor expansion of (sqrt 2) in n
8.151 * [taylor]: Taking taylor expansion of 2 in n
8.151 * [backup-simplify]: Simplify 2 into 2
8.152 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
8.152 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
8.152 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
8.152 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
8.152 * [taylor]: Taking taylor expansion of 2 in n
8.152 * [backup-simplify]: Simplify 2 into 2
8.152 * [taylor]: Taking taylor expansion of (* n PI) in n
8.152 * [taylor]: Taking taylor expansion of n in n
8.152 * [backup-simplify]: Simplify 0 into 0
8.152 * [backup-simplify]: Simplify 1 into 1
8.152 * [taylor]: Taking taylor expansion of PI in n
8.152 * [backup-simplify]: Simplify PI into PI
8.153 * [backup-simplify]: Simplify (* 0 PI) into 0
8.153 * [backup-simplify]: Simplify (* 2 0) into 0
8.154 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.155 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
8.155 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.155 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
8.155 * [taylor]: Taking taylor expansion of (* n PI) in n
8.155 * [taylor]: Taking taylor expansion of n in n
8.155 * [backup-simplify]: Simplify 0 into 0
8.155 * [backup-simplify]: Simplify 1 into 1
8.155 * [taylor]: Taking taylor expansion of PI in n
8.155 * [backup-simplify]: Simplify PI into PI
8.156 * [backup-simplify]: Simplify (* 0 PI) into 0
8.157 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.157 * [backup-simplify]: Simplify (sqrt 0) into 0
8.158 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
8.158 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n
8.158 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n
8.158 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
8.158 * [taylor]: Taking taylor expansion of +nan.0 in n
8.158 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.158 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
8.158 * [taylor]: Taking taylor expansion of (sqrt 2) in n
8.158 * [taylor]: Taking taylor expansion of 2 in n
8.158 * [backup-simplify]: Simplify 2 into 2
8.158 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
8.159 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
8.159 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
8.159 * [taylor]: Taking taylor expansion of (* n PI) in n
8.159 * [taylor]: Taking taylor expansion of n in n
8.159 * [backup-simplify]: Simplify 0 into 0
8.159 * [backup-simplify]: Simplify 1 into 1
8.159 * [taylor]: Taking taylor expansion of PI in n
8.159 * [backup-simplify]: Simplify PI into PI
8.159 * [backup-simplify]: Simplify (* 0 PI) into 0
8.160 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.160 * [backup-simplify]: Simplify (sqrt 0) into 0
8.161 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
8.161 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n
8.161 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n
8.161 * [taylor]: Taking taylor expansion of +nan.0 in n
8.161 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.161 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n
8.161 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n
8.161 * [taylor]: Taking taylor expansion of (sqrt 2) in n
8.161 * [taylor]: Taking taylor expansion of 2 in n
8.161 * [backup-simplify]: Simplify 2 into 2
8.162 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
8.162 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
8.162 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
8.162 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
8.162 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
8.162 * [taylor]: Taking taylor expansion of 2 in n
8.162 * [backup-simplify]: Simplify 2 into 2
8.162 * [taylor]: Taking taylor expansion of (* n PI) in n
8.162 * [taylor]: Taking taylor expansion of n in n
8.162 * [backup-simplify]: Simplify 0 into 0
8.162 * [backup-simplify]: Simplify 1 into 1
8.162 * [taylor]: Taking taylor expansion of PI in n
8.162 * [backup-simplify]: Simplify PI into PI
8.162 * [backup-simplify]: Simplify (* 0 PI) into 0
8.163 * [backup-simplify]: Simplify (* 2 0) into 0
8.164 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.165 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
8.165 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.166 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.166 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
8.166 * [taylor]: Taking taylor expansion of (* n PI) in n
8.166 * [taylor]: Taking taylor expansion of n in n
8.166 * [backup-simplify]: Simplify 0 into 0
8.166 * [backup-simplify]: Simplify 1 into 1
8.166 * [taylor]: Taking taylor expansion of PI in n
8.166 * [backup-simplify]: Simplify PI into PI
8.167 * [backup-simplify]: Simplify (* 0 PI) into 0
8.168 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.168 * [backup-simplify]: Simplify (sqrt 0) into 0
8.169 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
8.170 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.171 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
8.172 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
8.172 * [backup-simplify]: Simplify (* +nan.0 0) into 0
8.172 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
8.173 * [backup-simplify]: Simplify (* +nan.0 0) into 0
8.173 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.174 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.176 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2)
8.177 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2))
8.178 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0
8.178 * [backup-simplify]: Simplify (* +nan.0 0) into 0
8.178 * [backup-simplify]: Simplify (- 0) into 0
8.178 * [backup-simplify]: Simplify (+ 0 0) into 0
8.179 * [backup-simplify]: Simplify (- 0) into 0
8.179 * [backup-simplify]: Simplify (+ 0 0) into 0
8.179 * [backup-simplify]: Simplify (- 0) into 0
8.179 * [backup-simplify]: Simplify 0 into 0
8.180 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
8.180 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
8.182 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
8.184 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.185 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
8.188 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))
8.195 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))
8.198 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
8.204 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
8.208 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
8.217 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))
8.226 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))))
8.234 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))))
8.236 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
8.240 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
8.241 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0
8.247 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
8.256 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
8.268 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
8.272 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
8.281 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))))))
8.281 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
8.281 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0
8.281 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
8.281 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
8.281 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
8.281 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
8.281 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
8.281 * [taylor]: Taking taylor expansion of 1/2 in n
8.281 * [backup-simplify]: Simplify 1/2 into 1/2
8.281 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
8.281 * [taylor]: Taking taylor expansion of 1 in n
8.281 * [backup-simplify]: Simplify 1 into 1
8.281 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.281 * [taylor]: Taking taylor expansion of k in n
8.281 * [backup-simplify]: Simplify k into k
8.281 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.281 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
8.281 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
8.281 * [taylor]: Taking taylor expansion of 2 in n
8.281 * [backup-simplify]: Simplify 2 into 2
8.281 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.282 * [taylor]: Taking taylor expansion of PI in n
8.282 * [backup-simplify]: Simplify PI into PI
8.282 * [taylor]: Taking taylor expansion of n in n
8.282 * [backup-simplify]: Simplify 0 into 0
8.282 * [backup-simplify]: Simplify 1 into 1
8.282 * [backup-simplify]: Simplify (/ PI 1) into PI
8.282 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.283 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.283 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
8.283 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
8.283 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
8.284 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
8.285 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
8.285 * [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)))))
8.285 * [taylor]: Taking taylor expansion of (sqrt k) in n
8.285 * [taylor]: Taking taylor expansion of k in n
8.285 * [backup-simplify]: Simplify k into k
8.286 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
8.286 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
8.286 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
8.286 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
8.286 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
8.286 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
8.286 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
8.286 * [taylor]: Taking taylor expansion of 1/2 in k
8.286 * [backup-simplify]: Simplify 1/2 into 1/2
8.286 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
8.286 * [taylor]: Taking taylor expansion of 1 in k
8.286 * [backup-simplify]: Simplify 1 into 1
8.286 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.286 * [taylor]: Taking taylor expansion of k in k
8.286 * [backup-simplify]: Simplify 0 into 0
8.286 * [backup-simplify]: Simplify 1 into 1
8.286 * [backup-simplify]: Simplify (/ 1 1) into 1
8.286 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
8.286 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
8.286 * [taylor]: Taking taylor expansion of 2 in k
8.286 * [backup-simplify]: Simplify 2 into 2
8.286 * [taylor]: Taking taylor expansion of (/ PI n) in k
8.286 * [taylor]: Taking taylor expansion of PI in k
8.286 * [backup-simplify]: Simplify PI into PI
8.286 * [taylor]: Taking taylor expansion of n in k
8.286 * [backup-simplify]: Simplify n into n
8.286 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
8.286 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
8.286 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
8.287 * [backup-simplify]: Simplify (- 1) into -1
8.287 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.287 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
8.287 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
8.287 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
8.287 * [taylor]: Taking taylor expansion of (sqrt k) in k
8.287 * [taylor]: Taking taylor expansion of k in k
8.287 * [backup-simplify]: Simplify 0 into 0
8.287 * [backup-simplify]: Simplify 1 into 1
8.288 * [backup-simplify]: Simplify (sqrt 0) into 0
8.289 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
8.289 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
8.289 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
8.289 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
8.289 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
8.289 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
8.289 * [taylor]: Taking taylor expansion of 1/2 in k
8.289 * [backup-simplify]: Simplify 1/2 into 1/2
8.289 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
8.289 * [taylor]: Taking taylor expansion of 1 in k
8.289 * [backup-simplify]: Simplify 1 into 1
8.289 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.289 * [taylor]: Taking taylor expansion of k in k
8.289 * [backup-simplify]: Simplify 0 into 0
8.289 * [backup-simplify]: Simplify 1 into 1
8.289 * [backup-simplify]: Simplify (/ 1 1) into 1
8.289 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
8.289 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
8.289 * [taylor]: Taking taylor expansion of 2 in k
8.289 * [backup-simplify]: Simplify 2 into 2
8.289 * [taylor]: Taking taylor expansion of (/ PI n) in k
8.289 * [taylor]: Taking taylor expansion of PI in k
8.289 * [backup-simplify]: Simplify PI into PI
8.289 * [taylor]: Taking taylor expansion of n in k
8.289 * [backup-simplify]: Simplify n into n
8.289 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
8.289 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
8.289 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
8.290 * [backup-simplify]: Simplify (- 1) into -1
8.290 * [backup-simplify]: Simplify (+ 0 -1) into -1
8.290 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
8.290 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
8.290 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
8.290 * [taylor]: Taking taylor expansion of (sqrt k) in k
8.290 * [taylor]: Taking taylor expansion of k in k
8.290 * [backup-simplify]: Simplify 0 into 0
8.290 * [backup-simplify]: Simplify 1 into 1
8.291 * [backup-simplify]: Simplify (sqrt 0) into 0
8.291 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
8.292 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0
8.292 * [taylor]: Taking taylor expansion of 0 in n
8.292 * [backup-simplify]: Simplify 0 into 0
8.292 * [backup-simplify]: Simplify 0 into 0
8.292 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
8.292 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
8.292 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
8.292 * [taylor]: Taking taylor expansion of +nan.0 in n
8.292 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.292 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
8.292 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
8.292 * [taylor]: Taking taylor expansion of 1/2 in n
8.292 * [backup-simplify]: Simplify 1/2 into 1/2
8.292 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
8.292 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
8.292 * [taylor]: Taking taylor expansion of 1 in n
8.292 * [backup-simplify]: Simplify 1 into 1
8.292 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.292 * [taylor]: Taking taylor expansion of k in n
8.292 * [backup-simplify]: Simplify k into k
8.292 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.292 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
8.292 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
8.292 * [taylor]: Taking taylor expansion of 2 in n
8.292 * [backup-simplify]: Simplify 2 into 2
8.292 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.292 * [taylor]: Taking taylor expansion of PI in n
8.292 * [backup-simplify]: Simplify PI into PI
8.292 * [taylor]: Taking taylor expansion of n in n
8.292 * [backup-simplify]: Simplify 0 into 0
8.292 * [backup-simplify]: Simplify 1 into 1
8.293 * [backup-simplify]: Simplify (/ PI 1) into PI
8.293 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.294 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.294 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
8.294 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
8.295 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
8.295 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
8.296 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
8.297 * [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)))))
8.298 * [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))))))
8.298 * [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)))))))
8.299 * [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)))))))
8.299 * [backup-simplify]: Simplify 0 into 0
8.302 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
8.303 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
8.303 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
8.303 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
8.303 * [taylor]: Taking taylor expansion of +nan.0 in n
8.303 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.303 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
8.303 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
8.303 * [taylor]: Taking taylor expansion of 1/2 in n
8.303 * [backup-simplify]: Simplify 1/2 into 1/2
8.303 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
8.303 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
8.303 * [taylor]: Taking taylor expansion of 1 in n
8.303 * [backup-simplify]: Simplify 1 into 1
8.303 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.303 * [taylor]: Taking taylor expansion of k in n
8.303 * [backup-simplify]: Simplify k into k
8.303 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.303 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
8.303 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
8.303 * [taylor]: Taking taylor expansion of 2 in n
8.303 * [backup-simplify]: Simplify 2 into 2
8.303 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.304 * [taylor]: Taking taylor expansion of PI in n
8.304 * [backup-simplify]: Simplify PI into PI
8.304 * [taylor]: Taking taylor expansion of n in n
8.304 * [backup-simplify]: Simplify 0 into 0
8.304 * [backup-simplify]: Simplify 1 into 1
8.304 * [backup-simplify]: Simplify (/ PI 1) into PI
8.305 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.306 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.306 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
8.306 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
8.307 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
8.309 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
8.310 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
8.311 * [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)))))
8.312 * [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))))))
8.314 * [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)))))))
8.315 * [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)))))))
8.316 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.317 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
8.319 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
8.319 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
8.320 * [backup-simplify]: Simplify (- 0) into 0
8.320 * [backup-simplify]: Simplify (+ 0 0) into 0
8.321 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
8.323 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
8.324 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0
8.326 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
8.328 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
8.328 * [backup-simplify]: Simplify (- 0) into 0
8.328 * [backup-simplify]: Simplify 0 into 0
8.328 * [backup-simplify]: Simplify 0 into 0
8.333 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
8.334 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
8.334 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
8.334 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
8.334 * [taylor]: Taking taylor expansion of +nan.0 in n
8.334 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.334 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
8.334 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
8.334 * [taylor]: Taking taylor expansion of 1/2 in n
8.334 * [backup-simplify]: Simplify 1/2 into 1/2
8.334 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
8.334 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
8.334 * [taylor]: Taking taylor expansion of 1 in n
8.334 * [backup-simplify]: Simplify 1 into 1
8.334 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.334 * [taylor]: Taking taylor expansion of k in n
8.334 * [backup-simplify]: Simplify k into k
8.334 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.334 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
8.334 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
8.334 * [taylor]: Taking taylor expansion of 2 in n
8.334 * [backup-simplify]: Simplify 2 into 2
8.334 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.334 * [taylor]: Taking taylor expansion of PI in n
8.334 * [backup-simplify]: Simplify PI into PI
8.335 * [taylor]: Taking taylor expansion of n in n
8.335 * [backup-simplify]: Simplify 0 into 0
8.335 * [backup-simplify]: Simplify 1 into 1
8.335 * [backup-simplify]: Simplify (/ PI 1) into PI
8.336 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.337 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.337 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
8.337 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
8.338 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
8.339 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
8.341 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
8.342 * [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)))))
8.343 * [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))))))
8.344 * [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)))))))
8.345 * [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)))))))
8.350 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) 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))))))))
8.350 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
8.350 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0
8.351 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
8.351 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
8.351 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
8.351 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
8.351 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
8.351 * [taylor]: Taking taylor expansion of 1/2 in n
8.351 * [backup-simplify]: Simplify 1/2 into 1/2
8.351 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
8.351 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.351 * [taylor]: Taking taylor expansion of k in n
8.351 * [backup-simplify]: Simplify k into k
8.351 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.351 * [taylor]: Taking taylor expansion of 1 in n
8.351 * [backup-simplify]: Simplify 1 into 1
8.351 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
8.351 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
8.351 * [taylor]: Taking taylor expansion of -2 in n
8.351 * [backup-simplify]: Simplify -2 into -2
8.351 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.351 * [taylor]: Taking taylor expansion of PI in n
8.351 * [backup-simplify]: Simplify PI into PI
8.351 * [taylor]: Taking taylor expansion of n in n
8.351 * [backup-simplify]: Simplify 0 into 0
8.351 * [backup-simplify]: Simplify 1 into 1
8.352 * [backup-simplify]: Simplify (/ PI 1) into PI
8.352 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
8.353 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
8.353 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
8.353 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
8.355 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
8.356 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
8.357 * [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)))))
8.357 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
8.357 * [taylor]: Taking taylor expansion of (/ -1 k) in n
8.357 * [taylor]: Taking taylor expansion of -1 in n
8.357 * [backup-simplify]: Simplify -1 into -1
8.357 * [taylor]: Taking taylor expansion of k in n
8.357 * [backup-simplify]: Simplify k into k
8.357 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
8.358 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
8.358 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
8.358 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
8.359 * [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)))
8.359 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
8.359 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
8.359 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
8.359 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
8.359 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
8.359 * [taylor]: Taking taylor expansion of 1/2 in k
8.359 * [backup-simplify]: Simplify 1/2 into 1/2
8.359 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
8.359 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.359 * [taylor]: Taking taylor expansion of k in k
8.359 * [backup-simplify]: Simplify 0 into 0
8.359 * [backup-simplify]: Simplify 1 into 1
8.360 * [backup-simplify]: Simplify (/ 1 1) into 1
8.360 * [taylor]: Taking taylor expansion of 1 in k
8.360 * [backup-simplify]: Simplify 1 into 1
8.360 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
8.360 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
8.360 * [taylor]: Taking taylor expansion of -2 in k
8.360 * [backup-simplify]: Simplify -2 into -2
8.360 * [taylor]: Taking taylor expansion of (/ PI n) in k
8.360 * [taylor]: Taking taylor expansion of PI in k
8.360 * [backup-simplify]: Simplify PI into PI
8.360 * [taylor]: Taking taylor expansion of n in k
8.360 * [backup-simplify]: Simplify n into n
8.360 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
8.360 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
8.361 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
8.361 * [backup-simplify]: Simplify (+ 1 0) into 1
8.361 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
8.362 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
8.362 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
8.362 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
8.362 * [taylor]: Taking taylor expansion of (/ -1 k) in k
8.362 * [taylor]: Taking taylor expansion of -1 in k
8.362 * [backup-simplify]: Simplify -1 into -1
8.362 * [taylor]: Taking taylor expansion of k in k
8.362 * [backup-simplify]: Simplify 0 into 0
8.362 * [backup-simplify]: Simplify 1 into 1
8.362 * [backup-simplify]: Simplify (/ -1 1) into -1
8.363 * [backup-simplify]: Simplify (sqrt 0) into 0
8.364 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
8.364 * [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)))))
8.364 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
8.364 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
8.364 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
8.364 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
8.364 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
8.365 * [taylor]: Taking taylor expansion of 1/2 in k
8.365 * [backup-simplify]: Simplify 1/2 into 1/2
8.365 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
8.365 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.365 * [taylor]: Taking taylor expansion of k in k
8.365 * [backup-simplify]: Simplify 0 into 0
8.365 * [backup-simplify]: Simplify 1 into 1
8.365 * [backup-simplify]: Simplify (/ 1 1) into 1
8.365 * [taylor]: Taking taylor expansion of 1 in k
8.365 * [backup-simplify]: Simplify 1 into 1
8.365 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
8.365 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
8.365 * [taylor]: Taking taylor expansion of -2 in k
8.365 * [backup-simplify]: Simplify -2 into -2
8.365 * [taylor]: Taking taylor expansion of (/ PI n) in k
8.365 * [taylor]: Taking taylor expansion of PI in k
8.365 * [backup-simplify]: Simplify PI into PI
8.365 * [taylor]: Taking taylor expansion of n in k
8.365 * [backup-simplify]: Simplify n into n
8.365 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
8.366 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
8.366 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
8.366 * [backup-simplify]: Simplify (+ 1 0) into 1
8.367 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
8.367 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
8.367 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
8.367 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
8.367 * [taylor]: Taking taylor expansion of (/ -1 k) in k
8.367 * [taylor]: Taking taylor expansion of -1 in k
8.367 * [backup-simplify]: Simplify -1 into -1
8.367 * [taylor]: Taking taylor expansion of k in k
8.367 * [backup-simplify]: Simplify 0 into 0
8.367 * [backup-simplify]: Simplify 1 into 1
8.367 * [backup-simplify]: Simplify (/ -1 1) into -1
8.368 * [backup-simplify]: Simplify (sqrt 0) into 0
8.370 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
8.370 * [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)))))
8.370 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
8.370 * [taylor]: Taking taylor expansion of +nan.0 in n
8.370 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.370 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
8.370 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
8.370 * [taylor]: Taking taylor expansion of 1/2 in n
8.370 * [backup-simplify]: Simplify 1/2 into 1/2
8.370 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
8.370 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
8.370 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
8.370 * [taylor]: Taking taylor expansion of -2 in n
8.370 * [backup-simplify]: Simplify -2 into -2
8.370 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.370 * [taylor]: Taking taylor expansion of PI in n
8.370 * [backup-simplify]: Simplify PI into PI
8.370 * [taylor]: Taking taylor expansion of n in n
8.370 * [backup-simplify]: Simplify 0 into 0
8.370 * [backup-simplify]: Simplify 1 into 1
8.371 * [backup-simplify]: Simplify (/ PI 1) into PI
8.371 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
8.373 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
8.373 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
8.373 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.373 * [taylor]: Taking taylor expansion of k in n
8.373 * [backup-simplify]: Simplify k into k
8.373 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.373 * [taylor]: Taking taylor expansion of 1 in n
8.373 * [backup-simplify]: Simplify 1 into 1
8.374 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
8.374 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
8.376 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
8.377 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
8.378 * [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)))))
8.380 * [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))))))
8.381 * [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))))))
8.382 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
8.385 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
8.386 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))
8.386 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
8.386 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
8.386 * [taylor]: Taking taylor expansion of +nan.0 in n
8.387 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.387 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
8.387 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
8.387 * [taylor]: Taking taylor expansion of 1/2 in n
8.387 * [backup-simplify]: Simplify 1/2 into 1/2
8.387 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
8.387 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
8.387 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
8.387 * [taylor]: Taking taylor expansion of -2 in n
8.387 * [backup-simplify]: Simplify -2 into -2
8.387 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.387 * [taylor]: Taking taylor expansion of PI in n
8.387 * [backup-simplify]: Simplify PI into PI
8.387 * [taylor]: Taking taylor expansion of n in n
8.387 * [backup-simplify]: Simplify 0 into 0
8.387 * [backup-simplify]: Simplify 1 into 1
8.387 * [backup-simplify]: Simplify (/ PI 1) into PI
8.388 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
8.389 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
8.389 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
8.389 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.389 * [taylor]: Taking taylor expansion of k in n
8.389 * [backup-simplify]: Simplify k into k
8.389 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.389 * [taylor]: Taking taylor expansion of 1 in n
8.389 * [backup-simplify]: Simplify 1 into 1
8.391 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
8.391 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
8.392 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
8.393 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
8.400 * [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)))))
8.401 * [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))))))
8.403 * [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)))))))
8.404 * [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)))))))
8.405 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
8.406 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
8.406 * [backup-simplify]: Simplify (+ 0 0) into 0
8.407 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.408 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
8.410 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
8.411 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0
8.412 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0
8.414 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
8.415 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0
8.415 * [backup-simplify]: Simplify 0 into 0
8.415 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.418 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
8.419 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))
8.419 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
8.419 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
8.419 * [taylor]: Taking taylor expansion of +nan.0 in n
8.419 * [backup-simplify]: Simplify +nan.0 into +nan.0
8.419 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
8.419 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
8.419 * [taylor]: Taking taylor expansion of 1/2 in n
8.419 * [backup-simplify]: Simplify 1/2 into 1/2
8.419 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
8.419 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
8.419 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
8.419 * [taylor]: Taking taylor expansion of -2 in n
8.419 * [backup-simplify]: Simplify -2 into -2
8.419 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.419 * [taylor]: Taking taylor expansion of PI in n
8.419 * [backup-simplify]: Simplify PI into PI
8.419 * [taylor]: Taking taylor expansion of n in n
8.419 * [backup-simplify]: Simplify 0 into 0
8.419 * [backup-simplify]: Simplify 1 into 1
8.419 * [backup-simplify]: Simplify (/ PI 1) into PI
8.420 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
8.420 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
8.420 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
8.420 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.421 * [taylor]: Taking taylor expansion of k in n
8.421 * [backup-simplify]: Simplify k into k
8.421 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.421 * [taylor]: Taking taylor expansion of 1 in n
8.421 * [backup-simplify]: Simplify 1 into 1
8.421 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
8.422 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
8.422 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
8.423 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
8.424 * [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)))))
8.424 * [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))))))
8.425 * [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)))))))
8.426 * [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)))))))
8.429 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +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))))))))))))
8.429 * * * [progress]: simplifying candidates
8.429 * * * * [progress]: [ 1 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
8.429 * * * * [progress]: [ 2 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
8.429 * * * * [progress]: [ 3 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
8.429 * * * * [progress]: [ 4 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
8.429 * * * * [progress]: [ 5 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
8.429 * * * * [progress]: [ 6 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
8.429 * * * * [progress]: [ 7 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
8.429 * * * * [progress]: [ 8 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))))>
8.429 * * * * [progress]: [ 9 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2)))))>
8.429 * * * * [progress]: [ 10 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2)))))>
8.429 * * * * [progress]: [ 11 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2)))))>
8.429 * * * * [progress]: [ 12 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2)))))>
8.429 * * * * [progress]: [ 13 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2))))>
8.429 * * * * [progress]: [ 14 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2)))))>
8.429 * * * * [progress]: [ 15 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2)))))>
8.429 * * * * [progress]: [ 16 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2))))>
8.429 * * * * [progress]: [ 17 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2)))))>
8.430 * * * * [progress]: [ 18 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
8.430 * * * * [progress]: [ 19 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (- 1 k) 2))))>
8.430 * * * * [progress]: [ 20 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2)))))>
8.430 * * * * [progress]: [ 21 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2)))))>
8.430 * * * * [progress]: [ 22 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2))))>
8.430 * * * * [progress]: [ 23 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2)))))>
8.430 * * * * [progress]: [ 24 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2)))))>
8.430 * * * * [progress]: [ 25 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))))>
8.430 * * * * [progress]: [ 26 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2)))))>
8.430 * * * * [progress]: [ 27 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
8.430 * * * * [progress]: [ 28 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (- 1 k) 2))))>
8.430 * * * * [progress]: [ 29 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
8.430 * * * * [progress]: [ 30 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (- 1 k)) (/ 1 2))))>
8.430 * * * * [progress]: [ 31 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))))>
8.430 * * * * [progress]: [ 32 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (- 1 k) 2)) 1)))>
