58.474 * [progress]: [Phase 1 of 3] Setting up.
0.001 * * * [progress]: [1/2] Preparing points
0.220 * * * [progress]: [2/2] Setting up program.
0.226 * [progress]: [Phase 2 of 3] Improving.
0.226 * * * * [progress]: [ 1 / 1 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
0.226 * [simplify]: Simplifying:
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.226 * * [simplify]: iteration 0: 13 enodes
0.232 * * [simplify]: iteration 1: 31 enodes
0.244 * * [simplify]: iteration 2: 62 enodes
0.267 * * [simplify]: iteration 3: 124 enodes
0.325 * * [simplify]: iteration 4: 327 enodes
0.551 * * [simplify]: iteration 5: 929 enodes
0.844 * * [simplify]: iteration 6: 2011 enodes
1.252 * * [simplify]: iteration complete: 2011 enodes
1.252 * * [simplify]: Extracting #0: cost 1 inf + 0
1.253 * * [simplify]: Extracting #1: cost 89 inf + 0
1.253 * * [simplify]: Extracting #2: cost 322 inf + 1
1.255 * * [simplify]: Extracting #3: cost 468 inf + 46
1.257 * * [simplify]: Extracting #4: cost 453 inf + 3452
1.264 * * [simplify]: Extracting #5: cost 339 inf + 22215
1.303 * * [simplify]: Extracting #6: cost 152 inf + 141923
1.358 * * [simplify]: Extracting #7: cost 5 inf + 283438
1.431 * * [simplify]: Extracting #8: cost 0 inf + 285235
1.514 * * [simplify]: Extracting #9: cost 0 inf + 284972
1.593 * * [simplify]: Extracting #10: cost 0 inf + 284459
1.637 * [simplify]: Simplified to:
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
1.641 * * [progress]: iteration 1 / 4
1.641 * * * [progress]: picking best candidate
1.646 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))>
1.647 * * * [progress]: localizing error
1.676 * * * [progress]: generating rewritten candidates
1.676 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
1.712 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1)
1.740 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
1.760 * * * [progress]: generating series expansions
1.760 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
1.760 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
1.760 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
1.760 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
1.760 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
1.761 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
1.761 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
1.761 * [taylor]: Taking taylor expansion of 1/2 in k
1.761 * [backup-simplify]: Simplify 1/2 into 1/2
1.761 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
1.761 * [taylor]: Taking taylor expansion of 1/2 in k
1.761 * [backup-simplify]: Simplify 1/2 into 1/2
1.761 * [taylor]: Taking taylor expansion of k in k
1.761 * [backup-simplify]: Simplify 0 into 0
1.761 * [backup-simplify]: Simplify 1 into 1
1.761 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
1.761 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
1.761 * [taylor]: Taking taylor expansion of 2 in k
1.761 * [backup-simplify]: Simplify 2 into 2
1.761 * [taylor]: Taking taylor expansion of (* n PI) in k
1.761 * [taylor]: Taking taylor expansion of n in k
1.761 * [backup-simplify]: Simplify n into n
1.761 * [taylor]: Taking taylor expansion of PI in k
1.761 * [backup-simplify]: Simplify PI into PI
1.761 * [backup-simplify]: Simplify (* n PI) into (* n PI)
1.761 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
1.761 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
1.761 * [backup-simplify]: Simplify (* 1/2 0) into 0
1.762 * [backup-simplify]: Simplify (- 0) into 0
1.762 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
1.762 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
1.762 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
1.762 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
1.762 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
1.762 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
1.762 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
1.762 * [taylor]: Taking taylor expansion of 1/2 in n
1.762 * [backup-simplify]: Simplify 1/2 into 1/2
1.762 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
1.762 * [taylor]: Taking taylor expansion of 1/2 in n
1.762 * [backup-simplify]: Simplify 1/2 into 1/2
1.762 * [taylor]: Taking taylor expansion of k in n
1.762 * [backup-simplify]: Simplify k into k
1.762 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.762 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.762 * [taylor]: Taking taylor expansion of 2 in n
1.762 * [backup-simplify]: Simplify 2 into 2
1.762 * [taylor]: Taking taylor expansion of (* n PI) in n
1.762 * [taylor]: Taking taylor expansion of n in n
1.762 * [backup-simplify]: Simplify 0 into 0
1.762 * [backup-simplify]: Simplify 1 into 1
1.763 * [taylor]: Taking taylor expansion of PI in n
1.763 * [backup-simplify]: Simplify PI into PI
1.763 * [backup-simplify]: Simplify (* 0 PI) into 0
1.763 * [backup-simplify]: Simplify (* 2 0) into 0
1.764 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.765 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.766 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.766 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
1.766 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
1.766 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
1.767 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.768 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
1.769 * [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)))))
1.769 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
1.769 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
1.769 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
1.769 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