8.430 * * * * [progress]: [ 33 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.430 * * * * [progress]: [ 34 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (log (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.430 * * * * [progress]: [ 35 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.430 * * * * [progress]: [ 36 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (cbrt (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.430 * * * * [progress]: [ 37 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.430 * * * * [progress]: [ 38 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.430 * * * * [progress]: [ 39 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
8.430 * * * * [progress]: [ 40 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (posit16->real (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.430 * * * * [progress]: [ 41 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) -1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.430 * * * * [progress]: [ 42 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.430 * * * * [progress]: [ 43 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) (- 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 44 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow k (- (/ 1 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 45 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (/ 1 (sqrt k)) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 46 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (- (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 47 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (- 0 (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 48 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (- (log 1) (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 49 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (log (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 50 / 188 ] simplifiying candidate #<alt (λ (k n) (* (log (exp (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 51 / 188 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 52 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 53 / 188 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 54 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 55 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (- 1) (- (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 56 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1) (cbrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 57 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1) (sqrt (cbrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 58 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 59 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (/ (cbrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 60 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 61 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 62 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1) (cbrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 63 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1) (sqrt (cbrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 64 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 65 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt 1)) (/ (sqrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 66 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 67 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) 1) (/ (sqrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 68 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1 (cbrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.431 * * * * [progress]: [ 69 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1 (sqrt (cbrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 70 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 71 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt 1)) (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 72 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 73 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 1) (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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8.432 * * * * [progress]: [ 76 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt k) 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 77 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 78 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 79 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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8.432 * * * * [progress]: [ 82 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 83 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt k) (cbrt 1))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 84 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt k) (sqrt 1))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 85 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt k) 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 86 / 188 ] simplifiying candidate #<alt (λ (k n) (* (posit16->real (real->posit16 (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 87 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 88 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 89 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 90 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (+ (+ (log 2) (log PI)) (log n))) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 91 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (+ (log (* 2 PI)) (log n))) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 92 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (log (* (* 2 PI) n))) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 93 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (log (exp (* (* 2 PI) n))) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 94 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))) (/ (- 1 k) 2))))>
8.432 * * * * [progress]: [ 95 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))) (/ (- 1 k) 2))))>
8.433 * * * * [progress]: [ 96 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) (cbrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
8.433 * * * * [progress]: [ 97 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))) (/ (- 1 k) 2))))>
8.433 * * * * [progress]: [ 98 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (sqrt (* (* 2 PI) n)) (sqrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
8.433 * * * * [progress]: [ 99 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 1 (* (* 2 PI) n)) (/ (- 1 k) 2))))>
8.433 * * * * [progress]: [ 100 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1 k) 2))))>
8.433 * * * * [progress]: [ 101 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (sqrt n)) (sqrt n)) (/ (- 1 k) 2))))>
8.433 * * * * [progress]: [ 102 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) 1) n) (/ (- 1 k) 2))))>
8.433 * * * * [progress]: [ 103 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* PI n)) (/ (- 1 k) 2))))>
8.433 * * * * [progress]: [ 104 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (posit16->real (real->posit16 (* (* 2 PI) n))) (/ (- 1 k) 2))))>
8.433 * * * * [progress]: [ 105 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))>
8.433 * * * * [progress]: [ 106 / 188 ] simplifiying candidate #<alt (λ (k n) (pow (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1))>
8.433 * * * * [progress]: [ 107 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
8.433 * * * * [progress]: [ 108 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
8.433 * * * * [progress]: [ 109 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
8.433 * * * * [progress]: [ 110 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
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8.433 * * * * [progress]: [ 112 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
8.433 * * * * [progress]: [ 113 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
8.433 * * * * [progress]: [ 114 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
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8.433 * * * * [progress]: [ 117 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
8.433 * * * * [progress]: [ 118 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
8.433 * * * * [progress]: [ 119 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
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8.433 * * * * [progress]: [ 122 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
8.434 * * * * [progress]: [ 123 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
8.434 * * * * [progress]: [ 124 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
8.434 * * * * [progress]: [ 125 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
8.434 * * * * [progress]: [ 126 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.434 * * * * [progress]: [ 127 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.434 * * * * [progress]: [ 128 / 188 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.434 * * * * [progress]: [ 129 / 188 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.434 * * * * [progress]: [ 130 / 188 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.434 * * * * [progress]: [ 131 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.434 * * * * [progress]: [ 132 / 188 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.434 * * * * [progress]: [ 133 / 188 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.434 * * * * [progress]: [ 134 / 188 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ 1 2))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))))>
8.434 * * * * [progress]: [ 135 / 188 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.434 * * * * [progress]: [ 136 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.434 * * * * [progress]: [ 137 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
8.434 * * * * [progress]: [ 138 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.434 * * * * [progress]: [ 139 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
8.434 * * * * [progress]: [ 140 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.434 * * * * [progress]: [ 141 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
8.434 * * * * [progress]: [ 142 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.434 * * * * [progress]: [ 143 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
8.434 * * * * [progress]: [ 144 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.434 * * * * [progress]: [ 145 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
8.434 * * * * [progress]: [ 146 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))))>
8.434 * * * * [progress]: [ 147 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 148 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 149 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.435 * * * * [progress]: [ 150 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))>
8.435 * * * * [progress]: [ 151 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 152 / 188 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (sqrt k))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 153 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ (cbrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 154 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (* (/ (cbrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 155 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 156 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 157 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 158 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) 1) (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 159 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ (sqrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 160 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))) (* (/ (sqrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 161 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (sqrt k))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 162 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt 1)) (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 163 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (sqrt k))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 164 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) 1) (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 165 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ 1 (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 166 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (* (/ 1 (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 167 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 168 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 169 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.435 * * * * [progress]: [ 170 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.436 * * * * [progress]: [ 171 / 188 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.436 * * * * [progress]: [ 172 / 188 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
8.436 * * * * [progress]: [ 173 / 188 ] simplifiying candidate #<alt (λ (k n) (/ (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))) (pow (* (* 2 PI) n) (/ k 2))))>
8.436 * * * * [progress]: [ 174 / 188 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt k)))>
8.436 * * * * [progress]: [ 175 / 188 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
8.436 * * * * [progress]: [ 176 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
8.436 * * * * [progress]: [ 177 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 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)))))))>
8.436 * * * * [progress]: [ 178 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))))>
8.436 * * * * [progress]: [ 179 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))>
8.436 * * * * [progress]: [ 180 / 188 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.436 * * * * [progress]: [ 181 / 188 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.436 * * * * [progress]: [ 182 / 188 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
8.436 * * * * [progress]: [ 183 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
8.436 * * * * [progress]: [ 184 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
8.436 * * * * [progress]: [ 185 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
8.436 * * * * [progress]: [ 186 / 188 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))>
8.436 * * * * [progress]: [ 187 / 188 ] 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)))))))))>
8.436 * * * * [progress]: [ 188 / 188 ] 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)))))))))))))>
8.438 * [simplify]: Simplifying:
  (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2))
  (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2))
  (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
  (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (pow (* (* 2 PI) n) (/ 1 2))
  (pow (* (* 2 PI) n) (/ k 2))
  (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2)))
  (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
  (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) 1))
  (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ 1 (sqrt 2)))
  (pow (* (* 2 PI) n) (/ 1 1))
  (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) 1))
  (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) 1))
  (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ 1 (sqrt 2)))
  (pow (* (* 2 PI) n) (/ 1 1))
  (pow (* (* 2 PI) n) 1)
  (pow (* (* 2 PI) n) (- 1 k))
  (pow (* 2 PI) (/ (- 1 k) 2))
  (pow n (/ (- 1 k) 2))
  (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
  (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
  (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (- 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)))
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (+ (+ (log 2) (log PI)) (log n))
  (+ (log (* 2 PI)) (log n))
  (log (* (* 2 PI) n))
  (exp (* (* 2 PI) n))
  (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))
  (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n)))
  (cbrt (* (* 2 PI) n))
  (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))
  (sqrt (* (* 2 PI) n))
  (sqrt (* (* 2 PI) n))
  (* (* 2 PI) (* (cbrt n) (cbrt n)))
  (* (* 2 PI) (sqrt n))
  (* (* 2 PI) 1)
  (* PI n)
  (real->posit16 (* (* 2 PI) n))
  (+ (- (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (+ (- 0 (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (+ (- (log 1) (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (+ (log (/ 1 (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))
  (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* 1 (pow (* (* 2 PI) n) (/ 1 2)))
  (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))
  (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt k)) 1)
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2)))
  (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (real->posit16 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* 1/2 (* (- 1 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 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 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))))))))))))
8.442 * * [simplify]: iteration 0: 345 enodes
8.634 * * [simplify]: iteration 1: 931 enodes
9.174 * * [simplify]: iteration 2: 2858 enodes
10.199 * * [simplify]: iteration complete: 5001 enodes
10.200 * * [simplify]: Extracting #0: cost 91 inf + 0
10.202 * * [simplify]: Extracting #1: cost 535 inf + 3
10.207 * * [simplify]: Extracting #2: cost 1080 inf + 1670
10.226 * * [simplify]: Extracting #3: cost 1353 inf + 44765
10.302 * * [simplify]: Extracting #4: cost 777 inf + 222222
10.424 * * [simplify]: Extracting #5: cost 211 inf + 406683
10.541 * * [simplify]: Extracting #6: cost 18 inf + 491631
10.683 * * [simplify]: Extracting #7: cost 1 inf + 499114
10.815 * * [simplify]: Extracting #8: cost 0 inf + 499609
10.933 * * [simplify]: Extracting #9: cost 0 inf + 499209
11.040 * [simplify]: Simplified to:
  (* (/ (- 1 k) 2) (log (* (* n 2) PI)))
  (* (/ (- 1 k) 2) (log (* (* n 2) PI)))
  (* (/ (- 1 k) 2) (log (* (* n 2) PI)))
  (* (/ (- 1 k) 2) (log (* (* n 2) PI)))
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (sqrt (* (* n 2) PI))
  (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 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* (* n 2) PI) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* (* n 2) PI) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (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)))
  (pow (* (* n 2) PI) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ 1 (sqrt 2)))
  (* (* n 2) PI)
  (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)))
  (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)))
  (pow (* (* n 2) PI) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ 1 (sqrt 2)))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (pow (* (* n 2) PI) (- 1 k))
  (pow (* PI 2) (/ (- 1 k) 2))
  (pow n (/ (- 1 k) 2))
  (* (/ (- 1 k) 2) (log (* (* n 2) PI)))
  (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 (pow (* (* n 2) PI) (/ (- 1 k) 2)) 3)
  (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))
  (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2)))
  (pow (* (* n 2) PI) (/ (- 1 k) 4))
  (pow (* (* n 2) PI) (/ (- 1 k) 4))
  (real->posit16 (pow (* (* n 2) PI) (/ (- 1 k) 2)))
  -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 k) (sqrt k))
  (sqrt (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  -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
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 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
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 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
  (/ 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
  (/ 1 (sqrt (sqrt k)))
  1
  (sqrt k)
  (sqrt k)
  (sqrt k)
  (real->posit16 (/ 1 (sqrt k)))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (log (* (* n 2) PI))
  (log (* (* n 2) PI))
  (log (* (* n 2) PI))
  (exp (+ (* PI n) (* PI n)))
  (* n (* 8 (* (* PI (* PI PI)) (* n n))))
  (* (* (* n 2) PI) (* (* (* n 2) PI) (* (* n 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))
  (* PI (* 2 (* (cbrt n) (cbrt n))))
  (* 2 (* PI (sqrt n)))
  (* PI 2)
  (* PI n)
  (real->posit16 (* (* n 2) PI))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* (* n 2) PI))) (log (sqrt k)))
  (exp (/ (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)))
  (* (* (/ (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)))
  (* (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)))
  (sqrt (* (* n 2) PI))
  (* (sqrt k) (pow (* (* n 2) PI) (/ 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))))
  (* (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (/ 1 (sqrt k))))
  (* (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (/ 1 (sqrt k))))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (/ (- 1 k) 2)) (sqrt k))
  (* (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1 k) 2))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 4)) (sqrt k))
  (* (cbrt (/ 1 (sqrt k))) (pow (* (* n 2) PI) (/ (- 1 k) 2)))
  (* (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (/ 1 (sqrt k))))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt (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 (* (* n 2) PI)) (sqrt k))
  (pow (* (* n 2) PI) (/ (- 1 k) 2))
  (real->posit16 (/ (pow (* (* n 2) PI) (/ (- 1 k) 2)) (sqrt k)))
  (- (+ (+ (sqrt (* (* n 2) PI)) (* (* (* 1/8 (sqrt (* (* n 2) PI))) (* (log n) (log n))) (* k k))) (+ (* 1/8 (* (* (log (* PI 2)) (log (* PI 2))) (* (sqrt (* (* n 2) PI)) (* k k)))) (* (* 1/4 (log (* PI 2))) (* (* (sqrt (* (* n 2) PI)) (* k k)) (log n))))) (/ (* k (+ (* (sqrt (* (* n 2) PI)) (log n)) (* (log (* PI 2)) (sqrt (* (* n 2) PI))))) 2))
  (exp (* (/ (log (* (* n 2) PI)) 2) (- 1 k)))
  (sqrt (exp (* (- 1 k) (- (log (* PI -2)) (log (/ -1 n))))))
  (+ (* (- (* 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))))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (* (* n 2) PI)
  (+ (+ (- (* (* +nan.0 (sqrt 2)) (* PI n)) (* (* (* (log (* PI 2)) (sqrt 2)) (* (* PI n) k)) +nan.0)) (* (* +nan.0 (sqrt 2)) (- (* n (* (log n) (* k PI))) (* (* PI n) (* PI n))))) (- (* (* (* (* PI n) k) (sqrt 2)) +nan.0)))
  (- (* (- +nan.0) (/ (exp (* (/ (log (* (* n 2) PI)) 2) (- 1 k))) k)) (+ (* (/ (exp (* (/ (log (* (* n 2) PI)) 2) (- 1 k))) (* k k)) (/ +nan.0 k)) (* (/ (exp (* (/ (log (* (* n 2) PI)) 2) (- 1 k))) (* k k)) (- +nan.0))))
  (+ (- (/ (* (sqrt (exp (* (- 1 k) (- (log (* PI -2)) (log (/ -1 n)))))) +nan.0) (* k k)) (* +nan.0 (sqrt (exp (* (- 1 k) (- (log (* PI -2)) (log (/ -1 n)))))))) (- (/ (* +nan.0 (sqrt (exp (* (- 1 k) (- (log (* PI -2)) (log (/ -1 n))))))) k)))
11.057 * * * [progress]: adding candidates to table
11.828 * * [progress]: iteration 3 / 4
11.828 * * * [progress]: picking best candidate
11.852 * * * * [pick]: Picked  #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
11.852 * * * [progress]: localizing error
11.891 * * * [progress]: generating rewritten candidates
11.891 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1)
11.924 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1)
11.958 * * * * [progress]: [ 3 / 4 ] rewriting at (2)
12.010 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 1)
12.039 * * * [progress]: generating series expansions
12.039 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1)
12.039 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
12.039 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
12.039 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
12.039 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
12.039 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
12.039 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
12.039 * [taylor]: Taking taylor expansion of 1/2 in k
12.039 * [backup-simplify]: Simplify 1/2 into 1/2
12.039 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
12.039 * [taylor]: Taking taylor expansion of 1/2 in k
12.039 * [backup-simplify]: Simplify 1/2 into 1/2
12.039 * [taylor]: Taking taylor expansion of k in k
12.039 * [backup-simplify]: Simplify 0 into 0
12.039 * [backup-simplify]: Simplify 1 into 1
12.039 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
12.039 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
12.039 * [taylor]: Taking taylor expansion of 2 in k
12.039 * [backup-simplify]: Simplify 2 into 2
12.039 * [taylor]: Taking taylor expansion of (* n PI) in k
12.039 * [taylor]: Taking taylor expansion of n in k
12.039 * [backup-simplify]: Simplify n into n
12.039 * [taylor]: Taking taylor expansion of PI in k
12.039 * [backup-simplify]: Simplify PI into PI
12.039 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.039 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
12.040 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
12.040 * [backup-simplify]: Simplify (* 1/2 0) into 0
12.040 * [backup-simplify]: Simplify (- 0) into 0
12.041 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.041 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
12.041 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
12.041 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
12.041 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
12.041 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
12.041 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
12.041 * [taylor]: Taking taylor expansion of 1/2 in n
12.041 * [backup-simplify]: Simplify 1/2 into 1/2
12.041 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
12.041 * [taylor]: Taking taylor expansion of 1/2 in n
12.041 * [backup-simplify]: Simplify 1/2 into 1/2
12.041 * [taylor]: Taking taylor expansion of k in n
12.041 * [backup-simplify]: Simplify k into k
12.041 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.041 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.041 * [taylor]: Taking taylor expansion of 2 in n
12.041 * [backup-simplify]: Simplify 2 into 2
12.041 * [taylor]: Taking taylor expansion of (* n PI) in n
12.041 * [taylor]: Taking taylor expansion of n in n
12.041 * [backup-simplify]: Simplify 0 into 0
12.041 * [backup-simplify]: Simplify 1 into 1
12.041 * [taylor]: Taking taylor expansion of PI in n
12.041 * [backup-simplify]: Simplify PI into PI
12.041 * [backup-simplify]: Simplify (* 0 PI) into 0
12.042 * [backup-simplify]: Simplify (* 2 0) into 0
12.043 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.044 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.044 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.044 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
12.044 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
12.044 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
12.045 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.046 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
12.047 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
12.047 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
12.047 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
12.047 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
12.047 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
12.047 * [taylor]: Taking taylor expansion of 1/2 in n
12.047 * [backup-simplify]: Simplify 1/2 into 1/2
12.047 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
12.047 * [taylor]: Taking taylor expansion of 1/2 in n
12.047 * [backup-simplify]: Simplify 1/2 into 1/2
12.047 * [taylor]: Taking taylor expansion of k in n
12.047 * [backup-simplify]: Simplify k into k
12.047 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.047 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.047 * [taylor]: Taking taylor expansion of 2 in n
12.047 * [backup-simplify]: Simplify 2 into 2
12.047 * [taylor]: Taking taylor expansion of (* n PI) in n
12.047 * [taylor]: Taking taylor expansion of n in n
12.047 * [backup-simplify]: Simplify 0 into 0
12.047 * [backup-simplify]: Simplify 1 into 1
12.047 * [taylor]: Taking taylor expansion of PI in n
12.047 * [backup-simplify]: Simplify PI into PI
12.047 * [backup-simplify]: Simplify (* 0 PI) into 0
12.048 * [backup-simplify]: Simplify (* 2 0) into 0
12.049 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.050 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.050 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.050 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
12.050 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
12.050 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
12.051 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.052 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
12.053 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
12.053 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
12.053 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
12.053 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
12.053 * [taylor]: Taking taylor expansion of 1/2 in k
12.053 * [backup-simplify]: Simplify 1/2 into 1/2
12.053 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
12.053 * [taylor]: Taking taylor expansion of 1/2 in k
12.053 * [backup-simplify]: Simplify 1/2 into 1/2
12.053 * [taylor]: Taking taylor expansion of k in k
12.053 * [backup-simplify]: Simplify 0 into 0
12.053 * [backup-simplify]: Simplify 1 into 1
12.053 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
12.053 * [taylor]: Taking taylor expansion of (log n) in k
12.053 * [taylor]: Taking taylor expansion of n in k
12.053 * [backup-simplify]: Simplify n into n
12.053 * [backup-simplify]: Simplify (log n) into (log n)
12.053 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
12.053 * [taylor]: Taking taylor expansion of (* 2 PI) in k
12.054 * [taylor]: Taking taylor expansion of 2 in k
12.054 * [backup-simplify]: Simplify 2 into 2
12.054 * [taylor]: Taking taylor expansion of PI in k
12.054 * [backup-simplify]: Simplify PI into PI
12.054 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.055 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.055 * [backup-simplify]: Simplify (* 1/2 0) into 0
12.056 * [backup-simplify]: Simplify (- 0) into 0
12.056 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.057 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.058 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
12.060 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
12.061 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
12.062 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.063 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
12.065 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.065 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
12.066 * [backup-simplify]: Simplify (- 0) into 0
12.066 * [backup-simplify]: Simplify (+ 0 0) into 0
12.067 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.069 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
12.071 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.071 * [taylor]: Taking taylor expansion of 0 in k
12.071 * [backup-simplify]: Simplify 0 into 0
12.071 * [backup-simplify]: Simplify 0 into 0
12.072 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
12.072 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.074 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.075 * [backup-simplify]: Simplify (+ 0 0) into 0
12.075 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
12.076 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.076 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.078 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
12.081 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
12.084 * [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)))))))
12.085 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.086 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.090 * [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
12.090 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
12.091 * [backup-simplify]: Simplify (- 0) into 0
12.091 * [backup-simplify]: Simplify (+ 0 0) into 0
12.093 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.101 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.103 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.103 * [taylor]: Taking taylor expansion of 0 in k
12.103 * [backup-simplify]: Simplify 0 into 0
12.103 * [backup-simplify]: Simplify 0 into 0
12.103 * [backup-simplify]: Simplify 0 into 0
12.104 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
12.105 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.107 * [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
12.107 * [backup-simplify]: Simplify (+ 0 0) into 0
12.107 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
12.108 * [backup-simplify]: Simplify (- 0) into 0
12.108 * [backup-simplify]: Simplify (+ 0 0) into 0
12.109 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.112 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
12.115 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
12.121 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
12.121 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
12.121 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
12.121 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
12.121 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
12.121 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
12.121 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
12.121 * [taylor]: Taking taylor expansion of 1/2 in k
12.121 * [backup-simplify]: Simplify 1/2 into 1/2
12.121 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.121 * [taylor]: Taking taylor expansion of 1/2 in k
12.121 * [backup-simplify]: Simplify 1/2 into 1/2
12.121 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.121 * [taylor]: Taking taylor expansion of k in k
12.121 * [backup-simplify]: Simplify 0 into 0
12.121 * [backup-simplify]: Simplify 1 into 1
12.122 * [backup-simplify]: Simplify (/ 1 1) into 1
12.122 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
12.122 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
12.122 * [taylor]: Taking taylor expansion of 2 in k
12.122 * [backup-simplify]: Simplify 2 into 2
12.122 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.122 * [taylor]: Taking taylor expansion of PI in k
12.122 * [backup-simplify]: Simplify PI into PI
12.122 * [taylor]: Taking taylor expansion of n in k
12.122 * [backup-simplify]: Simplify n into n
12.122 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.122 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
12.122 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
12.122 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.122 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.123 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.123 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
12.123 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
12.123 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
12.123 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.123 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.123 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.123 * [taylor]: Taking taylor expansion of 1/2 in n
12.123 * [backup-simplify]: Simplify 1/2 into 1/2
12.123 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.123 * [taylor]: Taking taylor expansion of 1/2 in n
12.123 * [backup-simplify]: Simplify 1/2 into 1/2
12.123 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.123 * [taylor]: Taking taylor expansion of k in n
12.123 * [backup-simplify]: Simplify k into k
12.123 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.123 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.123 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.123 * [taylor]: Taking taylor expansion of 2 in n
12.123 * [backup-simplify]: Simplify 2 into 2
12.123 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.123 * [taylor]: Taking taylor expansion of PI in n
12.123 * [backup-simplify]: Simplify PI into PI
12.123 * [taylor]: Taking taylor expansion of n in n
12.123 * [backup-simplify]: Simplify 0 into 0
12.123 * [backup-simplify]: Simplify 1 into 1
12.123 * [backup-simplify]: Simplify (/ PI 1) into PI
12.124 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.124 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.125 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.125 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
12.125 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
12.126 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.127 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
12.128 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
12.129 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
12.129 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.129 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.129 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.129 * [taylor]: Taking taylor expansion of 1/2 in n
12.129 * [backup-simplify]: Simplify 1/2 into 1/2
12.129 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.129 * [taylor]: Taking taylor expansion of 1/2 in n
12.129 * [backup-simplify]: Simplify 1/2 into 1/2
12.129 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.129 * [taylor]: Taking taylor expansion of k in n
12.129 * [backup-simplify]: Simplify k into k
12.129 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.129 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.129 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.129 * [taylor]: Taking taylor expansion of 2 in n
12.129 * [backup-simplify]: Simplify 2 into 2
12.129 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.129 * [taylor]: Taking taylor expansion of PI in n
12.129 * [backup-simplify]: Simplify PI into PI
12.129 * [taylor]: Taking taylor expansion of n in n
12.129 * [backup-simplify]: Simplify 0 into 0
12.129 * [backup-simplify]: Simplify 1 into 1
12.130 * [backup-simplify]: Simplify (/ PI 1) into PI
12.130 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.131 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.131 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.131 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
12.131 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
12.133 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.134 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
12.135 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
12.135 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
12.135 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
12.135 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
12.135 * [taylor]: Taking taylor expansion of 1/2 in k
12.135 * [backup-simplify]: Simplify 1/2 into 1/2
12.136 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.136 * [taylor]: Taking taylor expansion of 1/2 in k
12.136 * [backup-simplify]: Simplify 1/2 into 1/2
12.136 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.136 * [taylor]: Taking taylor expansion of k in k