1.769 * [taylor]: Taking taylor expansion of 1/2 in n
1.769 * [backup-simplify]: Simplify 1/2 into 1/2
1.769 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
1.769 * [taylor]: Taking taylor expansion of 1/2 in n
1.769 * [backup-simplify]: Simplify 1/2 into 1/2
1.769 * [taylor]: Taking taylor expansion of k in n
1.769 * [backup-simplify]: Simplify k into k
1.769 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.769 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.769 * [taylor]: Taking taylor expansion of 2 in n
1.769 * [backup-simplify]: Simplify 2 into 2
1.769 * [taylor]: Taking taylor expansion of (* n PI) in n
1.769 * [taylor]: Taking taylor expansion of n in n
1.769 * [backup-simplify]: Simplify 0 into 0
1.769 * [backup-simplify]: Simplify 1 into 1
1.769 * [taylor]: Taking taylor expansion of PI in n
1.769 * [backup-simplify]: Simplify PI into PI
1.769 * [backup-simplify]: Simplify (* 0 PI) into 0
1.770 * [backup-simplify]: Simplify (* 2 0) into 0
1.771 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.772 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.772 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.772 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
1.772 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
1.772 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
1.773 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.774 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
1.775 * [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)))))
1.775 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
1.775 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
1.775 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
1.775 * [taylor]: Taking taylor expansion of 1/2 in k
1.775 * [backup-simplify]: Simplify 1/2 into 1/2
1.775 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
1.775 * [taylor]: Taking taylor expansion of 1/2 in k
1.775 * [backup-simplify]: Simplify 1/2 into 1/2
1.775 * [taylor]: Taking taylor expansion of k in k
1.775 * [backup-simplify]: Simplify 0 into 0
1.775 * [backup-simplify]: Simplify 1 into 1
1.775 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
1.775 * [taylor]: Taking taylor expansion of (log n) in k
1.775 * [taylor]: Taking taylor expansion of n in k
1.775 * [backup-simplify]: Simplify n into n
1.775 * [backup-simplify]: Simplify (log n) into (log n)
1.775 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.775 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.775 * [taylor]: Taking taylor expansion of 2 in k
1.775 * [backup-simplify]: Simplify 2 into 2
1.775 * [taylor]: Taking taylor expansion of PI in k
1.775 * [backup-simplify]: Simplify PI into PI
1.775 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.776 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.776 * [backup-simplify]: Simplify (* 1/2 0) into 0
1.777 * [backup-simplify]: Simplify (- 0) into 0
1.777 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
1.778 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.778 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
1.779 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.780 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.780 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
1.781 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
1.782 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.783 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
1.783 * [backup-simplify]: Simplify (- 0) into 0
1.783 * [backup-simplify]: Simplify (+ 0 0) into 0
1.785 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.786 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
1.788 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.788 * [taylor]: Taking taylor expansion of 0 in k
1.788 * [backup-simplify]: Simplify 0 into 0
1.788 * [backup-simplify]: Simplify 0 into 0
1.789 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
1.790 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.791 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.792 * [backup-simplify]: Simplify (+ 0 0) into 0
1.793 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
1.793 * [backup-simplify]: Simplify (- 1/2) into -1/2
1.793 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
1.795 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
1.798 * [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)))))))
1.801 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
1.803 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
1.804 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
1.807 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
1.808 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
1.809 * [backup-simplify]: Simplify (- 0) into 0
1.809 * [backup-simplify]: Simplify (+ 0 0) into 0
1.811 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.812 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.814 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.815 * [taylor]: Taking taylor expansion of 0 in k
1.815 * [backup-simplify]: Simplify 0 into 0
1.815 * [backup-simplify]: Simplify 0 into 0
1.815 * [backup-simplify]: Simplify 0 into 0
1.816 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
1.817 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.824 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
1.825 * [backup-simplify]: Simplify (+ 0 0) into 0
1.826 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
1.826 * [backup-simplify]: Simplify (- 0) into 0
1.826 * [backup-simplify]: Simplify (+ 0 0) into 0
1.828 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.833 * [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)))))