12.136 * [backup-simplify]: Simplify 0 into 0
12.136 * [backup-simplify]: Simplify 1 into 1
12.136 * [backup-simplify]: Simplify (/ 1 1) into 1
12.136 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
12.136 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
12.136 * [taylor]: Taking taylor expansion of (* 2 PI) in k
12.136 * [taylor]: Taking taylor expansion of 2 in k
12.136 * [backup-simplify]: Simplify 2 into 2
12.136 * [taylor]: Taking taylor expansion of PI in k
12.136 * [backup-simplify]: Simplify PI into PI
12.137 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.138 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.138 * [taylor]: Taking taylor expansion of (log n) in k
12.138 * [taylor]: Taking taylor expansion of n in k
12.138 * [backup-simplify]: Simplify n into n
12.138 * [backup-simplify]: Simplify (log n) into (log n)
12.138 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.139 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.139 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.139 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.140 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
12.141 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
12.143 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
12.144 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
12.145 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.146 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.147 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.148 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.148 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
12.148 * [backup-simplify]: Simplify (- 0) into 0
12.149 * [backup-simplify]: Simplify (+ 0 0) into 0
12.150 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.152 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
12.154 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
12.154 * [taylor]: Taking taylor expansion of 0 in k
12.154 * [backup-simplify]: Simplify 0 into 0
12.154 * [backup-simplify]: Simplify 0 into 0
12.154 * [backup-simplify]: Simplify 0 into 0
12.155 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.156 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.159 * [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
12.160 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.161 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
12.161 * [backup-simplify]: Simplify (- 0) into 0
12.162 * [backup-simplify]: Simplify (+ 0 0) into 0
12.163 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.165 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
12.167 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.167 * [taylor]: Taking taylor expansion of 0 in k
12.167 * [backup-simplify]: Simplify 0 into 0
12.168 * [backup-simplify]: Simplify 0 into 0
12.168 * [backup-simplify]: Simplify 0 into 0
12.168 * [backup-simplify]: Simplify 0 into 0
12.169 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.169 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.172 * [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
12.173 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.173 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
12.174 * [backup-simplify]: Simplify (- 0) into 0
12.174 * [backup-simplify]: Simplify (+ 0 0) into 0
12.175 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.176 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
12.178 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
12.178 * [taylor]: Taking taylor expansion of 0 in k
12.178 * [backup-simplify]: Simplify 0 into 0
12.178 * [backup-simplify]: Simplify 0 into 0
12.179 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
12.179 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
12.179 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
12.179 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
12.179 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
12.179 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
12.179 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
12.179 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.179 * [taylor]: Taking taylor expansion of 1/2 in k
12.179 * [backup-simplify]: Simplify 1/2 into 1/2
12.179 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.179 * [taylor]: Taking taylor expansion of k in k
12.179 * [backup-simplify]: Simplify 0 into 0
12.179 * [backup-simplify]: Simplify 1 into 1
12.180 * [backup-simplify]: Simplify (/ 1 1) into 1
12.180 * [taylor]: Taking taylor expansion of 1/2 in k
12.180 * [backup-simplify]: Simplify 1/2 into 1/2
12.180 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
12.180 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
12.180 * [taylor]: Taking taylor expansion of -2 in k
12.180 * [backup-simplify]: Simplify -2 into -2
12.180 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.180 * [taylor]: Taking taylor expansion of PI in k
12.180 * [backup-simplify]: Simplify PI into PI
12.180 * [taylor]: Taking taylor expansion of n in k
12.180 * [backup-simplify]: Simplify n into n
12.180 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.180 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
12.180 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
12.181 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.181 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.181 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
12.182 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
12.182 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
12.182 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
12.182 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
12.182 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
12.182 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.182 * [taylor]: Taking taylor expansion of 1/2 in n
12.182 * [backup-simplify]: Simplify 1/2 into 1/2
12.182 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.182 * [taylor]: Taking taylor expansion of k in n
12.182 * [backup-simplify]: Simplify k into k
12.182 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.182 * [taylor]: Taking taylor expansion of 1/2 in n
12.182 * [backup-simplify]: Simplify 1/2 into 1/2
12.182 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.182 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.182 * [taylor]: Taking taylor expansion of -2 in n
12.182 * [backup-simplify]: Simplify -2 into -2
12.182 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.182 * [taylor]: Taking taylor expansion of PI in n
12.182 * [backup-simplify]: Simplify PI into PI
12.182 * [taylor]: Taking taylor expansion of n in n
12.182 * [backup-simplify]: Simplify 0 into 0
12.182 * [backup-simplify]: Simplify 1 into 1
12.183 * [backup-simplify]: Simplify (/ PI 1) into PI
12.183 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.184 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.184 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.184 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
12.186 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.187 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
12.188 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
12.188 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
12.188 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
12.188 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
12.188 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
12.188 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.188 * [taylor]: Taking taylor expansion of 1/2 in n
12.188 * [backup-simplify]: Simplify 1/2 into 1/2
12.188 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.188 * [taylor]: Taking taylor expansion of k in n
12.189 * [backup-simplify]: Simplify k into k
12.189 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.189 * [taylor]: Taking taylor expansion of 1/2 in n
12.189 * [backup-simplify]: Simplify 1/2 into 1/2
12.189 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.189 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.189 * [taylor]: Taking taylor expansion of -2 in n
12.189 * [backup-simplify]: Simplify -2 into -2
12.189 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.189 * [taylor]: Taking taylor expansion of PI in n
12.189 * [backup-simplify]: Simplify PI into PI
12.189 * [taylor]: Taking taylor expansion of n in n
12.189 * [backup-simplify]: Simplify 0 into 0
12.189 * [backup-simplify]: Simplify 1 into 1
12.189 * [backup-simplify]: Simplify (/ PI 1) into PI
12.190 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.191 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.191 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.191 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
12.193 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.194 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
12.195 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
12.195 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
12.195 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
12.195 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
12.195 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.195 * [taylor]: Taking taylor expansion of 1/2 in k
12.195 * [backup-simplify]: Simplify 1/2 into 1/2
12.195 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.195 * [taylor]: Taking taylor expansion of k in k
12.195 * [backup-simplify]: Simplify 0 into 0
12.195 * [backup-simplify]: Simplify 1 into 1
12.196 * [backup-simplify]: Simplify (/ 1 1) into 1
12.196 * [taylor]: Taking taylor expansion of 1/2 in k
12.196 * [backup-simplify]: Simplify 1/2 into 1/2
12.196 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
12.196 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
12.196 * [taylor]: Taking taylor expansion of (* -2 PI) in k
12.196 * [taylor]: Taking taylor expansion of -2 in k
12.196 * [backup-simplify]: Simplify -2 into -2
12.196 * [taylor]: Taking taylor expansion of PI in k
12.196 * [backup-simplify]: Simplify PI into PI
12.196 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.198 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.198 * [taylor]: Taking taylor expansion of (log n) in k
12.198 * [taylor]: Taking taylor expansion of n in k
12.198 * [backup-simplify]: Simplify n into n
12.198 * [backup-simplify]: Simplify (log n) into (log n)
12.198 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.199 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.199 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.200 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
12.201 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
12.202 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
12.203 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
12.204 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.205 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
12.206 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
12.206 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.206 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
12.206 * [backup-simplify]: Simplify (+ 0 0) into 0
12.207 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.208 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
12.209 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
12.209 * [taylor]: Taking taylor expansion of 0 in k
12.209 * [backup-simplify]: Simplify 0 into 0
12.209 * [backup-simplify]: Simplify 0 into 0
12.209 * [backup-simplify]: Simplify 0 into 0
12.210 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.211 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
12.213 * [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
12.213 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.213 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
12.214 * [backup-simplify]: Simplify (+ 0 0) into 0
12.218 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.219 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
12.221 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.221 * [taylor]: Taking taylor expansion of 0 in k
12.221 * [backup-simplify]: Simplify 0 into 0
12.221 * [backup-simplify]: Simplify 0 into 0
12.221 * [backup-simplify]: Simplify 0 into 0
12.221 * [backup-simplify]: Simplify 0 into 0
12.222 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.222 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.226 * [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
12.226 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.227 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
12.227 * [backup-simplify]: Simplify (+ 0 0) into 0
12.228 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.229 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
12.231 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
12.231 * [taylor]: Taking taylor expansion of 0 in k
12.231 * [backup-simplify]: Simplify 0 into 0
12.231 * [backup-simplify]: Simplify 0 into 0
12.232 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
12.232 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1)
12.232 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
12.232 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
12.232 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
12.232 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
12.232 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
12.232 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
12.232 * [taylor]: Taking taylor expansion of 1/2 in k
12.232 * [backup-simplify]: Simplify 1/2 into 1/2
12.232 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
12.232 * [taylor]: Taking taylor expansion of 1/2 in k
12.232 * [backup-simplify]: Simplify 1/2 into 1/2
12.232 * [taylor]: Taking taylor expansion of k in k
12.232 * [backup-simplify]: Simplify 0 into 0
12.232 * [backup-simplify]: Simplify 1 into 1
12.232 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
12.232 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
12.232 * [taylor]: Taking taylor expansion of 2 in k
12.232 * [backup-simplify]: Simplify 2 into 2
12.232 * [taylor]: Taking taylor expansion of (* n PI) in k
12.232 * [taylor]: Taking taylor expansion of n in k
12.232 * [backup-simplify]: Simplify n into n
12.232 * [taylor]: Taking taylor expansion of PI in k
12.232 * [backup-simplify]: Simplify PI into PI
12.232 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.232 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
12.232 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
12.232 * [backup-simplify]: Simplify (* 1/2 0) into 0
12.233 * [backup-simplify]: Simplify (- 0) into 0
12.233 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.233 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
12.233 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
12.233 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
12.233 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
12.233 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
12.233 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
12.233 * [taylor]: Taking taylor expansion of 1/2 in n
12.233 * [backup-simplify]: Simplify 1/2 into 1/2
12.233 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
12.233 * [taylor]: Taking taylor expansion of 1/2 in n
12.233 * [backup-simplify]: Simplify 1/2 into 1/2
12.233 * [taylor]: Taking taylor expansion of k in n
12.233 * [backup-simplify]: Simplify k into k
12.233 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.233 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.233 * [taylor]: Taking taylor expansion of 2 in n
12.233 * [backup-simplify]: Simplify 2 into 2
12.233 * [taylor]: Taking taylor expansion of (* n PI) in n
12.233 * [taylor]: Taking taylor expansion of n in n
12.233 * [backup-simplify]: Simplify 0 into 0
12.233 * [backup-simplify]: Simplify 1 into 1
12.233 * [taylor]: Taking taylor expansion of PI in n
12.233 * [backup-simplify]: Simplify PI into PI
12.234 * [backup-simplify]: Simplify (* 0 PI) into 0
12.234 * [backup-simplify]: Simplify (* 2 0) into 0
12.235 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.236 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.237 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.237 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
12.237 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
12.237 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
12.238 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.238 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
12.239 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
12.239 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
12.239 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
12.239 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
12.239 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
12.239 * [taylor]: Taking taylor expansion of 1/2 in n
12.239 * [backup-simplify]: Simplify 1/2 into 1/2
12.239 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
12.239 * [taylor]: Taking taylor expansion of 1/2 in n
12.239 * [backup-simplify]: Simplify 1/2 into 1/2
12.239 * [taylor]: Taking taylor expansion of k in n
12.239 * [backup-simplify]: Simplify k into k
12.239 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.239 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.239 * [taylor]: Taking taylor expansion of 2 in n
12.239 * [backup-simplify]: Simplify 2 into 2
12.239 * [taylor]: Taking taylor expansion of (* n PI) in n
12.239 * [taylor]: Taking taylor expansion of n in n
12.239 * [backup-simplify]: Simplify 0 into 0
12.239 * [backup-simplify]: Simplify 1 into 1
12.239 * [taylor]: Taking taylor expansion of PI in n
12.239 * [backup-simplify]: Simplify PI into PI
12.240 * [backup-simplify]: Simplify (* 0 PI) into 0
12.240 * [backup-simplify]: Simplify (* 2 0) into 0
12.241 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.242 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.243 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.243 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
12.243 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
12.243 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
12.244 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.244 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
12.245 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
12.245 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
12.245 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
12.245 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
12.245 * [taylor]: Taking taylor expansion of 1/2 in k
12.245 * [backup-simplify]: Simplify 1/2 into 1/2
12.245 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
12.245 * [taylor]: Taking taylor expansion of 1/2 in k
12.245 * [backup-simplify]: Simplify 1/2 into 1/2
12.245 * [taylor]: Taking taylor expansion of k in k
12.245 * [backup-simplify]: Simplify 0 into 0
12.245 * [backup-simplify]: Simplify 1 into 1
12.245 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
12.245 * [taylor]: Taking taylor expansion of (log n) in k
12.245 * [taylor]: Taking taylor expansion of n in k
12.245 * [backup-simplify]: Simplify n into n
12.245 * [backup-simplify]: Simplify (log n) into (log n)
12.245 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
12.245 * [taylor]: Taking taylor expansion of (* 2 PI) in k
12.245 * [taylor]: Taking taylor expansion of 2 in k
12.245 * [backup-simplify]: Simplify 2 into 2
12.245 * [taylor]: Taking taylor expansion of PI in k
12.245 * [backup-simplify]: Simplify PI into PI
12.246 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.246 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.247 * [backup-simplify]: Simplify (* 1/2 0) into 0
12.247 * [backup-simplify]: Simplify (- 0) into 0
12.247 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.248 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.249 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
12.249 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
12.250 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
12.251 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.251 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
12.252 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.253 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
12.253 * [backup-simplify]: Simplify (- 0) into 0
12.253 * [backup-simplify]: Simplify (+ 0 0) into 0
12.254 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.255 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
12.256 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.256 * [taylor]: Taking taylor expansion of 0 in k
12.256 * [backup-simplify]: Simplify 0 into 0
12.256 * [backup-simplify]: Simplify 0 into 0
12.256 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
12.257 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.258 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.258 * [backup-simplify]: Simplify (+ 0 0) into 0
12.259 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
12.259 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.259 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.260 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
12.262 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
12.265 * [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)))))))
12.266 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.267 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.271 * [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
12.272 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
12.272 * [backup-simplify]: Simplify (- 0) into 0
12.273 * [backup-simplify]: Simplify (+ 0 0) into 0
12.274 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.276 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.278 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.278 * [taylor]: Taking taylor expansion of 0 in k
12.278 * [backup-simplify]: Simplify 0 into 0
12.278 * [backup-simplify]: Simplify 0 into 0
12.278 * [backup-simplify]: Simplify 0 into 0
12.280 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
12.281 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.285 * [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
12.285 * [backup-simplify]: Simplify (+ 0 0) into 0
12.286 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
12.286 * [backup-simplify]: Simplify (- 0) into 0
12.287 * [backup-simplify]: Simplify (+ 0 0) into 0
12.289 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.293 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
12.296 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
12.301 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
12.302 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
12.302 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
12.302 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
12.302 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
12.302 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
12.302 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
12.302 * [taylor]: Taking taylor expansion of 1/2 in k
12.302 * [backup-simplify]: Simplify 1/2 into 1/2
12.302 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.302 * [taylor]: Taking taylor expansion of 1/2 in k
12.302 * [backup-simplify]: Simplify 1/2 into 1/2
12.302 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.302 * [taylor]: Taking taylor expansion of k in k
12.302 * [backup-simplify]: Simplify 0 into 0
12.302 * [backup-simplify]: Simplify 1 into 1
12.302 * [backup-simplify]: Simplify (/ 1 1) into 1
12.302 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
12.302 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
12.302 * [taylor]: Taking taylor expansion of 2 in k
12.302 * [backup-simplify]: Simplify 2 into 2
12.302 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.302 * [taylor]: Taking taylor expansion of PI in k
12.302 * [backup-simplify]: Simplify PI into PI
12.302 * [taylor]: Taking taylor expansion of n in k
12.302 * [backup-simplify]: Simplify n into n
12.302 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.302 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
12.302 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
12.303 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.303 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.303 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.303 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
12.303 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
12.303 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
12.303 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.303 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.303 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.303 * [taylor]: Taking taylor expansion of 1/2 in n
12.303 * [backup-simplify]: Simplify 1/2 into 1/2
12.303 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.303 * [taylor]: Taking taylor expansion of 1/2 in n
12.303 * [backup-simplify]: Simplify 1/2 into 1/2
12.303 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.304 * [taylor]: Taking taylor expansion of k in n
12.304 * [backup-simplify]: Simplify k into k
12.304 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.304 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.304 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.304 * [taylor]: Taking taylor expansion of 2 in n
12.304 * [backup-simplify]: Simplify 2 into 2
12.304 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.304 * [taylor]: Taking taylor expansion of PI in n
12.304 * [backup-simplify]: Simplify PI into PI
12.304 * [taylor]: Taking taylor expansion of n in n
12.304 * [backup-simplify]: Simplify 0 into 0
12.304 * [backup-simplify]: Simplify 1 into 1
12.304 * [backup-simplify]: Simplify (/ PI 1) into PI
12.304 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.305 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.305 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.305 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
12.305 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
12.306 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.307 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
12.307 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
12.308 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
12.308 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.308 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.308 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.308 * [taylor]: Taking taylor expansion of 1/2 in n
12.308 * [backup-simplify]: Simplify 1/2 into 1/2
12.308 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.308 * [taylor]: Taking taylor expansion of 1/2 in n
12.308 * [backup-simplify]: Simplify 1/2 into 1/2
12.308 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.308 * [taylor]: Taking taylor expansion of k in n
12.308 * [backup-simplify]: Simplify k into k
12.308 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.308 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.308 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.308 * [taylor]: Taking taylor expansion of 2 in n
12.308 * [backup-simplify]: Simplify 2 into 2
12.308 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.308 * [taylor]: Taking taylor expansion of PI in n
12.308 * [backup-simplify]: Simplify PI into PI
12.308 * [taylor]: Taking taylor expansion of n in n
12.308 * [backup-simplify]: Simplify 0 into 0
12.308 * [backup-simplify]: Simplify 1 into 1
12.308 * [backup-simplify]: Simplify (/ PI 1) into PI
12.309 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.309 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.309 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.309 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
12.309 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
12.310 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.311 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
12.312 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
12.312 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
12.312 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
12.312 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
12.312 * [taylor]: Taking taylor expansion of 1/2 in k
12.312 * [backup-simplify]: Simplify 1/2 into 1/2
12.312 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.312 * [taylor]: Taking taylor expansion of 1/2 in k
12.312 * [backup-simplify]: Simplify 1/2 into 1/2
12.312 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.312 * [taylor]: Taking taylor expansion of k in k
12.312 * [backup-simplify]: Simplify 0 into 0
12.312 * [backup-simplify]: Simplify 1 into 1
12.313 * [backup-simplify]: Simplify (/ 1 1) into 1
12.313 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
12.313 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
12.313 * [taylor]: Taking taylor expansion of (* 2 PI) in k
12.313 * [taylor]: Taking taylor expansion of 2 in k
12.313 * [backup-simplify]: Simplify 2 into 2
12.313 * [taylor]: Taking taylor expansion of PI in k
12.313 * [backup-simplify]: Simplify PI into PI
12.313 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.314 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.314 * [taylor]: Taking taylor expansion of (log n) in k
12.314 * [taylor]: Taking taylor expansion of n in k
12.314 * [backup-simplify]: Simplify n into n
12.314 * [backup-simplify]: Simplify (log n) into (log n)
12.314 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.314 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.318 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.318 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.319 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
12.320 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
12.321 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
12.321 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
12.322 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.322 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.323 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.324 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.324 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
12.324 * [backup-simplify]: Simplify (- 0) into 0
12.324 * [backup-simplify]: Simplify (+ 0 0) into 0
12.326 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.327 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
12.329 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
12.329 * [taylor]: Taking taylor expansion of 0 in k
12.329 * [backup-simplify]: Simplify 0 into 0
12.329 * [backup-simplify]: Simplify 0 into 0
12.329 * [backup-simplify]: Simplify 0 into 0
12.330 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.331 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.334 * [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
12.335 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.335 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
12.336 * [backup-simplify]: Simplify (- 0) into 0
12.336 * [backup-simplify]: Simplify (+ 0 0) into 0
12.338 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.339 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
12.342 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.342 * [taylor]: Taking taylor expansion of 0 in k
12.342 * [backup-simplify]: Simplify 0 into 0
12.342 * [backup-simplify]: Simplify 0 into 0
12.342 * [backup-simplify]: Simplify 0 into 0
12.342 * [backup-simplify]: Simplify 0 into 0
12.343 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.344 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.350 * [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
12.350 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.351 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
12.352 * [backup-simplify]: Simplify (- 0) into 0
12.352 * [backup-simplify]: Simplify (+ 0 0) into 0
12.353 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.354 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
12.356 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
12.356 * [taylor]: Taking taylor expansion of 0 in k
12.356 * [backup-simplify]: Simplify 0 into 0
12.356 * [backup-simplify]: Simplify 0 into 0
12.357 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
12.357 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
12.357 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
12.357 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
12.357 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
12.357 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
12.357 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
12.357 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.357 * [taylor]: Taking taylor expansion of 1/2 in k
12.357 * [backup-simplify]: Simplify 1/2 into 1/2
12.357 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.357 * [taylor]: Taking taylor expansion of k in k
12.357 * [backup-simplify]: Simplify 0 into 0
12.357 * [backup-simplify]: Simplify 1 into 1
12.358 * [backup-simplify]: Simplify (/ 1 1) into 1
12.358 * [taylor]: Taking taylor expansion of 1/2 in k
12.358 * [backup-simplify]: Simplify 1/2 into 1/2
12.358 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
12.358 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
12.358 * [taylor]: Taking taylor expansion of -2 in k
12.358 * [backup-simplify]: Simplify -2 into -2
12.358 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.358 * [taylor]: Taking taylor expansion of PI in k
12.358 * [backup-simplify]: Simplify PI into PI
12.358 * [taylor]: Taking taylor expansion of n in k
12.358 * [backup-simplify]: Simplify n into n
12.358 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.358 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
12.358 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
12.358 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.358 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.358 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
12.359 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
12.359 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
12.359 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
12.359 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
12.359 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
12.359 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.359 * [taylor]: Taking taylor expansion of 1/2 in n
12.359 * [backup-simplify]: Simplify 1/2 into 1/2
12.359 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.359 * [taylor]: Taking taylor expansion of k in n
12.359 * [backup-simplify]: Simplify k into k
12.359 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.359 * [taylor]: Taking taylor expansion of 1/2 in n
12.359 * [backup-simplify]: Simplify 1/2 into 1/2
12.359 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.359 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.359 * [taylor]: Taking taylor expansion of -2 in n
12.359 * [backup-simplify]: Simplify -2 into -2
12.359 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.359 * [taylor]: Taking taylor expansion of PI in n
12.359 * [backup-simplify]: Simplify PI into PI
12.359 * [taylor]: Taking taylor expansion of n in n
12.359 * [backup-simplify]: Simplify 0 into 0
12.359 * [backup-simplify]: Simplify 1 into 1
12.359 * [backup-simplify]: Simplify (/ PI 1) into PI
12.360 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.360 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.360 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.360 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
12.361 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.362 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
12.363 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
12.363 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
12.363 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
12.363 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
12.363 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
12.363 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.363 * [taylor]: Taking taylor expansion of 1/2 in n
12.363 * [backup-simplify]: Simplify 1/2 into 1/2
12.363 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.363 * [taylor]: Taking taylor expansion of k in n
12.363 * [backup-simplify]: Simplify k into k
12.363 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.363 * [taylor]: Taking taylor expansion of 1/2 in n
12.363 * [backup-simplify]: Simplify 1/2 into 1/2
12.363 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.363 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.363 * [taylor]: Taking taylor expansion of -2 in n
12.363 * [backup-simplify]: Simplify -2 into -2
12.363 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.363 * [taylor]: Taking taylor expansion of PI in n
12.363 * [backup-simplify]: Simplify PI into PI
12.363 * [taylor]: Taking taylor expansion of n in n
12.363 * [backup-simplify]: Simplify 0 into 0
12.363 * [backup-simplify]: Simplify 1 into 1
12.364 * [backup-simplify]: Simplify (/ PI 1) into PI
12.364 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.365 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.365 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.365 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
12.366 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.367 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
12.367 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
12.367 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
12.367 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
12.367 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
12.367 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.367 * [taylor]: Taking taylor expansion of 1/2 in k
12.367 * [backup-simplify]: Simplify 1/2 into 1/2
12.368 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.368 * [taylor]: Taking taylor expansion of k in k
12.368 * [backup-simplify]: Simplify 0 into 0
12.368 * [backup-simplify]: Simplify 1 into 1
12.368 * [backup-simplify]: Simplify (/ 1 1) into 1
12.368 * [taylor]: Taking taylor expansion of 1/2 in k
12.368 * [backup-simplify]: Simplify 1/2 into 1/2
12.368 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
12.368 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
12.368 * [taylor]: Taking taylor expansion of (* -2 PI) in k
12.368 * [taylor]: Taking taylor expansion of -2 in k
12.368 * [backup-simplify]: Simplify -2 into -2
12.368 * [taylor]: Taking taylor expansion of PI in k
12.368 * [backup-simplify]: Simplify PI into PI
12.368 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.369 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.369 * [taylor]: Taking taylor expansion of (log n) in k
12.369 * [taylor]: Taking taylor expansion of n in k
12.369 * [backup-simplify]: Simplify n into n
12.369 * [backup-simplify]: Simplify (log n) into (log n)
12.370 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.370 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.370 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.371 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
12.371 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
12.372 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
12.373 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
12.373 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.374 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
12.375 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
12.375 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.375 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
12.375 * [backup-simplify]: Simplify (+ 0 0) into 0
12.376 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.377 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
12.378 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
12.378 * [taylor]: Taking taylor expansion of 0 in k
12.378 * [backup-simplify]: Simplify 0 into 0
12.378 * [backup-simplify]: Simplify 0 into 0
12.378 * [backup-simplify]: Simplify 0 into 0
12.379 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.380 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
12.381 * [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
12.382 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.382 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
12.382 * [backup-simplify]: Simplify (+ 0 0) into 0
12.383 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.384 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
12.387 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.387 * [taylor]: Taking taylor expansion of 0 in k
12.387 * [backup-simplify]: Simplify 0 into 0
12.387 * [backup-simplify]: Simplify 0 into 0
12.387 * [backup-simplify]: Simplify 0 into 0
12.387 * [backup-simplify]: Simplify 0 into 0
12.388 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.389 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.395 * [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
12.395 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.397 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
12.397 * [backup-simplify]: Simplify (+ 0 0) into 0
12.399 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.400 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
12.403 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
12.403 * [taylor]: Taking taylor expansion of 0 in k
12.403 * [backup-simplify]: Simplify 0 into 0
12.403 * [backup-simplify]: Simplify 0 into 0
12.405 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
12.405 * * * * [progress]: [ 3 / 4 ] generating series at (2)
12.405 * [backup-simplify]: Simplify (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))))
12.405 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0
12.405 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
12.405 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.405 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.405 * [taylor]: Taking taylor expansion of k in k
12.405 * [backup-simplify]: Simplify 0 into 0
12.405 * [backup-simplify]: Simplify 1 into 1
12.406 * [backup-simplify]: Simplify (/ 1 1) into 1
12.406 * [backup-simplify]: Simplify (sqrt 0) into 0
12.408 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.408 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
12.408 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
12.408 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
12.408 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
12.408 * [taylor]: Taking taylor expansion of 1/2 in k
12.408 * [backup-simplify]: Simplify 1/2 into 1/2
12.408 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
12.408 * [taylor]: Taking taylor expansion of 1/2 in k
12.408 * [backup-simplify]: Simplify 1/2 into 1/2
12.408 * [taylor]: Taking taylor expansion of k in k
12.408 * [backup-simplify]: Simplify 0 into 0
12.408 * [backup-simplify]: Simplify 1 into 1
12.408 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
12.408 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
12.408 * [taylor]: Taking taylor expansion of 2 in k
12.408 * [backup-simplify]: Simplify 2 into 2
12.408 * [taylor]: Taking taylor expansion of (* n PI) in k
12.408 * [taylor]: Taking taylor expansion of n in k
12.408 * [backup-simplify]: Simplify n into n
12.408 * [taylor]: Taking taylor expansion of PI in k
12.408 * [backup-simplify]: Simplify PI into PI
12.408 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.408 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
12.408 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
12.409 * [backup-simplify]: Simplify (* 1/2 0) into 0
12.409 * [backup-simplify]: Simplify (- 0) into 0
12.410 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.410 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
12.410 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
12.410 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
12.410 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
12.410 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.410 * [taylor]: Taking taylor expansion of k in n
12.410 * [backup-simplify]: Simplify k into k
12.410 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.410 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
12.410 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.410 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
12.410 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
12.410 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
12.410 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
12.411 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
12.411 * [taylor]: Taking taylor expansion of 1/2 in n
12.411 * [backup-simplify]: Simplify 1/2 into 1/2
12.411 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
12.411 * [taylor]: Taking taylor expansion of 1/2 in n
12.411 * [backup-simplify]: Simplify 1/2 into 1/2
12.411 * [taylor]: Taking taylor expansion of k in n
12.411 * [backup-simplify]: Simplify k into k
12.411 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.411 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.411 * [taylor]: Taking taylor expansion of 2 in n
12.411 * [backup-simplify]: Simplify 2 into 2
12.411 * [taylor]: Taking taylor expansion of (* n PI) in n
12.411 * [taylor]: Taking taylor expansion of n in n
12.411 * [backup-simplify]: Simplify 0 into 0
12.411 * [backup-simplify]: Simplify 1 into 1
12.411 * [taylor]: Taking taylor expansion of PI in n
12.411 * [backup-simplify]: Simplify PI into PI
12.412 * [backup-simplify]: Simplify (* 0 PI) into 0
12.412 * [backup-simplify]: Simplify (* 2 0) into 0
12.414 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.415 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.416 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.416 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
12.417 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
12.417 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
12.418 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.419 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
12.421 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
12.421 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
12.421 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
12.421 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.421 * [taylor]: Taking taylor expansion of k in n
12.421 * [backup-simplify]: Simplify k into k
12.421 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.421 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
12.421 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.421 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
12.421 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
12.421 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
12.421 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
12.421 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
12.421 * [taylor]: Taking taylor expansion of 1/2 in n
12.421 * [backup-simplify]: Simplify 1/2 into 1/2
12.421 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
12.421 * [taylor]: Taking taylor expansion of 1/2 in n
12.421 * [backup-simplify]: Simplify 1/2 into 1/2
12.421 * [taylor]: Taking taylor expansion of k in n
12.422 * [backup-simplify]: Simplify k into k
12.422 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
12.422 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.422 * [taylor]: Taking taylor expansion of 2 in n
12.422 * [backup-simplify]: Simplify 2 into 2
12.422 * [taylor]: Taking taylor expansion of (* n PI) in n
12.422 * [taylor]: Taking taylor expansion of n in n
12.422 * [backup-simplify]: Simplify 0 into 0
12.422 * [backup-simplify]: Simplify 1 into 1
12.422 * [taylor]: Taking taylor expansion of PI in n
12.422 * [backup-simplify]: Simplify PI into PI
12.422 * [backup-simplify]: Simplify (* 0 PI) into 0
12.423 * [backup-simplify]: Simplify (* 2 0) into 0
12.424 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.426 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.427 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.427 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
12.427 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
12.427 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
12.428 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.429 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
12.431 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
12.432 * [backup-simplify]: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k)))
12.432 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k
12.432 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
12.432 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
12.432 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
12.432 * [taylor]: Taking taylor expansion of 1/2 in k
12.432 * [backup-simplify]: Simplify 1/2 into 1/2
12.432 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
12.432 * [taylor]: Taking taylor expansion of 1/2 in k
12.432 * [backup-simplify]: Simplify 1/2 into 1/2
12.432 * [taylor]: Taking taylor expansion of k in k
12.432 * [backup-simplify]: Simplify 0 into 0
12.432 * [backup-simplify]: Simplify 1 into 1
12.432 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
12.432 * [taylor]: Taking taylor expansion of (log n) in k
12.432 * [taylor]: Taking taylor expansion of n in k
12.432 * [backup-simplify]: Simplify n into n
12.432 * [backup-simplify]: Simplify (log n) into (log n)
12.433 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
12.433 * [taylor]: Taking taylor expansion of (* 2 PI) in k
12.433 * [taylor]: Taking taylor expansion of 2 in k
12.433 * [backup-simplify]: Simplify 2 into 2
12.433 * [taylor]: Taking taylor expansion of PI in k
12.433 * [backup-simplify]: Simplify PI into PI
12.433 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.434 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.435 * [backup-simplify]: Simplify (* 1/2 0) into 0
12.435 * [backup-simplify]: Simplify (- 0) into 0
12.435 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.442 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.444 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
12.445 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
12.445 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.445 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.445 * [taylor]: Taking taylor expansion of k in k
12.445 * [backup-simplify]: Simplify 0 into 0
12.445 * [backup-simplify]: Simplify 1 into 1
12.445 * [backup-simplify]: Simplify (/ 1 1) into 1
12.446 * [backup-simplify]: Simplify (sqrt 0) into 0
12.447 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.449 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
12.449 * [backup-simplify]: Simplify 0 into 0
12.450 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.451 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
12.453 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.453 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
12.454 * [backup-simplify]: Simplify (- 0) into 0
12.454 * [backup-simplify]: Simplify (+ 0 0) into 0
12.455 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.457 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
12.459 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.460 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0
12.460 * [taylor]: Taking taylor expansion of 0 in k
12.460 * [backup-simplify]: Simplify 0 into 0
12.461 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
12.462 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.464 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.464 * [backup-simplify]: Simplify (+ 0 0) into 0
12.465 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
12.465 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.466 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.467 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
12.470 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
12.474 * [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)))))))
12.474 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
12.475 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.476 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.478 * [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
12.478 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
12.478 * [backup-simplify]: Simplify (- 0) into 0
12.479 * [backup-simplify]: Simplify (+ 0 0) into 0
12.480 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.481 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.482 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.482 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.483 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
12.484 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0
12.484 * [taylor]: Taking taylor expansion of 0 in k
12.484 * [backup-simplify]: Simplify 0 into 0
12.484 * [backup-simplify]: Simplify 0 into 0
12.484 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
12.486 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.487 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
12.488 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.490 * [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
12.490 * [backup-simplify]: Simplify (+ 0 0) into 0
12.490 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
12.491 * [backup-simplify]: Simplify (- 0) into 0
12.491 * [backup-simplify]: Simplify (+ 0 0) into 0
12.492 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
12.494 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
12.500 * [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))))))))
12.503 * [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))))))))
12.504 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.505 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
12.508 * [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
12.509 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
12.509 * [backup-simplify]: Simplify (- 0) into 0
12.510 * [backup-simplify]: Simplify (+ 0 0) into 0
12.511 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
12.512 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
12.513 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
12.514 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.514 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
12.515 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0
12.515 * [taylor]: Taking taylor expansion of 0 in k
12.515 * [backup-simplify]: Simplify 0 into 0
12.515 * [backup-simplify]: Simplify 0 into 0
12.515 * [backup-simplify]: Simplify 0 into 0
12.516 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.518 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.520 * [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
12.521 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.524 * [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
12.525 * [backup-simplify]: Simplify (+ 0 0) into 0
12.525 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
12.526 * [backup-simplify]: Simplify (- 0) into 0
12.526 * [backup-simplify]: Simplify (+ 0 0) into 0
12.527 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
12.531 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
12.546 * [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))))))))))))))
12.557 * [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))))))))))))))
12.576 * [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))))))))))))))))))))))
12.577 * [backup-simplify]: Simplify (* (sqrt (/ (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k)))) (sqrt (/ (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))
12.577 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
12.577 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
12.577 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.578 * [taylor]: Taking taylor expansion of k in k
12.578 * [backup-simplify]: Simplify 0 into 0
12.578 * [backup-simplify]: Simplify 1 into 1
12.578 * [backup-simplify]: Simplify (sqrt 0) into 0
12.580 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.580 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
12.580 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
12.580 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
12.580 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
12.580 * [taylor]: Taking taylor expansion of 1/2 in k
12.580 * [backup-simplify]: Simplify 1/2 into 1/2
12.580 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.580 * [taylor]: Taking taylor expansion of 1/2 in k
12.580 * [backup-simplify]: Simplify 1/2 into 1/2
12.580 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.580 * [taylor]: Taking taylor expansion of k in k
12.580 * [backup-simplify]: Simplify 0 into 0
12.580 * [backup-simplify]: Simplify 1 into 1
12.580 * [backup-simplify]: Simplify (/ 1 1) into 1
12.580 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
12.580 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
12.580 * [taylor]: Taking taylor expansion of 2 in k
12.580 * [backup-simplify]: Simplify 2 into 2
12.580 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.581 * [taylor]: Taking taylor expansion of PI in k
12.581 * [backup-simplify]: Simplify PI into PI
12.581 * [taylor]: Taking taylor expansion of n in k
12.581 * [backup-simplify]: Simplify n into n
12.581 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.581 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
12.581 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
12.581 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.582 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.582 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.582 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
12.582 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
12.583 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
12.583 * [taylor]: Taking taylor expansion of (sqrt k) in n
12.583 * [taylor]: Taking taylor expansion of k in n
12.583 * [backup-simplify]: Simplify k into k
12.583 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
12.583 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
12.583 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
12.583 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.583 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.583 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.583 * [taylor]: Taking taylor expansion of 1/2 in n
12.583 * [backup-simplify]: Simplify 1/2 into 1/2
12.583 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.583 * [taylor]: Taking taylor expansion of 1/2 in n
12.583 * [backup-simplify]: Simplify 1/2 into 1/2
12.583 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.583 * [taylor]: Taking taylor expansion of k in n
12.583 * [backup-simplify]: Simplify k into k
12.583 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.583 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.583 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.583 * [taylor]: Taking taylor expansion of 2 in n
12.583 * [backup-simplify]: Simplify 2 into 2
12.583 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.583 * [taylor]: Taking taylor expansion of PI in n
12.583 * [backup-simplify]: Simplify PI into PI
12.583 * [taylor]: Taking taylor expansion of n in n
12.583 * [backup-simplify]: Simplify 0 into 0
12.583 * [backup-simplify]: Simplify 1 into 1
12.584 * [backup-simplify]: Simplify (/ PI 1) into PI
12.585 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.586 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.586 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.586 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
12.586 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
12.587 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.589 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
12.590 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
12.590 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
12.590 * [taylor]: Taking taylor expansion of (sqrt k) in n
12.590 * [taylor]: Taking taylor expansion of k in n
12.590 * [backup-simplify]: Simplify k into k
12.590 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
12.590 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
12.590 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
12.590 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
12.590 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
12.590 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
12.590 * [taylor]: Taking taylor expansion of 1/2 in n
12.590 * [backup-simplify]: Simplify 1/2 into 1/2
12.590 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.590 * [taylor]: Taking taylor expansion of 1/2 in n
12.591 * [backup-simplify]: Simplify 1/2 into 1/2
12.591 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.591 * [taylor]: Taking taylor expansion of k in n
12.591 * [backup-simplify]: Simplify k into k
12.591 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.591 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
12.591 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.591 * [taylor]: Taking taylor expansion of 2 in n
12.591 * [backup-simplify]: Simplify 2 into 2
12.591 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.591 * [taylor]: Taking taylor expansion of PI in n
12.591 * [backup-simplify]: Simplify PI into PI
12.591 * [taylor]: Taking taylor expansion of n in n
12.591 * [backup-simplify]: Simplify 0 into 0
12.591 * [backup-simplify]: Simplify 1 into 1
12.591 * [backup-simplify]: Simplify (/ PI 1) into PI
12.592 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.593 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.593 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.593 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
12.593 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
12.595 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.596 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
12.597 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
12.599 * [backup-simplify]: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k))
12.599 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k
12.599 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
12.599 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
12.599 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
12.599 * [taylor]: Taking taylor expansion of 1/2 in k
12.599 * [backup-simplify]: Simplify 1/2 into 1/2
12.599 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.599 * [taylor]: Taking taylor expansion of 1/2 in k
12.599 * [backup-simplify]: Simplify 1/2 into 1/2
12.599 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.599 * [taylor]: Taking taylor expansion of k in k
12.599 * [backup-simplify]: Simplify 0 into 0
12.599 * [backup-simplify]: Simplify 1 into 1
12.599 * [backup-simplify]: Simplify (/ 1 1) into 1
12.599 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
12.599 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
12.600 * [taylor]: Taking taylor expansion of (* 2 PI) in k
12.600 * [taylor]: Taking taylor expansion of 2 in k
12.600 * [backup-simplify]: Simplify 2 into 2
12.600 * [taylor]: Taking taylor expansion of PI in k
12.600 * [backup-simplify]: Simplify PI into PI
12.600 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.601 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
12.601 * [taylor]: Taking taylor expansion of (log n) in k
12.601 * [taylor]: Taking taylor expansion of n in k
12.601 * [backup-simplify]: Simplify n into n
12.601 * [backup-simplify]: Simplify (log n) into (log n)
12.602 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.602 * [backup-simplify]: Simplify (- 1/2) into -1/2
12.603 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
12.603 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.604 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
12.605 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
12.606 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
12.606 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.607 * [taylor]: Taking taylor expansion of k in k
12.607 * [backup-simplify]: Simplify 0 into 0
12.607 * [backup-simplify]: Simplify 1 into 1
12.607 * [backup-simplify]: Simplify (sqrt 0) into 0
12.608 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.610 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0
12.610 * [backup-simplify]: Simplify 0 into 0
12.611 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.612 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.614 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
12.614 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.614 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
12.615 * [backup-simplify]: Simplify (- 0) into 0
12.615 * [backup-simplify]: Simplify (+ 0 0) into 0
12.617 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.618 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
12.620 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
12.622 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0
12.622 * [taylor]: Taking taylor expansion of 0 in k
12.622 * [backup-simplify]: Simplify 0 into 0
12.622 * [backup-simplify]: Simplify 0 into 0
12.623 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
12.625 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
12.626 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.627 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.631 * [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
12.631 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.632 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
12.632 * [backup-simplify]: Simplify (- 0) into 0
12.633 * [backup-simplify]: Simplify (+ 0 0) into 0
12.635 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.636 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
12.639 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.640 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
12.641 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0
12.641 * [taylor]: Taking taylor expansion of 0 in k
12.641 * [backup-simplify]: Simplify 0 into 0
12.641 * [backup-simplify]: Simplify 0 into 0
12.641 * [backup-simplify]: Simplify 0 into 0
12.645 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.647 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
12.648 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
12.649 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.651 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.657 * [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
12.657 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.659 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
12.659 * [backup-simplify]: Simplify (- 0) into 0
12.659 * [backup-simplify]: Simplify (+ 0 0) into 0
12.661 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
12.662 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
12.663 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
12.664 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
12.665 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0
12.665 * [taylor]: Taking taylor expansion of 0 in k
12.665 * [backup-simplify]: Simplify 0 into 0
12.665 * [backup-simplify]: Simplify 0 into 0
12.665 * [backup-simplify]: Simplify 0 into 0
12.665 * [backup-simplify]: Simplify 0 into 0
12.668 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.669 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
12.670 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
12.676 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
12.677 * [backup-simplify]: Simplify (* (sqrt (/ (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k))))) (sqrt (/ (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k)))
12.677 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0
12.677 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
12.677 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
12.677 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
12.677 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
12.677 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
12.677 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.677 * [taylor]: Taking taylor expansion of 1/2 in k
12.677 * [backup-simplify]: Simplify 1/2 into 1/2
12.677 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.677 * [taylor]: Taking taylor expansion of k in k
12.677 * [backup-simplify]: Simplify 0 into 0
12.677 * [backup-simplify]: Simplify 1 into 1
12.677 * [backup-simplify]: Simplify (/ 1 1) into 1
12.677 * [taylor]: Taking taylor expansion of 1/2 in k
12.677 * [backup-simplify]: Simplify 1/2 into 1/2
12.677 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
12.677 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
12.677 * [taylor]: Taking taylor expansion of -2 in k
12.677 * [backup-simplify]: Simplify -2 into -2
12.677 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.677 * [taylor]: Taking taylor expansion of PI in k
12.677 * [backup-simplify]: Simplify PI into PI
12.677 * [taylor]: Taking taylor expansion of n in k
12.677 * [backup-simplify]: Simplify n into n
12.677 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.677 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
12.677 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
12.678 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.678 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.678 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
12.678 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
12.678 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.678 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.678 * [taylor]: Taking taylor expansion of -1 in k
12.678 * [backup-simplify]: Simplify -1 into -1
12.678 * [taylor]: Taking taylor expansion of k in k
12.678 * [backup-simplify]: Simplify 0 into 0
12.678 * [backup-simplify]: Simplify 1 into 1
12.679 * [backup-simplify]: Simplify (/ -1 1) into -1
12.679 * [backup-simplify]: Simplify (sqrt 0) into 0
12.680 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.680 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
12.680 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
12.680 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
12.680 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
12.680 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
12.680 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
12.680 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.680 * [taylor]: Taking taylor expansion of 1/2 in n
12.680 * [backup-simplify]: Simplify 1/2 into 1/2
12.680 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.680 * [taylor]: Taking taylor expansion of k in n
12.680 * [backup-simplify]: Simplify k into k
12.680 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.680 * [taylor]: Taking taylor expansion of 1/2 in n
12.680 * [backup-simplify]: Simplify 1/2 into 1/2
12.680 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.680 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.680 * [taylor]: Taking taylor expansion of -2 in n
12.680 * [backup-simplify]: Simplify -2 into -2
12.680 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.680 * [taylor]: Taking taylor expansion of PI in n
12.680 * [backup-simplify]: Simplify PI into PI
12.680 * [taylor]: Taking taylor expansion of n in n
12.680 * [backup-simplify]: Simplify 0 into 0
12.680 * [backup-simplify]: Simplify 1 into 1
12.681 * [backup-simplify]: Simplify (/ PI 1) into PI
12.681 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.682 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.682 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.682 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
12.684 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.685 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
12.687 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
12.687 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
12.687 * [taylor]: Taking taylor expansion of (/ -1 k) in n
12.687 * [taylor]: Taking taylor expansion of -1 in n
12.687 * [backup-simplify]: Simplify -1 into -1
12.687 * [taylor]: Taking taylor expansion of k in n
12.687 * [backup-simplify]: Simplify k into k
12.687 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
12.687 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
12.687 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
12.688 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
12.689 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
12.689 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
12.689 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
12.689 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
12.689 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
12.689 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
12.689 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
12.689 * [taylor]: Taking taylor expansion of 1/2 in n
12.689 * [backup-simplify]: Simplify 1/2 into 1/2
12.689 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.689 * [taylor]: Taking taylor expansion of k in n
12.689 * [backup-simplify]: Simplify k into k
12.689 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.689 * [taylor]: Taking taylor expansion of 1/2 in n
12.689 * [backup-simplify]: Simplify 1/2 into 1/2
12.689 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
12.689 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.689 * [taylor]: Taking taylor expansion of -2 in n
12.689 * [backup-simplify]: Simplify -2 into -2
12.689 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.690 * [taylor]: Taking taylor expansion of PI in n
12.690 * [backup-simplify]: Simplify PI into PI
12.690 * [taylor]: Taking taylor expansion of n in n
12.690 * [backup-simplify]: Simplify 0 into 0
12.690 * [backup-simplify]: Simplify 1 into 1
12.690 * [backup-simplify]: Simplify (/ PI 1) into PI
12.691 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.692 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.692 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
12.692 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
12.693 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.694 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
12.696 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
12.696 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
12.696 * [taylor]: Taking taylor expansion of (/ -1 k) in n
12.696 * [taylor]: Taking taylor expansion of -1 in n
12.696 * [backup-simplify]: Simplify -1 into -1
12.696 * [taylor]: Taking taylor expansion of k in n
12.696 * [backup-simplify]: Simplify k into k
12.696 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
12.696 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
12.696 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
12.696 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
12.697 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
12.698 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k
12.698 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
12.698 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
12.698 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
12.698 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
12.698 * [taylor]: Taking taylor expansion of 1/2 in k
12.698 * [backup-simplify]: Simplify 1/2 into 1/2
12.698 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.698 * [taylor]: Taking taylor expansion of k in k
12.698 * [backup-simplify]: Simplify 0 into 0
12.698 * [backup-simplify]: Simplify 1 into 1
12.698 * [backup-simplify]: Simplify (/ 1 1) into 1
12.698 * [taylor]: Taking taylor expansion of 1/2 in k
12.698 * [backup-simplify]: Simplify 1/2 into 1/2
12.698 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
12.698 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
12.698 * [taylor]: Taking taylor expansion of (* -2 PI) in k
12.698 * [taylor]: Taking taylor expansion of -2 in k
12.698 * [backup-simplify]: Simplify -2 into -2
12.698 * [taylor]: Taking taylor expansion of PI in k
12.698 * [backup-simplify]: Simplify PI into PI
12.699 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.700 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
12.700 * [taylor]: Taking taylor expansion of (log n) in k
12.700 * [taylor]: Taking taylor expansion of n in k
12.700 * [backup-simplify]: Simplify n into n
12.700 * [backup-simplify]: Simplify (log n) into (log n)
12.701 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
12.701 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
12.701 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.702 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
12.703 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
12.705 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
12.705 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.705 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.705 * [taylor]: Taking taylor expansion of -1 in k
12.705 * [backup-simplify]: Simplify -1 into -1
12.705 * [taylor]: Taking taylor expansion of k in k
12.705 * [backup-simplify]: Simplify 0 into 0
12.705 * [backup-simplify]: Simplify 1 into 1
12.705 * [backup-simplify]: Simplify (/ -1 1) into -1
12.706 * [backup-simplify]: Simplify (sqrt 0) into 0
12.707 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.708 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
12.709 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
12.712 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.712 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
12.713 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