1.838 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
1.850 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
1.851 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
1.851 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
1.851 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
1.851 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
1.851 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
1.851 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
1.851 * [taylor]: Taking taylor expansion of 1/2 in k
1.851 * [backup-simplify]: Simplify 1/2 into 1/2
1.851 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
1.851 * [taylor]: Taking taylor expansion of 1/2 in k
1.851 * [backup-simplify]: Simplify 1/2 into 1/2
1.851 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.851 * [taylor]: Taking taylor expansion of k in k
1.851 * [backup-simplify]: Simplify 0 into 0
1.851 * [backup-simplify]: Simplify 1 into 1
1.852 * [backup-simplify]: Simplify (/ 1 1) into 1
1.852 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
1.852 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
1.852 * [taylor]: Taking taylor expansion of 2 in k
1.852 * [backup-simplify]: Simplify 2 into 2
1.852 * [taylor]: Taking taylor expansion of (/ PI n) in k
1.852 * [taylor]: Taking taylor expansion of PI in k
1.852 * [backup-simplify]: Simplify PI into PI
1.852 * [taylor]: Taking taylor expansion of n in k
1.852 * [backup-simplify]: Simplify n into n
1.853 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
1.853 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
1.853 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
1.854 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.854 * [backup-simplify]: Simplify (- 1/2) into -1/2
1.855 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
1.855 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
1.855 * [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))))
1.855 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
1.855 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
1.855 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
1.855 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
1.855 * [taylor]: Taking taylor expansion of 1/2 in n
1.855 * [backup-simplify]: Simplify 1/2 into 1/2
1.855 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
1.855 * [taylor]: Taking taylor expansion of 1/2 in n
1.855 * [backup-simplify]: Simplify 1/2 into 1/2
1.855 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.855 * [taylor]: Taking taylor expansion of k in n
1.855 * [backup-simplify]: Simplify k into k
1.855 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.855 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
1.855 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.856 * [taylor]: Taking taylor expansion of 2 in n
1.856 * [backup-simplify]: Simplify 2 into 2
1.856 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.856 * [taylor]: Taking taylor expansion of PI in n
1.856 * [backup-simplify]: Simplify PI into PI
1.856 * [taylor]: Taking taylor expansion of n in n
1.856 * [backup-simplify]: Simplify 0 into 0
1.856 * [backup-simplify]: Simplify 1 into 1
1.856 * [backup-simplify]: Simplify (/ PI 1) into PI
1.857 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.858 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.858 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
1.858 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
1.858 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
1.859 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.860 * [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)))
1.861 * [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))))
1.862 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
1.862 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
1.862 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
1.862 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
1.862 * [taylor]: Taking taylor expansion of 1/2 in n
1.862 * [backup-simplify]: Simplify 1/2 into 1/2
1.862 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
1.862 * [taylor]: Taking taylor expansion of 1/2 in n
1.862 * [backup-simplify]: Simplify 1/2 into 1/2
1.862 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.862 * [taylor]: Taking taylor expansion of k in n
1.862 * [backup-simplify]: Simplify k into k
1.862 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.862 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
1.862 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.862 * [taylor]: Taking taylor expansion of 2 in n
1.862 * [backup-simplify]: Simplify 2 into 2
1.862 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.862 * [taylor]: Taking taylor expansion of PI in n
1.862 * [backup-simplify]: Simplify PI into PI
1.862 * [taylor]: Taking taylor expansion of n in n
1.862 * [backup-simplify]: Simplify 0 into 0
1.862 * [backup-simplify]: Simplify 1 into 1
1.863 * [backup-simplify]: Simplify (/ PI 1) into PI
1.863 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.864 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.864 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
1.864 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
1.865 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
1.866 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.867 * [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)))
1.869 * [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))))
1.869 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
1.869 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
1.869 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