12.714 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.714 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
12.714 * [backup-simplify]: Simplify (+ 0 0) into 0
12.715 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.716 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
12.717 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
12.718 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
12.718 * [taylor]: Taking taylor expansion of 0 in k
12.718 * [backup-simplify]: Simplify 0 into 0
12.718 * [backup-simplify]: Simplify 0 into 0
12.718 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
12.720 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.721 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
12.722 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
12.723 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.724 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
12.726 * [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
12.726 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.726 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
12.726 * [backup-simplify]: Simplify (+ 0 0) into 0
12.727 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
12.728 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
12.730 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.730 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.730 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
12.731 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
12.731 * [taylor]: Taking taylor expansion of 0 in k
12.731 * [backup-simplify]: Simplify 0 into 0
12.731 * [backup-simplify]: Simplify 0 into 0
12.731 * [backup-simplify]: Simplify 0 into 0
12.732 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.736 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.740 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
12.741 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
12.745 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
12.745 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 1)
12.746 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI))
12.746 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
12.746 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.746 * [taylor]: Taking taylor expansion of 2 in n
12.746 * [backup-simplify]: Simplify 2 into 2
12.746 * [taylor]: Taking taylor expansion of (* n PI) in n
12.746 * [taylor]: Taking taylor expansion of n in n
12.746 * [backup-simplify]: Simplify 0 into 0
12.746 * [backup-simplify]: Simplify 1 into 1
12.746 * [taylor]: Taking taylor expansion of PI in n
12.746 * [backup-simplify]: Simplify PI into PI
12.746 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
12.746 * [taylor]: Taking taylor expansion of 2 in n
12.746 * [backup-simplify]: Simplify 2 into 2
12.746 * [taylor]: Taking taylor expansion of (* n PI) in n
12.746 * [taylor]: Taking taylor expansion of n in n
12.746 * [backup-simplify]: Simplify 0 into 0
12.746 * [backup-simplify]: Simplify 1 into 1
12.746 * [taylor]: Taking taylor expansion of PI in n
12.746 * [backup-simplify]: Simplify PI into PI
12.747 * [backup-simplify]: Simplify (* 0 PI) into 0
12.747 * [backup-simplify]: Simplify (* 2 0) into 0
12.747 * [backup-simplify]: Simplify 0 into 0
12.749 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.750 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
12.751 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.752 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.753 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
12.753 * [backup-simplify]: Simplify 0 into 0
12.754 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.756 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.756 * [backup-simplify]: Simplify 0 into 0
12.758 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.759 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
12.759 * [backup-simplify]: Simplify 0 into 0
12.761 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.762 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
12.762 * [backup-simplify]: Simplify 0 into 0
12.764 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.766 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
12.766 * [backup-simplify]: Simplify 0 into 0
12.768 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
12.770 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
12.770 * [backup-simplify]: Simplify 0 into 0
12.771 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
12.771 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n))
12.771 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
12.771 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.771 * [taylor]: Taking taylor expansion of 2 in n
12.771 * [backup-simplify]: Simplify 2 into 2
12.771 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.771 * [taylor]: Taking taylor expansion of PI in n
12.771 * [backup-simplify]: Simplify PI into PI
12.771 * [taylor]: Taking taylor expansion of n in n
12.771 * [backup-simplify]: Simplify 0 into 0
12.771 * [backup-simplify]: Simplify 1 into 1
12.772 * [backup-simplify]: Simplify (/ PI 1) into PI
12.772 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
12.772 * [taylor]: Taking taylor expansion of 2 in n
12.772 * [backup-simplify]: Simplify 2 into 2
12.772 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.772 * [taylor]: Taking taylor expansion of PI in n
12.772 * [backup-simplify]: Simplify PI into PI
12.772 * [taylor]: Taking taylor expansion of n in n
12.772 * [backup-simplify]: Simplify 0 into 0
12.772 * [backup-simplify]: Simplify 1 into 1
12.773 * [backup-simplify]: Simplify (/ PI 1) into PI
12.773 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.774 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
12.775 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.776 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
12.776 * [backup-simplify]: Simplify 0 into 0
12.777 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.778 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
12.778 * [backup-simplify]: Simplify 0 into 0
12.779 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.780 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.780 * [backup-simplify]: Simplify 0 into 0
12.781 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.783 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.783 * [backup-simplify]: Simplify 0 into 0
12.784 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.786 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.786 * [backup-simplify]: Simplify 0 into 0
12.787 * [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
12.789 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.789 * [backup-simplify]: Simplify 0 into 0
12.790 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
12.790 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n))
12.790 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
12.790 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.790 * [taylor]: Taking taylor expansion of -2 in n
12.790 * [backup-simplify]: Simplify -2 into -2
12.790 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.790 * [taylor]: Taking taylor expansion of PI in n
12.790 * [backup-simplify]: Simplify PI into PI
12.790 * [taylor]: Taking taylor expansion of n in n
12.790 * [backup-simplify]: Simplify 0 into 0
12.790 * [backup-simplify]: Simplify 1 into 1
12.791 * [backup-simplify]: Simplify (/ PI 1) into PI
12.791 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
12.791 * [taylor]: Taking taylor expansion of -2 in n
12.791 * [backup-simplify]: Simplify -2 into -2
12.791 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.791 * [taylor]: Taking taylor expansion of PI in n
12.791 * [backup-simplify]: Simplify PI into PI
12.791 * [taylor]: Taking taylor expansion of n in n
12.791 * [backup-simplify]: Simplify 0 into 0
12.791 * [backup-simplify]: Simplify 1 into 1
12.791 * [backup-simplify]: Simplify (/ PI 1) into PI
12.792 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.792 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
12.793 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.794 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
12.794 * [backup-simplify]: Simplify 0 into 0
12.795 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.796 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
12.796 * [backup-simplify]: Simplify 0 into 0
12.797 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.799 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.799 * [backup-simplify]: Simplify 0 into 0
12.800 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.801 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.801 * [backup-simplify]: Simplify 0 into 0
12.801 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.806 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.806 * [backup-simplify]: Simplify 0 into 0
12.807 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.808 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.808 * [backup-simplify]: Simplify 0 into 0
12.809 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
12.809 * * * [progress]: simplifying candidates
12.809 * * * * [progress]: [ 1 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (exp (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.809 * * * * [progress]: [ 2 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (exp (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.809 * * * * [progress]: [ 3 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.809 * * * * [progress]: [ 4 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.809 * * * * [progress]: [ 5 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))))>
12.809 * * * * [progress]: [ 6 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))))>
12.809 * * * * [progress]: [ 7 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))))>
12.809 * * * * [progress]: [ 8 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))))>
12.809 * * * * [progress]: [ 9 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))))>
12.809 * * * * [progress]: [ 10 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))))>
12.809 * * * * [progress]: [ 11 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))))>
12.809 * * * * [progress]: [ 12 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k)))))>
12.810 * * * * [progress]: [ 13 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt k)))))>
12.810 * * * * [progress]: [ 14 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))))>
12.810 * * * * [progress]: [ 15 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k)))))>
12.810 * * * * [progress]: [ 16 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k)))))>
12.810 * * * * [progress]: [ 17 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k)))))>
12.810 * * * * [progress]: [ 18 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (sqrt k)))))>
12.810 * * * * [progress]: [ 19 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (exp (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))))>
12.810 * * * * [progress]: [ 20 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (log (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))))>
12.810 * * * * [progress]: [ 21 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))))>
12.810 * * * * [progress]: [ 22 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (cbrt (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))))>
12.810 * * * * [progress]: [ 23 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))))>
12.810 * * * * [progress]: [ 24 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.810 * * * * [progress]: [ 25 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))))>
12.810 * * * * [progress]: [ 26 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (posit16->real (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))))>
12.810 * * * * [progress]: [ 27 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.810 * * * * [progress]: [ 28 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.810 * * * * [progress]: [ 29 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.810 * * * * [progress]: [ 30 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.810 * * * * [progress]: [ 31 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.810 * * * * [progress]: [ 32 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.810 * * * * [progress]: [ 33 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.810 * * * * [progress]: [ 34 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (/ (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.810 * * * * [progress]: [ 35 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.810 * * * * [progress]: [ 36 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.811 * * * * [progress]: [ 37 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.811 * * * * [progress]: [ 38 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.811 * * * * [progress]: [ 39 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.811 * * * * [progress]: [ 40 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.811 * * * * [progress]: [ 41 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.811 * * * * [progress]: [ 42 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.811 * * * * [progress]: [ 43 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.811 * * * * [progress]: [ 44 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.811 * * * * [progress]: [ 45 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.811 * * * * [progress]: [ 46 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (log (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.811 * * * * [progress]: [ 47 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.811 * * * * [progress]: [ 48 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (cbrt (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.811 * * * * [progress]: [ 49 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.811 * * * * [progress]: [ 50 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.811 * * * * [progress]: [ 51 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.811 * * * * [progress]: [ 52 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (posit16->real (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.811 * * * * [progress]: [ 53 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (+ 1/2 1/2)))>
12.811 * * * * [progress]: [ 54 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (+ 1/2 (/ 1 2))))>
12.811 * * * * [progress]: [ 55 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (+ 1 1)))>
12.811 * * * * [progress]: [ 56 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (+ (/ 1 2) 1/2)))>
12.811 * * * * [progress]: [ 57 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (+ (/ 1 2) (/ 1 2))))>
12.811 * * * * [progress]: [ 58 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) 1/2))>
12.811 * * * * [progress]: [ 59 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1))>
12.811 * * * * [progress]: [ 60 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (/ 1 2)))>
12.812 * * * * [progress]: [ 61 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) 2))>
12.812 * * * * [progress]: [ 62 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (+ 1 1)))>
12.812 * * * * [progress]: [ 63 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) 1))>
12.812 * * * * [progress]: [ 64 / 327 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (log (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.812 * * * * [progress]: [ 65 / 327 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.812 * * * * [progress]: [ 66 / 327 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.812 * * * * [progress]: [ 67 / 327 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.812 * * * * [progress]: [ 68 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (cbrt (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))) (cbrt (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.812 * * * * [progress]: [ 69 / 327 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.812 * * * * [progress]: [ 70 / 327 ] simplifiying candidate #<alt (λ (k n) (sqrt (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.812 * * * * [progress]: [ 71 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (sqrt (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.812 * * * * [progress]: [ 72 / 327 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))>
12.812 * * * * [progress]: [ 73 / 327 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (sqrt (sqrt k)) (sqrt (sqrt k)))))>
12.812 * * * * [progress]: [ 74 / 327 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.812 * * * * [progress]: [ 75 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))) (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.812 * * * * [progress]: [ 76 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (* (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (sqrt (* (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))) (* (sqrt (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.812 * * * * [progress]: [ 77 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.812 * * * * [progress]: [ 78 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.812 * * * * [progress]: [ 79 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))))))>
12.812 * * * * [progress]: [ 80 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))))))>
12.812 * * * * [progress]: [ 81 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))))))>
12.813 * * * * [progress]: [ 82 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))))))>
12.813 * * * * [progress]: [ 83 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.813 * * * * [progress]: [ 84 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.813 * * * * [progress]: [ 85 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.813 * * * * [progress]: [ 86 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.813 * * * * [progress]: [ 87 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1)))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))))>
12.813 * * * * [progress]: [ 88 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1)))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))))>
12.813 * * * * [progress]: [ 89 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.813 * * * * [progress]: [ 90 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.813 * * * * [progress]: [ 91 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.813 * * * * [progress]: [ 92 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.813 * * * * [progress]: [ 93 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) 1)) (sqrt (/ (pow (* (* n 2) PI) 1/2) 1))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))))>
12.813 * * * * [progress]: [ 94 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) 1)) (sqrt (/ (pow (* (* n 2) PI) 1/2) 1))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))))>
12.813 * * * * [progress]: [ 95 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))))))>
12.813 * * * * [progress]: [ 96 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))))))>
12.813 * * * * [progress]: [ 97 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))))))>
12.813 * * * * [progress]: [ 98 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))))))>
12.813 * * * * [progress]: [ 99 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.813 * * * * [progress]: [ 100 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.813 * * * * [progress]: [ 101 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.814 * * * * [progress]: [ 102 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.814 * * * * [progress]: [ 103 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1)))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))))>
12.814 * * * * [progress]: [ 104 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1)))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))))>
12.814 * * * * [progress]: [ 105 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.814 * * * * [progress]: [ 106 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.814 * * * * [progress]: [ 107 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.814 * * * * [progress]: [ 108 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))))))>
12.814 * * * * [progress]: [ 109 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) 1)) (sqrt (/ (pow (* (* n 2) PI) 1/2) 1))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))))>
12.814 * * * * [progress]: [ 110 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) 1/2) 1)) (sqrt (/ (pow (* (* n 2) PI) 1/2) 1))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))))>
12.814 * * * * [progress]: [ 111 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))))))>
12.814 * * * * [progress]: [ 112 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))))))>
12.814 * * * * [progress]: [ 113 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))))>
12.814 * * * * [progress]: [ 114 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))))>
12.814 * * * * [progress]: [ 115 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt 1))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt 1)))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
12.814 * * * * [progress]: [ 116 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))))>
12.814 * * * * [progress]: [ 117 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))))>
12.814 * * * * [progress]: [ 118 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) 1)) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) 1))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))))>
12.814 * * * * [progress]: [ 119 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))))>
12.814 * * * * [progress]: [ 120 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))))>
12.814 * * * * [progress]: [ 121 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.815 * * * * [progress]: [ 122 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.815 * * * * [progress]: [ 123 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt 1))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt 1)))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))))>
12.815 * * * * [progress]: [ 124 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.815 * * * * [progress]: [ 125 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.815 * * * * [progress]: [ 126 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) 1)) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) 1))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))))>
12.815 * * * * [progress]: [ 127 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))))>
12.815 * * * * [progress]: [ 128 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))))>
12.815 * * * * [progress]: [ 129 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.815 * * * * [progress]: [ 130 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.815 * * * * [progress]: [ 131 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt 1))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt 1)))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))))>
12.815 * * * * [progress]: [ 132 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.815 * * * * [progress]: [ 133 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.815 * * * * [progress]: [ 134 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1)) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))))))>
12.815 * * * * [progress]: [ 135 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))))>
12.815 * * * * [progress]: [ 136 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ 1 (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))))>
12.815 * * * * [progress]: [ 137 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))))>
12.815 * * * * [progress]: [ 138 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))))>
12.815 * * * * [progress]: [ 139 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt 1))) (sqrt (/ 1 (sqrt 1)))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.815 * * * * [progress]: [ 140 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))))>
12.816 * * * * [progress]: [ 141 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))))>
12.816 * * * * [progress]: [ 142 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 1)) (sqrt (/ 1 1))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.816 * * * * [progress]: [ 143 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))))))>
12.816 * * * * [progress]: [ 144 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k)))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))))))>
12.816 * * * * [progress]: [ 145 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.816 * * * * [progress]: [ 146 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.816 * * * * [progress]: [ 147 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
12.816 * * * * [progress]: [ 148 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.816 * * * * [progress]: [ 149 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.816 * * * * [progress]: [ 150 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1)) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
12.816 * * * * [progress]: [ 151 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt 1) (sqrt 1)) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.816 * * * * [progress]: [ 152 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))))))>
12.816 * * * * [progress]: [ 153 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.816 * * * * [progress]: [ 154 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.816 * * * * [progress]: [ 155 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* 1 1) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.816 * * * * [progress]: [ 156 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.816 * * * * [progress]: [ 157 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.816 * * * * [progress]: [ 158 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.816 * * * * [progress]: [ 159 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.816 * * * * [progress]: [ 160 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.817 * * * * [progress]: [ 161 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.817 * * * * [progress]: [ 162 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.817 * * * * [progress]: [ 163 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.817 * * * * [progress]: [ 164 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.817 * * * * [progress]: [ 165 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.817 * * * * [progress]: [ 166 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.817 * * * * [progress]: [ 167 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.817 * * * * [progress]: [ 168 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.817 * * * * [progress]: [ 169 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.817 * * * * [progress]: [ 170 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.817 * * * * [progress]: [ 171 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.817 * * * * [progress]: [ 172 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.817 * * * * [progress]: [ 173 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.817 * * * * [progress]: [ 174 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.817 * * * * [progress]: [ 175 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.817 * * * * [progress]: [ 176 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.817 * * * * [progress]: [ 177 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.817 * * * * [progress]: [ 178 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.817 * * * * [progress]: [ 179 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.817 * * * * [progress]: [ 180 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.818 * * * * [progress]: [ 181 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.818 * * * * [progress]: [ 182 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.818 * * * * [progress]: [ 183 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.818 * * * * [progress]: [ 184 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.818 * * * * [progress]: [ 185 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.818 * * * * [progress]: [ 186 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.818 * * * * [progress]: [ 187 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.818 * * * * [progress]: [ 188 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))))>
12.818 * * * * [progress]: [ 189 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.818 * * * * [progress]: [ 190 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))))>
12.818 * * * * [progress]: [ 191 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.818 * * * * [progress]: [ 192 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (* 2 1/2)))>
12.818 * * * * [progress]: [ 193 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (* 2 1)))>
12.818 * * * * [progress]: [ 194 / 327 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (* 2 (/ 1 2))))>
12.818 * * * * [progress]: [ 195 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.818 * * * * [progress]: [ 196 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))) (sqrt (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.818 * * * * [progress]: [ 197 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.818 * * * * [progress]: [ 198 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k))))))>
12.818 * * * * [progress]: [ 199 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k))))))>
12.818 * * * * [progress]: [ 200 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k))))))>
12.818 * * * * [progress]: [ 201 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k)))))>
12.819 * * * * [progress]: [ 202 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k))))))>
12.819 * * * * [progress]: [ 203 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) 1))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k)))))>
12.819 * * * * [progress]: [ 204 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k))))))>
12.819 * * * * [progress]: [ 205 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k))))))>
12.819 * * * * [progress]: [ 206 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k))))))>
12.819 * * * * [progress]: [ 207 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1)))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k)))))>
12.819 * * * * [progress]: [ 208 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k))))))>
12.819 * * * * [progress]: [ 209 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) 1/2) 1))) (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k)))))>
12.819 * * * * [progress]: [ 210 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k))))))>
12.819 * * * * [progress]: [ 211 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k))))))>
12.819 * * * * [progress]: [ 212 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
12.819 * * * * [progress]: [ 213 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt 1)))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))>
12.819 * * * * [progress]: [ 214 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k))))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
12.819 * * * * [progress]: [ 215 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) 1))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k)))))>
12.819 * * * * [progress]: [ 216 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))>
12.819 * * * * [progress]: [ 217 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k))))))>
12.819 * * * * [progress]: [ 218 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
12.819 * * * * [progress]: [ 219 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt 1)))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.819 * * * * [progress]: [ 220 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
12.819 * * * * [progress]: [ 221 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) 1))) (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.820 * * * * [progress]: [ 222 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))))>
12.820 * * * * [progress]: [ 223 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k))))))>
12.820 * * * * [progress]: [ 224 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
12.820 * * * * [progress]: [ 225 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt 1)))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.820 * * * * [progress]: [ 226 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
12.820 * * * * [progress]: [ 227 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)))))>
12.820 * * * * [progress]: [ 228 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k))))))>
12.820 * * * * [progress]: [ 229 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k))))))>
12.820 * * * * [progress]: [ 230 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
12.820 * * * * [progress]: [ 231 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt 1)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.820 * * * * [progress]: [ 232 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
12.820 * * * * [progress]: [ 233 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 1))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.820 * * * * [progress]: [ 234 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k))))))>
12.820 * * * * [progress]: [ 235 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k))))))>
12.820 * * * * [progress]: [ 236 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
12.820 * * * * [progress]: [ 237 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
12.820 * * * * [progress]: [ 238 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
12.820 * * * * [progress]: [ 239 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
12.820 * * * * [progress]: [ 240 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt 1)) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.820 * * * * [progress]: [ 241 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (/ 1 (sqrt k)))))>
12.820 * * * * [progress]: [ 242 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.821 * * * * [progress]: [ 243 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) 1) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.821 * * * * [progress]: [ 244 / 327 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.821 * * * * [progress]: [ 245 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))) (* (sqrt (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.821 * * * * [progress]: [ 246 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.821 * * * * [progress]: [ 247 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.821 * * * * [progress]: [ 248 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.821 * * * * [progress]: [ 249 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.821 * * * * [progress]: [ 250 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.821 * * * * [progress]: [ 251 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.821 * * * * [progress]: [ 252 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) 1)) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.821 * * * * [progress]: [ 253 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.821 * * * * [progress]: [ 254 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (* (cbrt k) (cbrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.821 * * * * [progress]: [ 255 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.821 * * * * [progress]: [ 256 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt 1))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.821 * * * * [progress]: [ 257 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) (sqrt (sqrt k)))) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.821 * * * * [progress]: [ 258 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) 1/2) 1)) (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.821 * * * * [progress]: [ 259 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.822 * * * * [progress]: [ 260 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.822 * * * * [progress]: [ 261 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.822 * * * * [progress]: [ 262 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt 1))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.822 * * * * [progress]: [ 263 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.822 * * * * [progress]: [ 264 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n 2) (- 1/2 (/ k 2))) 1)) (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.822 * * * * [progress]: [ 265 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.822 * * * * [progress]: [ 266 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k))))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.822 * * * * [progress]: [ 267 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.822 * * * * [progress]: [ 268 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt 1))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.822 * * * * [progress]: [ 269 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.822 * * * * [progress]: [ 270 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) 1)) (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.822 * * * * [progress]: [ 271 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.822 * * * * [progress]: [ 272 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k))))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.822 * * * * [progress]: [ 273 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.822 * * * * [progress]: [ 274 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt 1))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 275 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 276 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1)) (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 277 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 278 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (sqrt (* (cbrt k) (cbrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 279 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (sqrt (sqrt k)))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 280 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (sqrt 1))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 281 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (sqrt (sqrt k)))) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 282 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 1)) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 283 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 284 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k))))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 285 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 286 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 287 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 288 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1)) (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 289 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt 1) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 290 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (sqrt (/ 1 (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 291 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 292 / 327 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))))>
12.823 * * * * [progress]: [ 293 / 327 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))>
12.823 * * * * [progress]: [ 294 / 327 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (sqrt k))))>
12.824 * * * * [progress]: [ 295 / 327 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))))>
12.824 * * * * [progress]: [ 296 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 297 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 298 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 299 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 300 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (exp (+ (+ (log n) (log 2)) (log PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 301 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (exp (+ (log (* n 2)) (log PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 302 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (exp (log (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 303 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (log (exp (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 304 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (cbrt (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 305 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (cbrt (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 306 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 307 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (cbrt (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 308 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 309 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* 1 (* (* n 2) PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 310 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* (* n 2) (* (cbrt PI) (cbrt PI))) (cbrt PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 311 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 312 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* (* n 2) 1) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 313 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 314 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (posit16->real (real->posit16 (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 315 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))))>
12.824 * * * * [progress]: [ 316 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (- (+ (* 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)))))>
12.825 * * * * [progress]: [ 317 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k)))))>
12.825 * * * * [progress]: [ 318 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k)))))>
12.825 * * * * [progress]: [ 319 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (- (+ (* 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))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.825 * * * * [progress]: [ 320 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.825 * * * * [progress]: [ 321 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
12.825 * * * * [progress]: [ 322 / 327 ] 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)))))))))))))))))))))))>
12.825 * * * * [progress]: [ 323 / 327 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))))>
12.825 * * * * [progress]: [ 324 / 327 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))))>
12.825 * * * * [progress]: [ 325 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
12.825 * * * * [progress]: [ 326 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
12.825 * * * * [progress]: [ 327 / 327 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
12.831 * [simplify]: Simplifying:
  (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (/ k 2))
  (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (/ k 2))
  (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (+ 1/2 1/2)
  (+ 1/2 (/ 1 2))
  (+ 1 1)
  (+ (/ 1 2) 1/2)
  (+ (/ 1 2) (/ 1 2))
  (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))
  (+ 1 1)
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  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt 1))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) 1)))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt 1))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 1)))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1)))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt 1))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) 1)
  (* (cbrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (cbrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))
  (real->posit16 (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (+ (+ (log n) (log 2)) (log PI))
  (+ (log (* n 2)) (log PI))
  (log (* (* n 2) PI))
  (exp (* (* n 2) PI))
  (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI))
  (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI))
  (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI)))
  (cbrt (* (* n 2) PI))
  (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))
  (sqrt (* (* n 2) PI))
  (sqrt (* (* n 2) PI))
  (* (* n 2) (* (cbrt PI) (cbrt PI)))
  (* (* n 2) (sqrt PI))
  (* (* n 2) 1)
  (* 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 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (- (+ (* +nan.0 (* (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 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
12.847 * * [simplify]: iteration 0: 455 enodes
13.058 * * [simplify]: iteration 1: 946 enodes
13.507 * * [simplify]: iteration 2: 3062 enodes
14.483 * * [simplify]: iteration complete: 5001 enodes
14.484 * * [simplify]: Extracting #0: cost 144 inf + 0
14.485 * * [simplify]: Extracting #1: cost 716 inf + 2
14.489 * * [simplify]: Extracting #2: cost 1326 inf + 1040
14.505 * * [simplify]: Extracting #3: cost 1392 inf + 31738
14.530 * * [simplify]: Extracting #4: cost 929 inf + 189942
14.622 * * [simplify]: Extracting #5: cost 433 inf + 384292
14.738 * * [simplify]: Extracting #6: cost 213 inf + 522343
14.895 * * [simplify]: Extracting #7: cost 33 inf + 640088
15.039 * * [simplify]: Extracting #8: cost 0 inf + 661683
15.186 * * [simplify]: Extracting #9: cost 0 inf + 660563
15.328 * * [simplify]: Extracting #10: cost 0 inf + 660483
15.455 * [simplify]: Simplified to:
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* PI (+ n n)))
  (pow (* PI (+ n n)) (/ k 2))
  (pow (* PI (+ n n)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* PI (+ n n)) (sqrt (- 1/2 (/ k 2))))
  (* PI (+ n n))
  (pow (* PI (+ n n)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* PI (+ n n)) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* PI (+ n n))
  (sqrt (* PI (+ n n)))
  (pow (* PI (+ n n)) (/ (- k) 2))
  (sqrt (* PI (+ n n)))
  (pow (* PI (+ n n)) (/ (- k) 2))
  (pow (+ n n) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (exp (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  (* (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (* (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (pow (* PI (+ n n)) (- 1/2 (/ k 2)))))
  (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  (pow (* PI (+ n n)) (- 1/4 (/ k 4)))
  (pow (* PI (+ n n)) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* PI (+ n n)))
  (pow (* PI (+ n n)) (/ k 2))
  (pow (* PI (+ n n)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* PI (+ n n)) (sqrt (- 1/2 (/ k 2))))
  (* PI (+ n n))
  (pow (* PI (+ n n)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* PI (+ n n)) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* PI (+ n n))
  (sqrt (* PI (+ n n)))
  (pow (* PI (+ n n)) (/ (- k) 2))
  (sqrt (* PI (+ n n)))
  (pow (* PI (+ n n)) (/ (- k) 2))
  (pow (+ n n) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))
  (exp (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  (* (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (* (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (pow (* PI (+ n n)) (- 1/2 (/ k 2)))))
  (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  (pow (* PI (+ n n)) (- 1/4 (/ k 4)))
  (pow (* PI (+ n n)) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* PI (+ n n)) (- 1/2 (/ k 2))))
  1
  1
  2
  1
  1
  (* (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))
  (* (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  2
  (- (* (- 1/2 (/ k 2)) (log (* PI (+ n n)))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* PI (+ n n)))) (log (sqrt k)))
  (exp (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (* (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)) (* (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (cbrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (* (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)) (* (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (pow (* PI (+ n n)) (- 1/2 (/ k 2)))
  (sqrt k)
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))))
  (* (cbrt (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))))
  (* (cbrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (/ (sqrt (* PI (+ n n))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* PI (+ n n)) (/ (- k) 2)) (cbrt (sqrt k)))
  (/ (sqrt (* PI (+ n n))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* PI (+ n n)) (/ (- k) 2)) (cbrt (sqrt k)))
  (/ (sqrt (* PI (+ n n))) (fabs (cbrt k)))
  (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (cbrt k)))
  (/ (sqrt (* PI (+ n n))) (fabs (cbrt k)))
  (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (cbrt k)))
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  (* (sqrt (* (/ (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (fabs (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2))))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (fabs (cbrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2))))))
  (* (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2))))))
  (* (sqrt (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ 1 (fabs (cbrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (fabs (cbrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (pow (* PI (+ n n)) (- 1/4 (/ k 4)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (pow (* PI (+ n n)) (- 1/4 (/ k 4)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))))
  (* (sqrt (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (cbrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))))
  (* (sqrt (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (cbrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (cbrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (cbrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (cbrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (/ (- k) 2)) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow PI (- 1/2 (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (cbrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))
  (* (sqrt (/ (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt k))))
  (* (sqrt (/ (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (cbrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt k))))
  (* (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))
  (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))
  (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (cbrt (sqrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (sqrt (cbrt k)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (sqrt (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* PI (+ n n)) (- 1/4 (/ k 4))) (sqrt k))))
  (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt k))))
  (* (sqrt (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))) (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))))
  (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))))
  (* (sqrt (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (* PI (+ n n)) (- 1/2 (/ k 2)))))
  (real->posit16 (/ (pow (* PI (+ n n)) (- 1/2 (/ k 2))) (sqrt k)))
  (* PI (+ n n))
  (* PI (+ n n))
  (log (* PI (+ n n)))
  (log (* PI (+ n n)))
  (log (* PI (+ n n)))
  (exp (* PI (+ n n)))
  (* (* (* n n) n) (* (* 8 PI) (* PI PI)))
  (* (* PI (+ n n)) (* (* PI (+ n n)) (* PI (+ n n))))
  (* (cbrt (* PI (+ n n))) (cbrt (* PI (+ n n))))
  (cbrt (* PI (+ n n)))
  (* (* PI (+ n n)) (* (* PI (+ n n)) (* PI (+ n n))))
  (sqrt (* PI (+ n n)))
  (sqrt (* PI (+ n n)))
  (* (+ n n) (* (cbrt PI) (cbrt PI)))
  (* (+ n n) (sqrt PI))
  (+ n n)
  (+ PI PI)
  (real->posit16 (* PI (+ n n)))
  (+ (+ (+ (* (* (sqrt (* PI (+ n n))) (* (log (+ PI PI)) (log (+ PI PI)))) (* (* k k) 1/8)) (sqrt (* PI (+ n n)))) (- (* (* 1/8 (* (* (log n) (log n)) (sqrt (* PI (+ n n))))) (* k k)) (* 1/2 (+ (* (log n) (* k (sqrt (* PI (+ n n))))) (* (* k (sqrt (* PI (+ n n)))) (log (+ PI PI))))))) (* (* (log (+ PI PI)) (sqrt (* PI (+ n n)))) (* (* (log n) (* k k)) 1/4)))
  (exp (* (- 1/2 (/ k 2)) (log (* PI (+ n n)))))
  (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (/ k 2))))
  (+ (+ (+ (* (* (sqrt (* PI (+ n n))) (* (log (+ PI PI)) (log (+ PI PI)))) (* (* k k) 1/8)) (sqrt (* PI (+ n n)))) (- (* (* 1/8 (* (* (log n) (log n)) (sqrt (* PI (+ n n))))) (* k k)) (* 1/2 (+ (* (log n) (* k (sqrt (* PI (+ n n))))) (* (* k (sqrt (* PI (+ n n)))) (log (+ PI PI))))))) (* (* (log (+ PI PI)) (sqrt (* PI (+ n n)))) (* (* (log n) (* k k)) 1/4)))
  (exp (* (- 1/2 (/ k 2)) (log (* PI (+ n n)))))
  (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (/ k 2))))
  (- (- (* (* +nan.0 (log (+ PI PI))) (* (sqrt (* PI (+ n n))) (* (log n) (* k k)))) (+ (- (* (* (log (+ PI PI)) (* (sqrt (* PI (+ n n))) (* k k))) +nan.0) (* (* (* (sqrt (* PI (+ n n))) +nan.0) (* (log n) (log n))) (* k k))) (- (* (* k (sqrt (* PI (+ n n)))) +nan.0) (+ (- (* (sqrt (* PI (+ n n))) +nan.0) (* +nan.0 (* (* (log (+ PI PI)) (log (+ PI PI))) (* (sqrt (* PI (+ n n))) (* k k))))) (+ (- (* +nan.0 (* (sqrt (* PI (+ n n))) (* (log n) (* k k)))) (* (* (sqrt (* PI (+ n n))) (* k k)) +nan.0)) (* +nan.0 (- (* (* k (sqrt (* PI (+ n n)))) (log (+ PI PI))) (* (log n) (* k (sqrt (* PI (+ n n)))))))))))))
  (- (- (* (/ (exp (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))) (* k k)) (/ +nan.0 k)) (* +nan.0 (- (/ (exp (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))) k) (/ (exp (* (- 1/2 (/ k 2)) (log (* PI (+ n n))))) (* k k))))))
  (+ (* +nan.0 (- (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (/ k 2)))) k))) (* +nan.0 (- (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (/ k 2)))) (* k k)) (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (/ k 2)))))))
  (* PI (+ n n))
  (* PI (+ n n))
  (* PI (+ n n))
15.496 * * * [progress]: adding candidates to table
17.087 * * [progress]: iteration 4 / 4
17.088 * * * [progress]: picking best candidate
17.120 * * * * [pick]: Picked  #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.121 * * * [progress]: localizing error
17.195 * * * [progress]: generating rewritten candidates
17.195 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1)
17.219 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1 1)
17.245 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1 2 1)
17.258 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1 1 1)
17.281 * * * [progress]: generating series expansions
17.281 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1)
17.281 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
17.281 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
17.281 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
17.281 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
17.281 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
17.281 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
17.281 * [taylor]: Taking taylor expansion of 1/2 in k
17.281 * [backup-simplify]: Simplify 1/2 into 1/2
17.281 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
17.281 * [taylor]: Taking taylor expansion of 1/2 in k
17.281 * [backup-simplify]: Simplify 1/2 into 1/2
17.281 * [taylor]: Taking taylor expansion of k in k
17.281 * [backup-simplify]: Simplify 0 into 0
17.281 * [backup-simplify]: Simplify 1 into 1
17.281 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
17.281 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
17.281 * [taylor]: Taking taylor expansion of 2 in k
17.281 * [backup-simplify]: Simplify 2 into 2
17.281 * [taylor]: Taking taylor expansion of (* n PI) in k
17.281 * [taylor]: Taking taylor expansion of n in k
17.281 * [backup-simplify]: Simplify n into n
17.281 * [taylor]: Taking taylor expansion of PI in k
17.281 * [backup-simplify]: Simplify PI into PI
17.281 * [backup-simplify]: Simplify (* n PI) into (* n PI)
17.281 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
17.282 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
17.282 * [backup-simplify]: Simplify (* 1/2 0) into 0
17.282 * [backup-simplify]: Simplify (- 0) into 0
17.283 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.283 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
17.283 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
17.283 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
17.283 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
17.283 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
17.283 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
17.283 * [taylor]: Taking taylor expansion of 1/2 in n
17.283 * [backup-simplify]: Simplify 1/2 into 1/2
17.283 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
17.283 * [taylor]: Taking taylor expansion of 1/2 in n
17.283 * [backup-simplify]: Simplify 1/2 into 1/2
17.283 * [taylor]: Taking taylor expansion of k in n
17.283 * [backup-simplify]: Simplify k into k
17.283 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
17.283 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
17.283 * [taylor]: Taking taylor expansion of 2 in n
17.283 * [backup-simplify]: Simplify 2 into 2
17.283 * [taylor]: Taking taylor expansion of (* n PI) in n
17.283 * [taylor]: Taking taylor expansion of n in n
17.283 * [backup-simplify]: Simplify 0 into 0
17.283 * [backup-simplify]: Simplify 1 into 1
17.283 * [taylor]: Taking taylor expansion of PI in n
17.283 * [backup-simplify]: Simplify PI into PI
17.283 * [backup-simplify]: Simplify (* 0 PI) into 0
17.284 * [backup-simplify]: Simplify (* 2 0) into 0
17.285 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
17.286 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
17.286 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.286 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
17.287 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
17.287 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
17.288 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.288 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
17.289 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
17.289 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
17.289 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
17.289 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
17.289 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
17.289 * [taylor]: Taking taylor expansion of 1/2 in n
17.289 * [backup-simplify]: Simplify 1/2 into 1/2
17.289 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
17.289 * [taylor]: Taking taylor expansion of 1/2 in n
17.289 * [backup-simplify]: Simplify 1/2 into 1/2
17.289 * [taylor]: Taking taylor expansion of k in n
17.289 * [backup-simplify]: Simplify k into k
17.289 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
17.289 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
17.289 * [taylor]: Taking taylor expansion of 2 in n
17.289 * [backup-simplify]: Simplify 2 into 2
17.290 * [taylor]: Taking taylor expansion of (* n PI) in n
17.290 * [taylor]: Taking taylor expansion of n in n
17.290 * [backup-simplify]: Simplify 0 into 0
17.290 * [backup-simplify]: Simplify 1 into 1
17.290 * [taylor]: Taking taylor expansion of PI in n
17.290 * [backup-simplify]: Simplify PI into PI
17.290 * [backup-simplify]: Simplify (* 0 PI) into 0
17.290 * [backup-simplify]: Simplify (* 2 0) into 0
17.291 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
17.292 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
17.293 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.293 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
17.293 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
17.293 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
17.294 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.295 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
17.295 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
17.295 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
17.295 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
17.295 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
17.295 * [taylor]: Taking taylor expansion of 1/2 in k
17.295 * [backup-simplify]: Simplify 1/2 into 1/2
17.295 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
17.295 * [taylor]: Taking taylor expansion of 1/2 in k
17.295 * [backup-simplify]: Simplify 1/2 into 1/2
17.296 * [taylor]: Taking taylor expansion of k in k
17.296 * [backup-simplify]: Simplify 0 into 0
17.296 * [backup-simplify]: Simplify 1 into 1
17.296 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
17.296 * [taylor]: Taking taylor expansion of (log n) in k
17.296 * [taylor]: Taking taylor expansion of n in k
17.296 * [backup-simplify]: Simplify n into n
17.296 * [backup-simplify]: Simplify (log n) into (log n)
17.296 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
17.296 * [taylor]: Taking taylor expansion of (* 2 PI) in k
17.296 * [taylor]: Taking taylor expansion of 2 in k
17.296 * [backup-simplify]: Simplify 2 into 2
17.296 * [taylor]: Taking taylor expansion of PI in k
17.296 * [backup-simplify]: Simplify PI into PI
17.296 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.297 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.297 * [backup-simplify]: Simplify (* 1/2 0) into 0
17.297 * [backup-simplify]: Simplify (- 0) into 0
17.298 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.298 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.299 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
17.300 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
17.300 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
17.301 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
17.303 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
17.305 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
17.305 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
17.305 * [backup-simplify]: Simplify (- 0) into 0
17.306 * [backup-simplify]: Simplify (+ 0 0) into 0
17.307 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.308 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
17.311 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
17.311 * [taylor]: Taking taylor expansion of 0 in k
17.311 * [backup-simplify]: Simplify 0 into 0
17.311 * [backup-simplify]: Simplify 0 into 0
17.311 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
17.312 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
17.313 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
17.314 * [backup-simplify]: Simplify (+ 0 0) into 0
17.314 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
17.314 * [backup-simplify]: Simplify (- 1/2) into -1/2
17.315 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
17.316 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
17.319 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
17.325 * [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)))))))
17.325 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
17.326 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
17.328 * [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
17.328 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
17.329 * [backup-simplify]: Simplify (- 0) into 0
17.329 * [backup-simplify]: Simplify (+ 0 0) into 0
17.330 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.331 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
17.332 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.332 * [taylor]: Taking taylor expansion of 0 in k
17.332 * [backup-simplify]: Simplify 0 into 0
17.332 * [backup-simplify]: Simplify 0 into 0
17.332 * [backup-simplify]: Simplify 0 into 0
17.333 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
17.334 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
17.336 * [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
17.336 * [backup-simplify]: Simplify (+ 0 0) into 0
17.337 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
17.337 * [backup-simplify]: Simplify (- 0) into 0
17.337 * [backup-simplify]: Simplify (+ 0 0) into 0
17.338 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
17.341 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
17.346 * [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)))))
17.355 * [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)))))
17.355 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
17.355 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
17.355 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
17.356 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
17.356 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
17.356 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
17.356 * [taylor]: Taking taylor expansion of 1/2 in k
17.356 * [backup-simplify]: Simplify 1/2 into 1/2
17.356 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.356 * [taylor]: Taking taylor expansion of 1/2 in k
17.356 * [backup-simplify]: Simplify 1/2 into 1/2
17.356 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.356 * [taylor]: Taking taylor expansion of k in k
17.356 * [backup-simplify]: Simplify 0 into 0
17.356 * [backup-simplify]: Simplify 1 into 1
17.356 * [backup-simplify]: Simplify (/ 1 1) into 1
17.356 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
17.356 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
17.356 * [taylor]: Taking taylor expansion of 2 in k
17.356 * [backup-simplify]: Simplify 2 into 2
17.356 * [taylor]: Taking taylor expansion of (/ PI n) in k
17.356 * [taylor]: Taking taylor expansion of PI in k
17.356 * [backup-simplify]: Simplify PI into PI
17.356 * [taylor]: Taking taylor expansion of n in k
17.356 * [backup-simplify]: Simplify n into n
17.356 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
17.357 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
17.357 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
17.357 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.357 * [backup-simplify]: Simplify (- 1/2) into -1/2
17.358 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
17.358 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
17.358 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
17.358 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
17.358 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
17.358 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
17.358 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
17.358 * [taylor]: Taking taylor expansion of 1/2 in n
17.358 * [backup-simplify]: Simplify 1/2 into 1/2
17.358 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.358 * [taylor]: Taking taylor expansion of 1/2 in n
17.358 * [backup-simplify]: Simplify 1/2 into 1/2
17.358 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.358 * [taylor]: Taking taylor expansion of k in n
17.358 * [backup-simplify]: Simplify k into k
17.358 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.358 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
17.358 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
17.359 * [taylor]: Taking taylor expansion of 2 in n
17.359 * [backup-simplify]: Simplify 2 into 2
17.359 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.359 * [taylor]: Taking taylor expansion of PI in n
17.359 * [backup-simplify]: Simplify PI into PI
17.359 * [taylor]: Taking taylor expansion of n in n
17.359 * [backup-simplify]: Simplify 0 into 0
17.359 * [backup-simplify]: Simplify 1 into 1
17.359 * [backup-simplify]: Simplify (/ PI 1) into PI
17.360 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.361 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.361 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.361 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
17.361 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
17.363 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.364 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
17.365 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
17.365 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
17.365 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
17.365 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
17.365 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
17.365 * [taylor]: Taking taylor expansion of 1/2 in n
17.365 * [backup-simplify]: Simplify 1/2 into 1/2
17.365 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.365 * [taylor]: Taking taylor expansion of 1/2 in n
17.365 * [backup-simplify]: Simplify 1/2 into 1/2
17.365 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.365 * [taylor]: Taking taylor expansion of k in n
17.365 * [backup-simplify]: Simplify k into k
17.365 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.365 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
17.365 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
17.365 * [taylor]: Taking taylor expansion of 2 in n
17.365 * [backup-simplify]: Simplify 2 into 2
17.365 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.365 * [taylor]: Taking taylor expansion of PI in n
17.365 * [backup-simplify]: Simplify PI into PI
17.365 * [taylor]: Taking taylor expansion of n in n
17.365 * [backup-simplify]: Simplify 0 into 0
17.365 * [backup-simplify]: Simplify 1 into 1
17.366 * [backup-simplify]: Simplify (/ PI 1) into PI
17.366 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.367 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.367 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.368 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
17.368 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
17.369 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.370 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
17.371 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
17.371 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
17.372 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
17.372 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
17.372 * [taylor]: Taking taylor expansion of 1/2 in k
17.372 * [backup-simplify]: Simplify 1/2 into 1/2
17.372 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.372 * [taylor]: Taking taylor expansion of 1/2 in k
17.372 * [backup-simplify]: Simplify 1/2 into 1/2
17.372 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.372 * [taylor]: Taking taylor expansion of k in k
17.372 * [backup-simplify]: Simplify 0 into 0
17.372 * [backup-simplify]: Simplify 1 into 1
17.372 * [backup-simplify]: Simplify (/ 1 1) into 1
17.372 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
17.372 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
17.372 * [taylor]: Taking taylor expansion of (* 2 PI) in k
17.372 * [taylor]: Taking taylor expansion of 2 in k
17.372 * [backup-simplify]: Simplify 2 into 2
17.372 * [taylor]: Taking taylor expansion of PI in k
17.372 * [backup-simplify]: Simplify PI into PI
17.373 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.374 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.374 * [taylor]: Taking taylor expansion of (log n) in k
17.374 * [taylor]: Taking taylor expansion of n in k
17.374 * [backup-simplify]: Simplify n into n
17.374 * [backup-simplify]: Simplify (log n) into (log n)
17.375 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.375 * [backup-simplify]: Simplify (- 1/2) into -1/2
17.376 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
17.376 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
17.377 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
17.378 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
17.379 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
17.381 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
17.382 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.383 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
17.385 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
17.385 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
17.385 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
17.386 * [backup-simplify]: Simplify (- 0) into 0
17.386 * [backup-simplify]: Simplify (+ 0 0) into 0
17.388 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.389 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
17.391 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
17.391 * [taylor]: Taking taylor expansion of 0 in k
17.391 * [backup-simplify]: Simplify 0 into 0
17.391 * [backup-simplify]: Simplify 0 into 0
17.391 * [backup-simplify]: Simplify 0 into 0
17.393 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.394 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
17.397 * [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
17.398 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.399 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
17.399 * [backup-simplify]: Simplify (- 0) into 0
17.399 * [backup-simplify]: Simplify (+ 0 0) into 0
17.401 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.403 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
17.405 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.405 * [taylor]: Taking taylor expansion of 0 in k
17.405 * [backup-simplify]: Simplify 0 into 0
17.405 * [backup-simplify]: Simplify 0 into 0
17.405 * [backup-simplify]: Simplify 0 into 0
17.405 * [backup-simplify]: Simplify 0 into 0
17.407 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.408 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.414 * [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
17.414 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.415 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
17.416 * [backup-simplify]: Simplify (- 0) into 0
17.416 * [backup-simplify]: Simplify (+ 0 0) into 0
17.418 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.419 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
17.422 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
17.422 * [taylor]: Taking taylor expansion of 0 in k
17.422 * [backup-simplify]: Simplify 0 into 0
17.422 * [backup-simplify]: Simplify 0 into 0
17.423 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
17.424 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
17.424 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
17.424 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
17.424 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
17.424 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
17.424 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
17.424 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.424 * [taylor]: Taking taylor expansion of 1/2 in k
17.424 * [backup-simplify]: Simplify 1/2 into 1/2
17.424 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.424 * [taylor]: Taking taylor expansion of k in k
17.424 * [backup-simplify]: Simplify 0 into 0
17.424 * [backup-simplify]: Simplify 1 into 1
17.424 * [backup-simplify]: Simplify (/ 1 1) into 1
17.424 * [taylor]: Taking taylor expansion of 1/2 in k
17.424 * [backup-simplify]: Simplify 1/2 into 1/2
17.424 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
17.424 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
17.424 * [taylor]: Taking taylor expansion of -2 in k
17.425 * [backup-simplify]: Simplify -2 into -2
17.425 * [taylor]: Taking taylor expansion of (/ PI n) in k
17.425 * [taylor]: Taking taylor expansion of PI in k
17.425 * [backup-simplify]: Simplify PI into PI
17.425 * [taylor]: Taking taylor expansion of n in k
17.425 * [backup-simplify]: Simplify n into n
17.425 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
17.425 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
17.425 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
17.425 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.426 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.426 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
17.426 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
17.426 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
17.426 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
17.426 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
17.426 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
17.426 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.426 * [taylor]: Taking taylor expansion of 1/2 in n
17.426 * [backup-simplify]: Simplify 1/2 into 1/2
17.426 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.426 * [taylor]: Taking taylor expansion of k in n
17.426 * [backup-simplify]: Simplify k into k
17.426 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.426 * [taylor]: Taking taylor expansion of 1/2 in n
17.426 * [backup-simplify]: Simplify 1/2 into 1/2
17.426 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
17.426 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
17.426 * [taylor]: Taking taylor expansion of -2 in n
17.426 * [backup-simplify]: Simplify -2 into -2
17.426 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.426 * [taylor]: Taking taylor expansion of PI in n
17.426 * [backup-simplify]: Simplify PI into PI
17.426 * [taylor]: Taking taylor expansion of n in n
17.427 * [backup-simplify]: Simplify 0 into 0
17.427 * [backup-simplify]: Simplify 1 into 1
17.427 * [backup-simplify]: Simplify (/ PI 1) into PI
17.427 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.428 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
17.429 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.429 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
17.430 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.432 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
17.433 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
17.433 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
17.433 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
17.433 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
17.433 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
17.433 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.433 * [taylor]: Taking taylor expansion of 1/2 in n