1.869 * [taylor]: Taking taylor expansion of 1/2 in k
1.869 * [backup-simplify]: Simplify 1/2 into 1/2
1.869 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
1.869 * [taylor]: Taking taylor expansion of 1/2 in k
1.869 * [backup-simplify]: Simplify 1/2 into 1/2
1.869 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.869 * [taylor]: Taking taylor expansion of k in k
1.869 * [backup-simplify]: Simplify 0 into 0
1.869 * [backup-simplify]: Simplify 1 into 1
1.869 * [backup-simplify]: Simplify (/ 1 1) into 1
1.869 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
1.869 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.869 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.869 * [taylor]: Taking taylor expansion of 2 in k
1.869 * [backup-simplify]: Simplify 2 into 2
1.869 * [taylor]: Taking taylor expansion of PI in k
1.870 * [backup-simplify]: Simplify PI into PI
1.870 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.871 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.871 * [taylor]: Taking taylor expansion of (log n) in k
1.871 * [taylor]: Taking taylor expansion of n in k
1.871 * [backup-simplify]: Simplify n into n
1.871 * [backup-simplify]: Simplify (log n) into (log n)
1.872 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.872 * [backup-simplify]: Simplify (- 1/2) into -1/2
1.872 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
1.872 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
1.874 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
1.875 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
1.876 * [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))))
1.877 * [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))))
1.878 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.879 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.881 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.881 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.882 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
1.882 * [backup-simplify]: Simplify (- 0) into 0
1.882 * [backup-simplify]: Simplify (+ 0 0) into 0
1.884 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.885 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
1.887 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
1.887 * [taylor]: Taking taylor expansion of 0 in k
1.887 * [backup-simplify]: Simplify 0 into 0
1.887 * [backup-simplify]: Simplify 0 into 0
1.887 * [backup-simplify]: Simplify 0 into 0
1.888 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.889 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.893 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
1.893 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.894 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
1.894 * [backup-simplify]: Simplify (- 0) into 0
1.895 * [backup-simplify]: Simplify (+ 0 0) into 0
1.896 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.898 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
1.900 * [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
1.900 * [taylor]: Taking taylor expansion of 0 in k
1.900 * [backup-simplify]: Simplify 0 into 0
1.900 * [backup-simplify]: Simplify 0 into 0
1.900 * [backup-simplify]: Simplify 0 into 0
1.900 * [backup-simplify]: Simplify 0 into 0
1.902 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.903 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.909 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
1.909 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.911 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
1.911 * [backup-simplify]: Simplify (- 0) into 0
1.912 * [backup-simplify]: Simplify (+ 0 0) into 0
1.913 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.915 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
1.918 * [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
1.918 * [taylor]: Taking taylor expansion of 0 in k
1.918 * [backup-simplify]: Simplify 0 into 0
1.918 * [backup-simplify]: Simplify 0 into 0
1.919 * [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)))))
1.920 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
1.920 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
1.920 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
1.920 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
1.920 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
1.920 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
1.920 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
1.920 * [taylor]: Taking taylor expansion of 1/2 in k
1.920 * [backup-simplify]: Simplify 1/2 into 1/2
1.920 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.920 * [taylor]: Taking taylor expansion of k in k
1.920 * [backup-simplify]: Simplify 0 into 0
1.920 * [backup-simplify]: Simplify 1 into 1
1.920 * [backup-simplify]: Simplify (/ 1 1) into 1
1.920 * [taylor]: Taking taylor expansion of 1/2 in k
1.920 * [backup-simplify]: Simplify 1/2 into 1/2
1.920 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
1.920 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
1.921 * [taylor]: Taking taylor expansion of -2 in k
1.921 * [backup-simplify]: Simplify -2 into -2
1.921 * [taylor]: Taking taylor expansion of (/ PI n) in k
1.921 * [taylor]: Taking taylor expansion of PI in k
1.921 * [backup-simplify]: Simplify PI into PI
1.921 * [taylor]: Taking taylor expansion of n in k
1.921 * [backup-simplify]: Simplify n into n
1.921 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
1.921 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
1.921 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
1.921 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.922 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