17.433 * [backup-simplify]: Simplify 1/2 into 1/2
17.433 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.433 * [taylor]: Taking taylor expansion of k in n
17.433 * [backup-simplify]: Simplify k into k
17.433 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.434 * [taylor]: Taking taylor expansion of 1/2 in n
17.434 * [backup-simplify]: Simplify 1/2 into 1/2
17.434 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
17.434 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
17.434 * [taylor]: Taking taylor expansion of -2 in n
17.434 * [backup-simplify]: Simplify -2 into -2
17.434 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.434 * [taylor]: Taking taylor expansion of PI in n
17.434 * [backup-simplify]: Simplify PI into PI
17.434 * [taylor]: Taking taylor expansion of n in n
17.434 * [backup-simplify]: Simplify 0 into 0
17.434 * [backup-simplify]: Simplify 1 into 1
17.434 * [backup-simplify]: Simplify (/ PI 1) into PI
17.435 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.436 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
17.436 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.436 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
17.438 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.439 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
17.440 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
17.440 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
17.440 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
17.440 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
17.440 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.440 * [taylor]: Taking taylor expansion of 1/2 in k
17.440 * [backup-simplify]: Simplify 1/2 into 1/2
17.440 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.440 * [taylor]: Taking taylor expansion of k in k
17.440 * [backup-simplify]: Simplify 0 into 0
17.440 * [backup-simplify]: Simplify 1 into 1
17.441 * [backup-simplify]: Simplify (/ 1 1) into 1
17.441 * [taylor]: Taking taylor expansion of 1/2 in k
17.441 * [backup-simplify]: Simplify 1/2 into 1/2
17.441 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
17.441 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
17.441 * [taylor]: Taking taylor expansion of (* -2 PI) in k
17.441 * [taylor]: Taking taylor expansion of -2 in k
17.441 * [backup-simplify]: Simplify -2 into -2
17.441 * [taylor]: Taking taylor expansion of PI in k
17.441 * [backup-simplify]: Simplify PI into PI
17.441 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.442 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
17.442 * [taylor]: Taking taylor expansion of (log n) in k
17.442 * [taylor]: Taking taylor expansion of n in k
17.442 * [backup-simplify]: Simplify n into n
17.442 * [backup-simplify]: Simplify (log n) into (log n)
17.442 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.442 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.442 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
17.443 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
17.444 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
17.445 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
17.445 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
17.446 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.446 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
17.448 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
17.448 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
17.448 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
17.453 * [backup-simplify]: Simplify (+ 0 0) into 0
17.455 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.456 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
17.457 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
17.457 * [taylor]: Taking taylor expansion of 0 in k
17.457 * [backup-simplify]: Simplify 0 into 0
17.457 * [backup-simplify]: Simplify 0 into 0
17.457 * [backup-simplify]: Simplify 0 into 0
17.458 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.459 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
17.461 * [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
17.461 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.462 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
17.463 * [backup-simplify]: Simplify (+ 0 0) into 0
17.464 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.466 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
17.468 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.468 * [taylor]: Taking taylor expansion of 0 in k
17.468 * [backup-simplify]: Simplify 0 into 0
17.468 * [backup-simplify]: Simplify 0 into 0
17.469 * [backup-simplify]: Simplify 0 into 0
17.469 * [backup-simplify]: Simplify 0 into 0
17.470 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.471 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.478 * [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
17.478 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.479 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
17.480 * [backup-simplify]: Simplify (+ 0 0) into 0
17.481 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.483 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
17.486 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
17.486 * [taylor]: Taking taylor expansion of 0 in k
17.486 * [backup-simplify]: Simplify 0 into 0
17.486 * [backup-simplify]: Simplify 0 into 0
17.488 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
17.488 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1 1)
17.488 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
17.488 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
17.488 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
17.488 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
17.488 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
17.488 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
17.488 * [taylor]: Taking taylor expansion of 1/2 in k
17.488 * [backup-simplify]: Simplify 1/2 into 1/2
17.488 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
17.488 * [taylor]: Taking taylor expansion of 1/2 in k
17.488 * [backup-simplify]: Simplify 1/2 into 1/2
17.488 * [taylor]: Taking taylor expansion of k in k
17.488 * [backup-simplify]: Simplify 0 into 0
17.488 * [backup-simplify]: Simplify 1 into 1
17.488 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
17.488 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
17.488 * [taylor]: Taking taylor expansion of 2 in k
17.488 * [backup-simplify]: Simplify 2 into 2
17.488 * [taylor]: Taking taylor expansion of (* n PI) in k
17.488 * [taylor]: Taking taylor expansion of n in k
17.489 * [backup-simplify]: Simplify n into n
17.489 * [taylor]: Taking taylor expansion of PI in k
17.489 * [backup-simplify]: Simplify PI into PI
17.489 * [backup-simplify]: Simplify (* n PI) into (* n PI)
17.489 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
17.489 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
17.489 * [backup-simplify]: Simplify (* 1/2 0) into 0
17.490 * [backup-simplify]: Simplify (- 0) into 0
17.490 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.490 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
17.490 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
17.490 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
17.490 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
17.490 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
17.490 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
17.490 * [taylor]: Taking taylor expansion of 1/2 in n
17.490 * [backup-simplify]: Simplify 1/2 into 1/2
17.490 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
17.490 * [taylor]: Taking taylor expansion of 1/2 in n
17.491 * [backup-simplify]: Simplify 1/2 into 1/2
17.491 * [taylor]: Taking taylor expansion of k in n
17.491 * [backup-simplify]: Simplify k into k
17.491 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
17.491 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
17.491 * [taylor]: Taking taylor expansion of 2 in n
17.491 * [backup-simplify]: Simplify 2 into 2
17.491 * [taylor]: Taking taylor expansion of (* n PI) in n
17.491 * [taylor]: Taking taylor expansion of n in n
17.491 * [backup-simplify]: Simplify 0 into 0
17.491 * [backup-simplify]: Simplify 1 into 1
17.491 * [taylor]: Taking taylor expansion of PI in n
17.491 * [backup-simplify]: Simplify PI into PI
17.491 * [backup-simplify]: Simplify (* 0 PI) into 0
17.492 * [backup-simplify]: Simplify (* 2 0) into 0
17.493 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
17.495 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
17.496 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.496 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
17.496 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
17.496 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
17.498 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.499 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
17.500 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
17.500 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
17.500 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
17.500 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
17.500 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
17.500 * [taylor]: Taking taylor expansion of 1/2 in n
17.500 * [backup-simplify]: Simplify 1/2 into 1/2
17.500 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
17.500 * [taylor]: Taking taylor expansion of 1/2 in n
17.500 * [backup-simplify]: Simplify 1/2 into 1/2
17.500 * [taylor]: Taking taylor expansion of k in n
17.500 * [backup-simplify]: Simplify k into k
17.501 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
17.501 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
17.501 * [taylor]: Taking taylor expansion of 2 in n
17.501 * [backup-simplify]: Simplify 2 into 2
17.501 * [taylor]: Taking taylor expansion of (* n PI) in n
17.501 * [taylor]: Taking taylor expansion of n in n
17.501 * [backup-simplify]: Simplify 0 into 0
17.501 * [backup-simplify]: Simplify 1 into 1
17.501 * [taylor]: Taking taylor expansion of PI in n
17.501 * [backup-simplify]: Simplify PI into PI
17.501 * [backup-simplify]: Simplify (* 0 PI) into 0
17.502 * [backup-simplify]: Simplify (* 2 0) into 0
17.503 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
17.505 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
17.506 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.506 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
17.506 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
17.506 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
17.508 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.509 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
17.510 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
17.510 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
17.510 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
17.510 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
17.510 * [taylor]: Taking taylor expansion of 1/2 in k
17.510 * [backup-simplify]: Simplify 1/2 into 1/2
17.510 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
17.510 * [taylor]: Taking taylor expansion of 1/2 in k
17.510 * [backup-simplify]: Simplify 1/2 into 1/2
17.510 * [taylor]: Taking taylor expansion of k in k
17.511 * [backup-simplify]: Simplify 0 into 0
17.511 * [backup-simplify]: Simplify 1 into 1
17.511 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
17.511 * [taylor]: Taking taylor expansion of (log n) in k
17.511 * [taylor]: Taking taylor expansion of n in k
17.511 * [backup-simplify]: Simplify n into n
17.511 * [backup-simplify]: Simplify (log n) into (log n)
17.511 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
17.511 * [taylor]: Taking taylor expansion of (* 2 PI) in k
17.511 * [taylor]: Taking taylor expansion of 2 in k
17.511 * [backup-simplify]: Simplify 2 into 2
17.511 * [taylor]: Taking taylor expansion of PI in k
17.511 * [backup-simplify]: Simplify PI into PI
17.511 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.512 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.513 * [backup-simplify]: Simplify (* 1/2 0) into 0
17.513 * [backup-simplify]: Simplify (- 0) into 0
17.514 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.515 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.516 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
17.517 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
17.518 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
17.519 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
17.520 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
17.522 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
17.522 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
17.523 * [backup-simplify]: Simplify (- 0) into 0
17.523 * [backup-simplify]: Simplify (+ 0 0) into 0
17.524 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.526 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
17.527 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
17.528 * [taylor]: Taking taylor expansion of 0 in k
17.528 * [backup-simplify]: Simplify 0 into 0
17.528 * [backup-simplify]: Simplify 0 into 0
17.528 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
17.529 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
17.530 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
17.530 * [backup-simplify]: Simplify (+ 0 0) into 0
17.531 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
17.531 * [backup-simplify]: Simplify (- 1/2) into -1/2
17.531 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
17.532 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
17.534 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
17.536 * [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)))))))
17.537 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
17.537 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
17.539 * [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
17.540 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
17.540 * [backup-simplify]: Simplify (- 0) into 0
17.540 * [backup-simplify]: Simplify (+ 0 0) into 0
17.541 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
17.542 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
17.543 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.544 * [taylor]: Taking taylor expansion of 0 in k
17.544 * [backup-simplify]: Simplify 0 into 0
17.544 * [backup-simplify]: Simplify 0 into 0
17.544 * [backup-simplify]: Simplify 0 into 0
17.545 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
17.545 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
17.547 * [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
17.547 * [backup-simplify]: Simplify (+ 0 0) into 0
17.548 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
17.548 * [backup-simplify]: Simplify (- 0) into 0
17.548 * [backup-simplify]: Simplify (+ 0 0) into 0
17.550 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
17.552 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
17.555 * [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)))))
17.564 * [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)))))
17.564 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
17.564 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
17.565 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
17.565 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
17.565 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
17.565 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
17.565 * [taylor]: Taking taylor expansion of 1/2 in k
17.565 * [backup-simplify]: Simplify 1/2 into 1/2
17.565 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.565 * [taylor]: Taking taylor expansion of 1/2 in k
17.565 * [backup-simplify]: Simplify 1/2 into 1/2
17.565 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.565 * [taylor]: Taking taylor expansion of k in k
17.565 * [backup-simplify]: Simplify 0 into 0
17.565 * [backup-simplify]: Simplify 1 into 1
17.565 * [backup-simplify]: Simplify (/ 1 1) into 1
17.565 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
17.565 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
17.565 * [taylor]: Taking taylor expansion of 2 in k
17.565 * [backup-simplify]: Simplify 2 into 2
17.565 * [taylor]: Taking taylor expansion of (/ PI n) in k
17.565 * [taylor]: Taking taylor expansion of PI in k
17.565 * [backup-simplify]: Simplify PI into PI
17.565 * [taylor]: Taking taylor expansion of n in k
17.565 * [backup-simplify]: Simplify n into n
17.565 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
17.566 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
17.566 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
17.566 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.566 * [backup-simplify]: Simplify (- 1/2) into -1/2
17.567 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
17.567 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
17.567 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
17.567 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
17.567 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
17.567 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
17.567 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
17.567 * [taylor]: Taking taylor expansion of 1/2 in n
17.567 * [backup-simplify]: Simplify 1/2 into 1/2
17.567 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.567 * [taylor]: Taking taylor expansion of 1/2 in n
17.567 * [backup-simplify]: Simplify 1/2 into 1/2
17.567 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.567 * [taylor]: Taking taylor expansion of k in n
17.567 * [backup-simplify]: Simplify k into k
17.567 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.567 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
17.568 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
17.568 * [taylor]: Taking taylor expansion of 2 in n
17.568 * [backup-simplify]: Simplify 2 into 2
17.568 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.568 * [taylor]: Taking taylor expansion of PI in n
17.568 * [backup-simplify]: Simplify PI into PI
17.568 * [taylor]: Taking taylor expansion of n in n
17.568 * [backup-simplify]: Simplify 0 into 0
17.568 * [backup-simplify]: Simplify 1 into 1
17.568 * [backup-simplify]: Simplify (/ PI 1) into PI
17.569 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.570 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.570 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.570 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
17.570 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
17.577 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.579 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
17.581 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
17.581 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
17.581 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
17.581 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
17.581 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
17.581 * [taylor]: Taking taylor expansion of 1/2 in n
17.581 * [backup-simplify]: Simplify 1/2 into 1/2
17.581 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.581 * [taylor]: Taking taylor expansion of 1/2 in n
17.581 * [backup-simplify]: Simplify 1/2 into 1/2
17.581 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.581 * [taylor]: Taking taylor expansion of k in n
17.581 * [backup-simplify]: Simplify k into k
17.581 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.581 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
17.581 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
17.581 * [taylor]: Taking taylor expansion of 2 in n
17.581 * [backup-simplify]: Simplify 2 into 2
17.581 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.581 * [taylor]: Taking taylor expansion of PI in n
17.581 * [backup-simplify]: Simplify PI into PI
17.581 * [taylor]: Taking taylor expansion of n in n
17.581 * [backup-simplify]: Simplify 0 into 0
17.581 * [backup-simplify]: Simplify 1 into 1
17.582 * [backup-simplify]: Simplify (/ PI 1) into PI
17.582 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.584 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.584 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.584 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
17.584 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
17.585 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.587 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
17.588 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
17.588 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
17.588 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
17.588 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
17.588 * [taylor]: Taking taylor expansion of 1/2 in k
17.588 * [backup-simplify]: Simplify 1/2 into 1/2
17.588 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.588 * [taylor]: Taking taylor expansion of 1/2 in k
17.588 * [backup-simplify]: Simplify 1/2 into 1/2
17.588 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.588 * [taylor]: Taking taylor expansion of k in k
17.588 * [backup-simplify]: Simplify 0 into 0
17.588 * [backup-simplify]: Simplify 1 into 1
17.589 * [backup-simplify]: Simplify (/ 1 1) into 1
17.589 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
17.589 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
17.589 * [taylor]: Taking taylor expansion of (* 2 PI) in k
17.589 * [taylor]: Taking taylor expansion of 2 in k
17.589 * [backup-simplify]: Simplify 2 into 2
17.589 * [taylor]: Taking taylor expansion of PI in k
17.589 * [backup-simplify]: Simplify PI into PI
17.590 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.591 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
17.591 * [taylor]: Taking taylor expansion of (log n) in k
17.591 * [taylor]: Taking taylor expansion of n in k
17.591 * [backup-simplify]: Simplify n into n
17.591 * [backup-simplify]: Simplify (log n) into (log n)
17.591 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.592 * [backup-simplify]: Simplify (- 1/2) into -1/2
17.592 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
17.592 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
17.593 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
17.595 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
17.596 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
17.597 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
17.598 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.599 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
17.601 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
17.601 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
17.602 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
17.602 * [backup-simplify]: Simplify (- 0) into 0
17.602 * [backup-simplify]: Simplify (+ 0 0) into 0
17.604 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.605 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
17.607 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
17.607 * [taylor]: Taking taylor expansion of 0 in k
17.608 * [backup-simplify]: Simplify 0 into 0
17.608 * [backup-simplify]: Simplify 0 into 0
17.608 * [backup-simplify]: Simplify 0 into 0
17.609 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.610 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
17.614 * [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
17.615 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.616 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
17.616 * [backup-simplify]: Simplify (- 0) into 0
17.616 * [backup-simplify]: Simplify (+ 0 0) into 0
17.618 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.620 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
17.622 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.622 * [taylor]: Taking taylor expansion of 0 in k
17.622 * [backup-simplify]: Simplify 0 into 0
17.622 * [backup-simplify]: Simplify 0 into 0
17.622 * [backup-simplify]: Simplify 0 into 0
17.622 * [backup-simplify]: Simplify 0 into 0
17.624 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.625 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.630 * [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
17.631 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.632 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
17.633 * [backup-simplify]: Simplify (- 0) into 0
17.633 * [backup-simplify]: Simplify (+ 0 0) into 0
17.635 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
17.637 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
17.640 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
17.641 * [taylor]: Taking taylor expansion of 0 in k
17.641 * [backup-simplify]: Simplify 0 into 0
17.641 * [backup-simplify]: Simplify 0 into 0
17.642 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
17.642 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
17.642 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
17.642 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
17.642 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
17.642 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
17.642 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
17.642 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.642 * [taylor]: Taking taylor expansion of 1/2 in k
17.642 * [backup-simplify]: Simplify 1/2 into 1/2
17.642 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.642 * [taylor]: Taking taylor expansion of k in k
17.642 * [backup-simplify]: Simplify 0 into 0
17.642 * [backup-simplify]: Simplify 1 into 1
17.643 * [backup-simplify]: Simplify (/ 1 1) into 1
17.643 * [taylor]: Taking taylor expansion of 1/2 in k
17.643 * [backup-simplify]: Simplify 1/2 into 1/2
17.643 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
17.643 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
17.643 * [taylor]: Taking taylor expansion of -2 in k
17.643 * [backup-simplify]: Simplify -2 into -2
17.643 * [taylor]: Taking taylor expansion of (/ PI n) in k
17.643 * [taylor]: Taking taylor expansion of PI in k
17.643 * [backup-simplify]: Simplify PI into PI
17.643 * [taylor]: Taking taylor expansion of n in k
17.643 * [backup-simplify]: Simplify n into n
17.643 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
17.643 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
17.643 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
17.644 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.644 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.644 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
17.644 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
17.644 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
17.645 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
17.645 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
17.645 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
17.645 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.645 * [taylor]: Taking taylor expansion of 1/2 in n
17.645 * [backup-simplify]: Simplify 1/2 into 1/2
17.645 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.645 * [taylor]: Taking taylor expansion of k in n
17.645 * [backup-simplify]: Simplify k into k
17.645 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.645 * [taylor]: Taking taylor expansion of 1/2 in n
17.645 * [backup-simplify]: Simplify 1/2 into 1/2
17.645 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
17.645 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
17.645 * [taylor]: Taking taylor expansion of -2 in n
17.645 * [backup-simplify]: Simplify -2 into -2
17.645 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.645 * [taylor]: Taking taylor expansion of PI in n
17.645 * [backup-simplify]: Simplify PI into PI
17.645 * [taylor]: Taking taylor expansion of n in n
17.645 * [backup-simplify]: Simplify 0 into 0
17.645 * [backup-simplify]: Simplify 1 into 1
17.646 * [backup-simplify]: Simplify (/ PI 1) into PI
17.646 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.647 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
17.647 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.647 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
17.649 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.650 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
17.651 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
17.651 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
17.651 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
17.651 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
17.651 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
17.651 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
17.651 * [taylor]: Taking taylor expansion of 1/2 in n
17.651 * [backup-simplify]: Simplify 1/2 into 1/2
17.651 * [taylor]: Taking taylor expansion of (/ 1 k) in n
17.651 * [taylor]: Taking taylor expansion of k in n
17.651 * [backup-simplify]: Simplify k into k
17.651 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
17.651 * [taylor]: Taking taylor expansion of 1/2 in n
17.651 * [backup-simplify]: Simplify 1/2 into 1/2
17.651 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
17.651 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
17.651 * [taylor]: Taking taylor expansion of -2 in n
17.651 * [backup-simplify]: Simplify -2 into -2
17.651 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.651 * [taylor]: Taking taylor expansion of PI in n
17.651 * [backup-simplify]: Simplify PI into PI
17.651 * [taylor]: Taking taylor expansion of n in n
17.651 * [backup-simplify]: Simplify 0 into 0
17.651 * [backup-simplify]: Simplify 1 into 1
17.652 * [backup-simplify]: Simplify (/ PI 1) into PI
17.652 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.653 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
17.653 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
17.654 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
17.655 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.656 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
17.657 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
17.657 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
17.657 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
17.657 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
17.657 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
17.657 * [taylor]: Taking taylor expansion of 1/2 in k
17.657 * [backup-simplify]: Simplify 1/2 into 1/2
17.657 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.657 * [taylor]: Taking taylor expansion of k in k
17.658 * [backup-simplify]: Simplify 0 into 0
17.658 * [backup-simplify]: Simplify 1 into 1
17.658 * [backup-simplify]: Simplify (/ 1 1) into 1
17.658 * [taylor]: Taking taylor expansion of 1/2 in k
17.658 * [backup-simplify]: Simplify 1/2 into 1/2
17.658 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
17.658 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
17.658 * [taylor]: Taking taylor expansion of (* -2 PI) in k
17.658 * [taylor]: Taking taylor expansion of -2 in k
17.658 * [backup-simplify]: Simplify -2 into -2
17.658 * [taylor]: Taking taylor expansion of PI in k
17.658 * [backup-simplify]: Simplify PI into PI
17.659 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.660 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
17.660 * [taylor]: Taking taylor expansion of (log n) in k
17.660 * [taylor]: Taking taylor expansion of n in k
17.660 * [backup-simplify]: Simplify n into n
17.660 * [backup-simplify]: Simplify (log n) into (log n)
17.660 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
17.661 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
17.661 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
17.662 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
17.663 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
17.664 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
17.665 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
17.666 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.667 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
17.668 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
17.669 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
17.669 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
17.669 * [backup-simplify]: Simplify (+ 0 0) into 0
17.671 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.672 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
17.674 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
17.674 * [taylor]: Taking taylor expansion of 0 in k
17.674 * [backup-simplify]: Simplify 0 into 0
17.674 * [backup-simplify]: Simplify 0 into 0
17.674 * [backup-simplify]: Simplify 0 into 0
17.675 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.676 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
17.680 * [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
17.680 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.681 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
17.681 * [backup-simplify]: Simplify (+ 0 0) into 0
17.682 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.684 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
17.686 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.686 * [taylor]: Taking taylor expansion of 0 in k
17.686 * [backup-simplify]: Simplify 0 into 0
17.686 * [backup-simplify]: Simplify 0 into 0
17.686 * [backup-simplify]: Simplify 0 into 0
17.687 * [backup-simplify]: Simplify 0 into 0
17.688 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.689 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.694 * [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
17.695 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
17.696 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
17.696 * [backup-simplify]: Simplify (+ 0 0) into 0
17.697 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
17.698 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
17.700 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
17.700 * [taylor]: Taking taylor expansion of 0 in k
17.700 * [backup-simplify]: Simplify 0 into 0
17.700 * [backup-simplify]: Simplify 0 into 0
17.701 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
17.701 * * * * [progress]: [ 3 / 4 ] generating series at (2 1 2 1)
17.701 * [backup-simplify]: Simplify (/ 1 (sqrt (sqrt k))) into (pow (/ 1 k) 1/4)
17.701 * [approximate]: Taking taylor expansion of (pow (/ 1 k) 1/4) in (k) around 0
17.701 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
17.701 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
17.701 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
17.701 * [taylor]: Taking taylor expansion of 1/4 in k
17.701 * [backup-simplify]: Simplify 1/4 into 1/4
17.701 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
17.701 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.701 * [taylor]: Taking taylor expansion of k in k
17.701 * [backup-simplify]: Simplify 0 into 0
17.701 * [backup-simplify]: Simplify 1 into 1
17.702 * [backup-simplify]: Simplify (/ 1 1) into 1
17.702 * [backup-simplify]: Simplify (log 1) into 0
17.702 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
17.702 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
17.702 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
17.702 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
17.702 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
17.702 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
17.702 * [taylor]: Taking taylor expansion of 1/4 in k
17.702 * [backup-simplify]: Simplify 1/4 into 1/4
17.702 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
17.702 * [taylor]: Taking taylor expansion of (/ 1 k) in k
17.702 * [taylor]: Taking taylor expansion of k in k
17.702 * [backup-simplify]: Simplify 0 into 0
17.702 * [backup-simplify]: Simplify 1 into 1
17.703 * [backup-simplify]: Simplify (/ 1 1) into 1
17.703 * [backup-simplify]: Simplify (log 1) into 0
17.703 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
17.703 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
17.703 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
17.703 * [backup-simplify]: Simplify (pow k -1/4) into (pow k -1/4)
17.704 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
17.705 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
17.705 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
17.705 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0
17.706 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
17.706 * [backup-simplify]: Simplify 0 into 0
17.706 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.708 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
17.708 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
17.709 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0
17.710 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.710 * [backup-simplify]: Simplify 0 into 0
17.710 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.713 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
17.714 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
17.719 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0
17.720 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
17.720 * [backup-simplify]: Simplify 0 into 0
17.721 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.728 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0
17.729 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
17.731 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0
17.734 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.734 * [backup-simplify]: Simplify 0 into 0
17.735 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.752 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0
17.753 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
17.755 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0
17.759 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
17.759 * [backup-simplify]: Simplify 0 into 0
17.760 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.778 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0
17.778 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
17.780 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0
17.784 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.784 * [backup-simplify]: Simplify 0 into 0
17.784 * [backup-simplify]: Simplify (pow k -1/4) into (pow k -1/4)
17.784 * [backup-simplify]: Simplify (/ 1 (sqrt (sqrt (/ 1 k)))) into (pow k 1/4)
17.784 * [approximate]: Taking taylor expansion of (pow k 1/4) in (k) around 0
17.784 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
17.784 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
17.784 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
17.784 * [taylor]: Taking taylor expansion of 1/4 in k
17.784 * [backup-simplify]: Simplify 1/4 into 1/4
17.784 * [taylor]: Taking taylor expansion of (log k) in k