1.922 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
1.922 * [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)))
1.922 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
1.922 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
1.922 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
1.922 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
1.922 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
1.922 * [taylor]: Taking taylor expansion of 1/2 in n
1.922 * [backup-simplify]: Simplify 1/2 into 1/2
1.922 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.923 * [taylor]: Taking taylor expansion of k in n
1.923 * [backup-simplify]: Simplify k into k
1.923 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.923 * [taylor]: Taking taylor expansion of 1/2 in n
1.923 * [backup-simplify]: Simplify 1/2 into 1/2
1.923 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
1.923 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.923 * [taylor]: Taking taylor expansion of -2 in n
1.923 * [backup-simplify]: Simplify -2 into -2
1.923 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.923 * [taylor]: Taking taylor expansion of PI in n
1.923 * [backup-simplify]: Simplify PI into PI
1.923 * [taylor]: Taking taylor expansion of n in n
1.923 * [backup-simplify]: Simplify 0 into 0
1.923 * [backup-simplify]: Simplify 1 into 1
1.924 * [backup-simplify]: Simplify (/ PI 1) into PI
1.924 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.925 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.925 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
1.925 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
1.927 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.927 * [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)))
1.928 * [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))))
1.928 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
1.928 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
1.928 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
1.928 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
1.928 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
1.928 * [taylor]: Taking taylor expansion of 1/2 in n
1.928 * [backup-simplify]: Simplify 1/2 into 1/2
1.928 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.928 * [taylor]: Taking taylor expansion of k in n
1.928 * [backup-simplify]: Simplify k into k
1.928 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.928 * [taylor]: Taking taylor expansion of 1/2 in n
1.928 * [backup-simplify]: Simplify 1/2 into 1/2
1.928 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
1.928 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.928 * [taylor]: Taking taylor expansion of -2 in n
1.928 * [backup-simplify]: Simplify -2 into -2
1.928 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.928 * [taylor]: Taking taylor expansion of PI in n
1.928 * [backup-simplify]: Simplify PI into PI
1.928 * [taylor]: Taking taylor expansion of n in n
1.928 * [backup-simplify]: Simplify 0 into 0
1.928 * [backup-simplify]: Simplify 1 into 1
1.929 * [backup-simplify]: Simplify (/ PI 1) into PI
1.929 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.930 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.930 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
1.930 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
1.931 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.931 * [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)))
1.932 * [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))))
1.932 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
1.932 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
1.932 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
1.932 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
1.932 * [taylor]: Taking taylor expansion of 1/2 in k
1.932 * [backup-simplify]: Simplify 1/2 into 1/2
1.932 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.932 * [taylor]: Taking taylor expansion of k in k
1.932 * [backup-simplify]: Simplify 0 into 0
1.932 * [backup-simplify]: Simplify 1 into 1
1.933 * [backup-simplify]: Simplify (/ 1 1) into 1
1.933 * [taylor]: Taking taylor expansion of 1/2 in k
1.933 * [backup-simplify]: Simplify 1/2 into 1/2
1.933 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
1.933 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
1.933 * [taylor]: Taking taylor expansion of (* -2 PI) in k
1.933 * [taylor]: Taking taylor expansion of -2 in k
1.933 * [backup-simplify]: Simplify -2 into -2
1.933 * [taylor]: Taking taylor expansion of PI in k
1.933 * [backup-simplify]: Simplify PI into PI
1.933 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.934 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.934 * [taylor]: Taking taylor expansion of (log n) in k
1.934 * [taylor]: Taking taylor expansion of n in k
1.934 * [backup-simplify]: Simplify n into n
1.934 * [backup-simplify]: Simplify (log n) into (log n)
1.934 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.934 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
1.934 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
1.935 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
1.936 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
1.936 * [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))))
1.937 * [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))))
1.938 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.938 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
1.939 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
1.939 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.940 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
1.940 * [backup-simplify]: Simplify (+ 0 0) into 0
1.941 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.941 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
1.943 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
1.943 * [taylor]: Taking taylor expansion of 0 in k
1.943 * [backup-simplify]: Simplify 0 into 0
1.943 * [backup-simplify]: Simplify 0 into 0
1.943 * [backup-simplify]: Simplify 0 into 0
1.943 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.944 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
1.946 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
1.946 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.946 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
1.947 * [backup-simplify]: Simplify (+ 0 0) into 0
1.948 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.949 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
1.950 * [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
1.950 * [taylor]: Taking taylor expansion of 0 in k
1.950 * [backup-simplify]: Simplify 0 into 0
1.950 * [backup-simplify]: Simplify 0 into 0
1.950 * [backup-simplify]: Simplify 0 into 0
1.950 * [backup-simplify]: Simplify 0 into 0
1.951 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.952 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.957 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
1.957 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.958 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
1.958 * [backup-simplify]: Simplify (+ 0 0) into 0
1.959 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.961 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
1.964 * [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
1.964 * [taylor]: Taking taylor expansion of 0 in k
1.964 * [backup-simplify]: Simplify 0 into 0
1.964 * [backup-simplify]: Simplify 0 into 0
1.965 * [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)))))
1.965 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1)
1.965 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI))
1.965 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
1.965 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.966 * [taylor]: Taking taylor expansion of 2 in n
1.966 * [backup-simplify]: Simplify 2 into 2
1.966 * [taylor]: Taking taylor expansion of (* n PI) in n
1.966 * [taylor]: Taking taylor expansion of n in n
1.966 * [backup-simplify]: Simplify 0 into 0
1.966 * [backup-simplify]: Simplify 1 into 1
1.966 * [taylor]: Taking taylor expansion of PI in n
1.966 * [backup-simplify]: Simplify PI into PI
1.966 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.966 * [taylor]: Taking taylor expansion of 2 in n
1.966 * [backup-simplify]: Simplify 2 into 2
1.966 * [taylor]: Taking taylor expansion of (* n PI) in n
1.966 * [taylor]: Taking taylor expansion of n in n
1.966 * [backup-simplify]: Simplify 0 into 0
1.966 * [backup-simplify]: Simplify 1 into 1
1.966 * [taylor]: Taking taylor expansion of PI in n
1.966 * [backup-simplify]: Simplify PI into PI
1.966 * [backup-simplify]: Simplify (* 0 PI) into 0
1.967 * [backup-simplify]: Simplify (* 2 0) into 0
1.967 * [backup-simplify]: Simplify 0 into 0
1.969 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.970 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.971 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.972 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
1.973 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
1.973 * [backup-simplify]: Simplify 0 into 0
1.974 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
1.975 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
1.975 * [backup-simplify]: Simplify 0 into 0
1.977 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
1.979 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
1.979 * [backup-simplify]: Simplify 0 into 0
1.980 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
1.982 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
1.982 * [backup-simplify]: Simplify 0 into 0
1.984 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
1.985 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
1.985 * [backup-simplify]: Simplify 0 into 0
1.987 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
1.989 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
1.989 * [backup-simplify]: Simplify 0 into 0
1.990 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
1.990 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n))
1.990 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
1.990 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.990 * [taylor]: Taking taylor expansion of 2 in n
1.990 * [backup-simplify]: Simplify 2 into 2
1.990 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.990 * [taylor]: Taking taylor expansion of PI in n
1.990 * [backup-simplify]: Simplify PI into PI
1.990 * [taylor]: Taking taylor expansion of n in n
1.990 * [backup-simplify]: Simplify 0 into 0
1.990 * [backup-simplify]: Simplify 1 into 1
1.991 * [backup-simplify]: Simplify (/ PI 1) into PI
1.991 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.991 * [taylor]: Taking taylor expansion of 2 in n
1.991 * [backup-simplify]: Simplify 2 into 2
1.991 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.991 * [taylor]: Taking taylor expansion of PI in n
1.991 * [backup-simplify]: Simplify PI into PI
1.991 * [taylor]: Taking taylor expansion of n in n
1.991 * [backup-simplify]: Simplify 0 into 0
1.991 * [backup-simplify]: Simplify 1 into 1
1.992 * [backup-simplify]: Simplify (/ PI 1) into PI
1.992 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.993 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.994 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.994 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.994 * [backup-simplify]: Simplify 0 into 0