17.784 * [taylor]: Taking taylor expansion of k in k
17.784 * [backup-simplify]: Simplify 0 into 0
17.784 * [backup-simplify]: Simplify 1 into 1
17.784 * [backup-simplify]: Simplify (log 1) into 0
17.785 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
17.785 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
17.785 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
17.785 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
17.785 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
17.785 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
17.785 * [taylor]: Taking taylor expansion of 1/4 in k
17.785 * [backup-simplify]: Simplify 1/4 into 1/4
17.785 * [taylor]: Taking taylor expansion of (log k) in k
17.785 * [taylor]: Taking taylor expansion of k in k
17.785 * [backup-simplify]: Simplify 0 into 0
17.785 * [backup-simplify]: Simplify 1 into 1
17.785 * [backup-simplify]: Simplify (log 1) into 0
17.785 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
17.785 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
17.785 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
17.786 * [backup-simplify]: Simplify (pow k 1/4) into (pow k 1/4)
17.786 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
17.787 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
17.787 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0
17.787 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
17.787 * [backup-simplify]: Simplify 0 into 0
17.790 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
17.790 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
17.791 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0
17.793 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.793 * [backup-simplify]: Simplify 0 into 0
17.798 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
17.799 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
17.800 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0
17.802 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
17.802 * [backup-simplify]: Simplify 0 into 0
17.814 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0
17.815 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
17.816 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0
17.819 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.819 * [backup-simplify]: Simplify 0 into 0
17.837 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0
17.837 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
17.840 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0
17.850 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
17.850 * [backup-simplify]: Simplify 0 into 0
17.867 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0
17.868 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
17.869 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0
17.872 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
17.872 * [backup-simplify]: Simplify 0 into 0
17.872 * [backup-simplify]: Simplify (pow (/ 1 k) 1/4) into (pow (/ 1 k) 1/4)
17.873 * [backup-simplify]: Simplify (/ 1 (sqrt (sqrt (/ 1 (- k))))) into (sqrt (/ 1 (sqrt (/ -1 k))))
17.873 * [approximate]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in (k) around 0
17.873 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k
17.873 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
17.873 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
17.873 * [taylor]: Taking taylor expansion of (/ -1 k) in k
17.873 * [taylor]: Taking taylor expansion of -1 in k
17.873 * [backup-simplify]: Simplify -1 into -1
17.873 * [taylor]: Taking taylor expansion of k in k
17.873 * [backup-simplify]: Simplify 0 into 0
17.873 * [backup-simplify]: Simplify 1 into 1
17.873 * [backup-simplify]: Simplify (/ -1 1) into -1
17.873 * [backup-simplify]: Simplify (sqrt 0) into 0
17.874 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
17.875 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
17.875 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
17.875 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
17.877 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
17.878 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
17.880 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
17.880 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k
17.880 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
17.880 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
17.880 * [taylor]: Taking taylor expansion of (/ -1 k) in k
17.880 * [taylor]: Taking taylor expansion of -1 in k
17.880 * [backup-simplify]: Simplify -1 into -1
17.880 * [taylor]: Taking taylor expansion of k in k
17.880 * [backup-simplify]: Simplify 0 into 0
17.880 * [backup-simplify]: Simplify 1 into 1
17.880 * [backup-simplify]: Simplify (/ -1 1) into -1
17.880 * [backup-simplify]: Simplify (sqrt 0) into 0
17.882 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
17.882 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
17.883 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
17.884 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
17.887 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
17.889 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
17.891 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
17.892 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
17.892 * [backup-simplify]: Simplify (/ +nan.0 (sqrt +nan.0)) into (/ +nan.0 (sqrt +nan.0))
17.894 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.898 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
17.902 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
17.908 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
17.916 * [backup-simplify]: Simplify (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) into (* 1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
17.925 * [backup-simplify]: Simplify (+ (* (* 1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0))) (pow (/ 1 (- k)) 2)) (+ (* (/ +nan.0 (sqrt +nan.0)) (/ 1 (- k))) (sqrt +nan.0))) into (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))))))))
17.925 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1 1 1)
17.925 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI))
17.925 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
17.925 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
17.925 * [taylor]: Taking taylor expansion of 2 in n
17.925 * [backup-simplify]: Simplify 2 into 2
17.925 * [taylor]: Taking taylor expansion of (* n PI) in n
17.925 * [taylor]: Taking taylor expansion of n in n
17.925 * [backup-simplify]: Simplify 0 into 0
17.925 * [backup-simplify]: Simplify 1 into 1
17.925 * [taylor]: Taking taylor expansion of PI in n
17.925 * [backup-simplify]: Simplify PI into PI
17.925 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
17.925 * [taylor]: Taking taylor expansion of 2 in n
17.925 * [backup-simplify]: Simplify 2 into 2
17.926 * [taylor]: Taking taylor expansion of (* n PI) in n
17.926 * [taylor]: Taking taylor expansion of n in n
17.926 * [backup-simplify]: Simplify 0 into 0
17.926 * [backup-simplify]: Simplify 1 into 1
17.926 * [taylor]: Taking taylor expansion of PI in n
17.926 * [backup-simplify]: Simplify PI into PI
17.926 * [backup-simplify]: Simplify (* 0 PI) into 0
17.927 * [backup-simplify]: Simplify (* 2 0) into 0
17.927 * [backup-simplify]: Simplify 0 into 0
17.928 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
17.930 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
17.930 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.931 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
17.932 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
17.932 * [backup-simplify]: Simplify 0 into 0
17.933 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
17.934 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
17.934 * [backup-simplify]: Simplify 0 into 0
17.936 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
17.937 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
17.937 * [backup-simplify]: Simplify 0 into 0
17.939 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
17.940 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
17.940 * [backup-simplify]: Simplify 0 into 0
17.942 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
17.944 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
17.944 * [backup-simplify]: Simplify 0 into 0
17.946 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
17.948 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
17.948 * [backup-simplify]: Simplify 0 into 0
17.949 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
17.949 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n))
17.949 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
17.949 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
17.949 * [taylor]: Taking taylor expansion of 2 in n
17.949 * [backup-simplify]: Simplify 2 into 2
17.949 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.949 * [taylor]: Taking taylor expansion of PI in n
17.949 * [backup-simplify]: Simplify PI into PI
17.949 * [taylor]: Taking taylor expansion of n in n
17.949 * [backup-simplify]: Simplify 0 into 0
17.949 * [backup-simplify]: Simplify 1 into 1
17.950 * [backup-simplify]: Simplify (/ PI 1) into PI
17.950 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
17.950 * [taylor]: Taking taylor expansion of 2 in n
17.950 * [backup-simplify]: Simplify 2 into 2
17.950 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.950 * [taylor]: Taking taylor expansion of PI in n
17.950 * [backup-simplify]: Simplify PI into PI
17.950 * [taylor]: Taking taylor expansion of n in n
17.950 * [backup-simplify]: Simplify 0 into 0
17.950 * [backup-simplify]: Simplify 1 into 1
17.951 * [backup-simplify]: Simplify (/ PI 1) into PI
17.951 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.952 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
17.953 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.954 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
17.954 * [backup-simplify]: Simplify 0 into 0
17.955 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.956 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
17.956 * [backup-simplify]: Simplify 0 into 0
17.958 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.959 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.959 * [backup-simplify]: Simplify 0 into 0
17.960 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.961 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
17.961 * [backup-simplify]: Simplify 0 into 0
17.963 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.964 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
17.964 * [backup-simplify]: Simplify 0 into 0
17.966 * [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
17.968 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
17.968 * [backup-simplify]: Simplify 0 into 0
17.968 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
17.968 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n))
17.969 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
17.969 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
17.969 * [taylor]: Taking taylor expansion of -2 in n
17.969 * [backup-simplify]: Simplify -2 into -2
17.969 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.969 * [taylor]: Taking taylor expansion of PI in n
17.969 * [backup-simplify]: Simplify PI into PI
17.969 * [taylor]: Taking taylor expansion of n in n
17.969 * [backup-simplify]: Simplify 0 into 0
17.969 * [backup-simplify]: Simplify 1 into 1
17.969 * [backup-simplify]: Simplify (/ PI 1) into PI
17.969 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
17.969 * [taylor]: Taking taylor expansion of -2 in n
17.969 * [backup-simplify]: Simplify -2 into -2
17.969 * [taylor]: Taking taylor expansion of (/ PI n) in n
17.969 * [taylor]: Taking taylor expansion of PI in n
17.969 * [backup-simplify]: Simplify PI into PI
17.969 * [taylor]: Taking taylor expansion of n in n
17.970 * [backup-simplify]: Simplify 0 into 0
17.970 * [backup-simplify]: Simplify 1 into 1
17.970 * [backup-simplify]: Simplify (/ PI 1) into PI
17.971 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.971 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
17.972 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
17.973 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
17.973 * [backup-simplify]: Simplify 0 into 0
17.981 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.982 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
17.982 * [backup-simplify]: Simplify 0 into 0
17.983 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.985 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
17.985 * [backup-simplify]: Simplify 0 into 0
17.985 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.986 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
17.986 * [backup-simplify]: Simplify 0 into 0
17.987 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
17.988 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
17.988 * [backup-simplify]: Simplify 0 into 0
17.988 * [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
17.989 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
17.990 * [backup-simplify]: Simplify 0 into 0
17.990 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
17.990 * * * [progress]: simplifying candidates
17.990 * * * * [progress]: [ 1 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (exp (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.990 * * * * [progress]: [ 2 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (exp (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.990 * * * * [progress]: [ 3 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.990 * * * * [progress]: [ 4 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.990 * * * * [progress]: [ 5 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.990 * * * * [progress]: [ 6 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.990 * * * * [progress]: [ 7 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.990 * * * * [progress]: [ 8 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (/ (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (/ k 2))) (sqrt (sqrt k))))))>
17.990 * * * * [progress]: [ 9 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.990 * * * * [progress]: [ 10 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 11 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 12 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 13 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 14 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 15 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 16 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 17 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 18 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 19 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (exp (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 20 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (log (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 21 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (* (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 22 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (cbrt (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 23 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 24 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (* 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 25 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 26 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (posit16->real (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 27 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (exp (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 28 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (exp (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 29 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 30 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 31 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.991 * * * * [progress]: [ 32 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 33 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 34 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (/ (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 35 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 36 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 37 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 38 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 39 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 40 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 41 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 42 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 43 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 44 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 45 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (exp (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 46 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (log (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 47 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 48 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (cbrt (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 49 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 50 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 51 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 52 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (posit16->real (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 53 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (sqrt (sqrt k)) -1))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 54 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (sqrt k) (- 1/2)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.992 * * * * [progress]: [ 55 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (sqrt (sqrt k)) (- 1)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 56 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow k (- (/ 1/2 2))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 57 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (sqrt k) (- (/ 1 2))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 58 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow k (- (/ (/ 1 2) 2))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 59 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (/ 1 (sqrt (sqrt k))) 1))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 60 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (exp (- (log (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 61 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (exp (- 0 (log (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 62 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (exp (- (log 1) (log (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 63 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (exp (log (/ 1 (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 64 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (log (exp (/ 1 (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 65 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (cbrt (/ (* (* 1 1) 1) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 66 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k))))) (cbrt (/ 1 (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 67 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (cbrt (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 68 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (sqrt (/ 1 (sqrt (sqrt k)))) (sqrt (/ 1 (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 69 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (- 1) (- (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 70 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt 1) (cbrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 71 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (cbrt 1) (sqrt (cbrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 72 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (cbrt 1) (sqrt (sqrt (cbrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 73 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1) (sqrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 74 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt 1))) (/ (cbrt 1) (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 75 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1) (sqrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 76 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (/ (cbrt 1) (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.993 * * * * [progress]: [ 77 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (sqrt k)))) (/ (cbrt 1) (sqrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 78 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 79 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (sqrt 1) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (sqrt 1) (cbrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 80 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (sqrt 1) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ (sqrt 1) (sqrt (cbrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 81 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (sqrt 1) (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ (sqrt 1) (sqrt (sqrt (cbrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 82 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (sqrt 1) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1) (sqrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 83 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (sqrt 1) (sqrt (sqrt 1))) (/ (sqrt 1) (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 84 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (sqrt 1) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1) (sqrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 85 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (sqrt 1) (sqrt 1)) (/ (sqrt 1) (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 86 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (sqrt 1) (sqrt (sqrt (sqrt k)))) (/ (sqrt 1) (sqrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 87 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ (sqrt 1) 1) (/ (sqrt 1) (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 88 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ 1 (cbrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 89 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (/ 1 (sqrt (cbrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 90 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (/ 1 (sqrt (sqrt (cbrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 91 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 92 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ 1 (sqrt (sqrt 1))) (/ 1 (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 93 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 94 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ 1 (sqrt 1)) (/ 1 (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 95 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ 1 (sqrt (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 96 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* (/ 1 1) (/ 1 (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 97 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* 1 (/ 1 (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 98 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (* 1 (/ 1 (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.994 * * * * [progress]: [ 99 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (/ (sqrt (sqrt k)) 1)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 100 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (cbrt (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 101 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (cbrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 102 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (cbrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 103 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 104 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ 1 (sqrt (sqrt 1))) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 105 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 106 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ 1 (sqrt 1)) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 107 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k)))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 108 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (/ 1 1) (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 109 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (sqrt k)) (cbrt 1))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 110 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (sqrt 1) (/ (sqrt (sqrt k)) (sqrt 1))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 111 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (/ (sqrt (sqrt k)) 1)))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 112 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (posit16->real (real->posit16 (/ 1 (sqrt (sqrt k))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 113 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 114 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 115 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 116 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (exp (+ (+ (log n) (log 2)) (log PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 117 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (exp (+ (log (* n 2)) (log PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 118 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (exp (log (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 119 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (log (exp (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 120 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (cbrt (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.995 * * * * [progress]: [ 121 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (cbrt (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 122 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 123 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (cbrt (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 124 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 125 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* 1 (* (* n 2) PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 126 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* (* n 2) (* (cbrt PI) (cbrt PI))) (cbrt PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 127 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 128 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* (* n 2) 1) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 129 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 130 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (posit16->real (real->posit16 (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 131 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 132 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (- (+ (* 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 (sqrt k))))))>
17.996 * * * * [progress]: [ 133 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 134 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 135 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (- (+ (* 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))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 136 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 137 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 138 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow k -1/4))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 139 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (pow (/ 1 k) 1/4))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 140 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2))))))))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 141 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 142 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.996 * * * * [progress]: [ 143 / 143 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))>
17.998 * [simplify]: Simplifying:
  (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (/ k 2))
  (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (/ k 2))
  (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* (* n 2) PI) 1/2)
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (- 1/2)
  (- 1)
  (- (/ 1/2 2))
  (- (/ 1 2))
  (- (/ (/ 1 2) 2))
  (- (log (sqrt (sqrt k))))
  (- 0 (log (sqrt (sqrt k))))
  (- (log 1) (log (sqrt (sqrt k))))
  (log (/ 1 (sqrt (sqrt k))))
  (exp (/ 1 (sqrt (sqrt k))))
  (/ (* (* 1 1) 1) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))
  (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k)))))
  (cbrt (/ 1 (sqrt (sqrt k))))
  (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (/ 1 (sqrt (sqrt k))))
  (sqrt (/ 1 (sqrt (sqrt k))))
  (sqrt (/ 1 (sqrt (sqrt k))))
  (- 1)
  (- (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (cbrt 1) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (cbrt 1) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (cbrt 1) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt 1)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt 1))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1) (cbrt 1)) 1)
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt 1) (cbrt (sqrt (sqrt k))))
  (/ (sqrt 1) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (sqrt 1) (sqrt (cbrt (sqrt k))))
  (/ (sqrt 1) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (sqrt 1) (sqrt (sqrt (cbrt k))))
  (/ (sqrt 1) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1) (sqrt (sqrt 1)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1) (sqrt 1))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1) 1)
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1 (cbrt (sqrt (sqrt k))))
  (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1 (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1 (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt 1)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 1)
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (sqrt (sqrt k)) 1)
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt 1)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 1)
  (/ (sqrt (sqrt k)) (cbrt 1))
  (/ (sqrt (sqrt k)) (sqrt 1))
  (/ (sqrt (sqrt k)) 1)
  (real->posit16 (/ 1 (sqrt (sqrt k))))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (+ (+ (log n) (log 2)) (log PI))
  (+ (log (* n 2)) (log PI))
  (log (* (* n 2) PI))
  (exp (* (* n 2) PI))
  (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI))
  (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI))
  (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI)))
  (cbrt (* (* n 2) PI))
  (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))
  (sqrt (* (* n 2) PI))
  (sqrt (* (* n 2) PI))
  (* (* n 2) (* (cbrt PI) (cbrt PI)))
  (* (* n 2) (sqrt PI))
  (* (* n 2) 1)
  (* 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 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (pow k -1/4)
  (pow (/ 1 k) 1/4)
  (- (sqrt +nan.0) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (+ (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))) (- (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
18.000 * * [simplify]: iteration 0: 232 enodes
18.120 * * [simplify]: iteration 1: 540 enodes
18.364 * * [simplify]: iteration 2: 1700 enodes
18.955 * * [simplify]: iteration complete: 5004 enodes
18.955 * * [simplify]: Extracting #0: cost 58 inf + 0
18.956 * * [simplify]: Extracting #1: cost 551 inf + 4
18.966 * * [simplify]: Extracting #2: cost 1233 inf + 31351
19.010 * * [simplify]: Extracting #3: cost 1314 inf + 126857
19.100 * * [simplify]: Extracting #4: cost 642 inf + 295056
19.208 * * [simplify]: Extracting #5: cost 169 inf + 458876
19.336 * * [simplify]: Extracting #6: cost 17 inf + 509911
19.466 * * [simplify]: Extracting #7: cost 0 inf + 514256
19.609 * * [simplify]: Extracting #8: cost 0 inf + 513996
19.791 * [simplify]: Simplified to:
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* (* n 2) PI))
  (pow (* (* n 2) PI) (/ k 2))
  (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2))))
  (* (* n 2) PI)
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n 2) PI) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* (* n 2) PI)
  (sqrt (* (* n 2) PI))
  (pow (* (* n 2) PI) (- (/ k 2)))
  (sqrt (* (* n 2) PI))
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) (- 1/4 (/ k 4)))
  (pow (* (* n 2) PI) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* (* n 2) PI))
  (pow (* (* n 2) PI) (/ k 2))
  (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2))))
  (* (* n 2) PI)
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n 2) PI) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* (* n 2) PI)
  (sqrt (* (* n 2) PI))
  (pow (* (* n 2) PI) (- (/ k 2)))
  (sqrt (* (* n 2) PI))
  (pow (* (* n 2) PI) (- (/ k 2)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))
  (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (* (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) (- 1/4 (/ k 4)))
  (pow (* (* n 2) PI) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))
  -1/2
  -1
  -1/4
  -1/2
  -1/4
  (- (log (sqrt (sqrt k))))
  (- (log (sqrt (sqrt k))))
  (- (log (sqrt (sqrt k))))
  (- (log (sqrt (sqrt k))))
  (exp (/ 1 (sqrt (sqrt k))))
  (/ (/ 1 (sqrt k)) (sqrt (sqrt k)))
  (* (cbrt (/ 1 (sqrt (sqrt k)))) (cbrt (/ 1 (sqrt (sqrt k)))))
  (cbrt (/ 1 (sqrt (sqrt k))))
  (/ (/ 1 (sqrt k)) (sqrt (sqrt k)))
  (sqrt (/ 1 (sqrt (sqrt k))))
  (sqrt (/ 1 (sqrt (sqrt k))))
  -1
  (- (sqrt (sqrt k)))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1 (cbrt (sqrt (sqrt k))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ 1 (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ 1 (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1 (cbrt (sqrt (sqrt k))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ 1 (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ 1 (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1 (cbrt (sqrt (sqrt k))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ 1 (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ 1 (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (sqrt (sqrt k))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (/ 1 (sqrt (sqrt (sqrt k))))
  1
  (sqrt (sqrt k))
  (sqrt (sqrt k))
  (sqrt (sqrt k))
  (real->posit16 (/ 1 (sqrt (sqrt k))))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (log (* (* n 2) PI))
  (log (* (* n 2) PI))
  (log (* (* n 2) PI))
  (exp (+ (* PI n) (* PI n)))
  (* PI (* (* n (* n n)) (* (* 8 PI) PI)))
  (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 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 PI)) (cbrt PI))
  (* (sqrt PI) (* n 2))
  (* n 2)
  (* 2 PI)
  (real->posit16 (* (* n 2) PI))
  (+ (+ (* (sqrt (* (* n 2) PI)) (+ (* 1/8 (* (* (log n) k) (* (log n) k))) (* (* (log (* 2 PI)) 1/4) (* (* (log n) k) k)))) (* 1/8 (* (sqrt (* (* n 2) PI)) (* (* k (log (* 2 PI))) (* k (log (* 2 PI))))))) (- (sqrt (* (* n 2) PI)) (/ (* (* (sqrt (* (* n 2) PI)) k) (log (* (* n 2) PI))) 2)))
  (exp (* (log (* (* n 2) PI)) (+ 1/2 (* -1/2 k))))
  (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (+ 1/2 (* -1/2 k))))
  (+ (+ (* (sqrt (* (* n 2) PI)) (+ (* 1/8 (* (* (log n) k) (* (log n) k))) (* (* (log (* 2 PI)) 1/4) (* (* (log n) k) k)))) (* 1/8 (* (sqrt (* (* n 2) PI)) (* (* k (log (* 2 PI))) (* k (log (* 2 PI))))))) (- (sqrt (* (* n 2) PI)) (/ (* (* (sqrt (* (* n 2) PI)) k) (log (* (* n 2) PI))) 2)))
  (exp (* (log (* (* n 2) PI)) (+ 1/2 (* -1/2 k))))
  (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (+ 1/2 (* -1/2 k))))
  (pow k -1/4)
  (pow (/ 1 k) 1/4)
  (- (+ (- (sqrt +nan.0) (/ (/ +nan.0 k) (sqrt +nan.0))) (/ (/ +nan.0 (* k k)) (* +nan.0 (sqrt +nan.0)))) (/ (/ +nan.0 (* k k)) (sqrt +nan.0)))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (* (* n 2) PI)
19.826 * * * [progress]: adding candidates to table
20.728 * [progress]: [Phase 3 of 3] Extracting.
20.729 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (/ (/ (sqrt (* (* 2 PI) n)) (pow (* (* 2 PI) n) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))> #<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>)
20.730 * * * [regime-changes]: Trying 4 branch expressions: ((* (* 2 PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) n k)
20.730 * * * * [regimes]: Trying to branch on (* (* 2 PI) n) from (#<alt (λ (k n) (/ (/ (sqrt (* (* 2 PI) n)) (pow (* (* 2 PI) n) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))> #<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>)
20.803 * * * * [regimes]: Trying to branch on (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) from (#<alt (λ (k n) (/ (/ (sqrt (* (* 2 PI) n)) (pow (* (* 2 PI) n) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))> #<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>)
20.914 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (/ (/ (sqrt (* (* 2 PI) n)) (pow (* (* 2 PI) n) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))> #<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>)
20.978 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (/ (/ (sqrt (* (* 2 PI) n)) (pow (* (* 2 PI) n) (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (sqrt k)))))> #<alt (λ (k n) (* (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt k))))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))))))> #<alt (λ (k n) (* (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k))) (/ (pow (* (* 2 PI) n) (* -1/2 k)) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>)
21.055 * * * [regime]: Found split indices: #<option (#s(si 6 255))>
21.055 * [simplify]: Simplifying:
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
21.055 * * [simplify]: iteration 0: 13 enodes
21.057 * * [simplify]: iteration 1: 18 enodes
21.058 * * [simplify]: iteration complete: 18 enodes
21.058 * * [simplify]: Extracting #0: cost 1 inf + 0
21.058 * * [simplify]: Extracting #1: cost 3 inf + 0
21.058 * * [simplify]: Extracting #2: cost 7 inf + 0
21.058 * * [simplify]: Extracting #3: cost 11 inf + 1
21.058 * * [simplify]: Extracting #4: cost 5 inf + 252
21.058 * * [simplify]: Extracting #5: cost 4 inf + 253
21.058 * * [simplify]: Extracting #6: cost 1 inf + 753
21.058 * * [simplify]: Extracting #7: cost 0 inf + 1248
21.058 * [simplify]: Simplified to:
  (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
29.866 * [regime-testing]: Baseline error score: 0.3901292900075434
29.869 * [regime-testing]: Oracle error score: 0.09343127695810291
29.873 * [regime-testing]: End program error score: 0.3901292900075434