1.995 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.996 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.997 * [backup-simplify]: Simplify 0 into 0
1.998 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.999 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.999 * [backup-simplify]: Simplify 0 into 0
2.000 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.001 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.001 * [backup-simplify]: Simplify 0 into 0
2.002 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.004 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.004 * [backup-simplify]: Simplify 0 into 0
2.005 * [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
2.007 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.007 * [backup-simplify]: Simplify 0 into 0
2.008 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
2.008 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n))
2.008 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
2.008 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.008 * [taylor]: Taking taylor expansion of -2 in n
2.008 * [backup-simplify]: Simplify -2 into -2
2.008 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.008 * [taylor]: Taking taylor expansion of PI in n
2.008 * [backup-simplify]: Simplify PI into PI
2.008 * [taylor]: Taking taylor expansion of n in n
2.008 * [backup-simplify]: Simplify 0 into 0
2.008 * [backup-simplify]: Simplify 1 into 1
2.009 * [backup-simplify]: Simplify (/ PI 1) into PI
2.009 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.009 * [taylor]: Taking taylor expansion of -2 in n
2.009 * [backup-simplify]: Simplify -2 into -2
2.009 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.009 * [taylor]: Taking taylor expansion of PI in n
2.009 * [backup-simplify]: Simplify PI into PI
2.009 * [taylor]: Taking taylor expansion of n in n
2.009 * [backup-simplify]: Simplify 0 into 0
2.009 * [backup-simplify]: Simplify 1 into 1
2.009 * [backup-simplify]: Simplify (/ PI 1) into PI
2.010 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.010 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.011 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.012 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.012 * [backup-simplify]: Simplify 0 into 0
2.013 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.014 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.014 * [backup-simplify]: Simplify 0 into 0
2.015 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.017 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.017 * [backup-simplify]: Simplify 0 into 0
2.018 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.019 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.019 * [backup-simplify]: Simplify 0 into 0
2.021 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.022 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.022 * [backup-simplify]: Simplify 0 into 0
2.023 * [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
2.025 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.025 * [backup-simplify]: Simplify 0 into 0
2.026 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
2.026 * * * * [progress]: [ 3 / 3 ] generating series at (2)
2.026 * [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))))
2.026 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0
2.026 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
2.026 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
2.026 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.026 * [taylor]: Taking taylor expansion of k in k
2.026 * [backup-simplify]: Simplify 0 into 0
2.026 * [backup-simplify]: Simplify 1 into 1
2.027 * [backup-simplify]: Simplify (/ 1 1) into 1
2.027 * [backup-simplify]: Simplify (sqrt 0) into 0
2.028 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.028 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
2.028 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
2.028 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
2.028 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
2.029 * [taylor]: Taking taylor expansion of 1/2 in k
2.029 * [backup-simplify]: Simplify 1/2 into 1/2
2.029 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
2.029 * [taylor]: Taking taylor expansion of 1/2 in k
2.029 * [backup-simplify]: Simplify 1/2 into 1/2
2.029 * [taylor]: Taking taylor expansion of k in k
2.029 * [backup-simplify]: Simplify 0 into 0
2.029 * [backup-simplify]: Simplify 1 into 1
2.029 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
2.029 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
2.029 * [taylor]: Taking taylor expansion of 2 in k
2.029 * [backup-simplify]: Simplify 2 into 2
2.029 * [taylor]: Taking taylor expansion of (* n PI) in k
2.029 * [taylor]: Taking taylor expansion of n in k
2.029 * [backup-simplify]: Simplify n into n
2.029 * [taylor]: Taking taylor expansion of PI in k
2.029 * [backup-simplify]: Simplify PI into PI
2.029 * [backup-simplify]: Simplify (* n PI) into (* n PI)
2.029 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
2.029 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
2.030 * [backup-simplify]: Simplify (* 1/2 0) into 0
2.030 * [backup-simplify]: Simplify (- 0) into 0
2.030 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.031 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
2.031 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
2.031 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
2.031 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
2.031 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.031 * [taylor]: Taking taylor expansion of k in n
2.031 * [backup-simplify]: Simplify k into k
2.031 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.031 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
2.031 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.031 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
2.031 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
2.031 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
2.031 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
2.031 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
2.031 * [taylor]: Taking taylor expansion of 1/2 in n
2.031 * [backup-simplify]: Simplify 1/2 into 1/2
2.031 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
2.031 * [taylor]: Taking taylor expansion of 1/2 in n
2.031 * [backup-simplify]: Simplify 1/2 into 1/2
2.031 * [taylor]: Taking taylor expansion of k in n
2.031 * [backup-simplify]: Simplify k into k
2.032 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
2.032 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.032 * [taylor]: Taking taylor expansion of 2 in n
2.032 * [backup-simplify]: Simplify 2 into 2
2.032 * [taylor]: Taking taylor expansion of (* n PI) in n
2.032 * [taylor]: Taking taylor expansion of n in n
2.032 * [backup-simplify]: Simplify 0 into 0
2.032 * [backup-simplify]: Simplify 1 into 1
2.032 * [taylor]: Taking taylor expansion of PI in n
2.032 * [backup-simplify]: Simplify PI into PI
2.032 * [backup-simplify]: Simplify (* 0 PI) into 0
2.033 * [backup-simplify]: Simplify (* 2 0) into 0
2.034 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.036 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.037 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.037 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
2.037 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
2.037 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
2.038 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.040 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
2.041 * [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)))))
2.041 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
2.041 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
2.041 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.041 * [taylor]: Taking taylor expansion of k in n
2.041 * [backup-simplify]: Simplify k into k
2.041 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.041 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
2.041 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.041 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
2.041 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
2.041 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
2.041 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
2.041 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
2.041 * [taylor]: Taking taylor expansion of 1/2 in n
2.041 * [backup-simplify]: Simplify 1/2 into 1/2
2.041 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
2.042 * [taylor]: Taking taylor expansion of 1/2 in n
2.042 * [backup-simplify]: Simplify 1/2 into 1/2
2.042 * [taylor]: Taking taylor expansion of k in n
2.042 * [backup-simplify]: Simplify k into k
2.042 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
2.042 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.042 * [taylor]: Taking taylor expansion of 2 in n
2.042 * [backup-simplify]: Simplify 2 into 2
2.042 * [taylor]: Taking taylor expansion of (* n PI) in n
2.042 * [taylor]: Taking taylor expansion of n in n
2.042 * [backup-simplify]: Simplify 0 into 0
2.042 * [backup-simplify]: Simplify 1 into 1
2.042 * [taylor]: Taking taylor expansion of PI in n
2.042 * [backup-simplify]: Simplify PI into PI
2.042 * [backup-simplify]: Simplify (* 0 PI) into 0
2.043 * [backup-simplify]: Simplify (* 2 0) into 0
2.044 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.046 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.047 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.047 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
2.047 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
2.047 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
2.048 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.050 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
2.051 * [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)))))
2.052 * [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)))
2.052 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k
2.052 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
2.052 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
2.052 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
2.052 * [taylor]: Taking taylor expansion of 1/2 in k
2.052 * [backup-simplify]: Simplify 1/2 into 1/2
2.052 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
2.052 * [taylor]: Taking taylor expansion of 1/2 in k
2.052 * [backup-simplify]: Simplify 1/2 into 1/2
2.052 * [taylor]: Taking taylor expansion of k in k
2.052 * [backup-simplify]: Simplify 0 into 0
2.053 * [backup-simplify]: Simplify 1 into 1
2.053 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
2.053 * [taylor]: Taking taylor expansion of (log n) in k
2.053 * [taylor]: Taking taylor expansion of n in k
2.053 * [backup-simplify]: Simplify n into n
2.053 * [backup-simplify]: Simplify (log n) into (log n)
2.053 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.053 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.053 * [taylor]: Taking taylor expansion of 2 in k
2.053 * [backup-simplify]: Simplify 2 into 2
2.053 * [taylor]: Taking taylor expansion of PI in k
2.053 * [backup-simplify]: Simplify PI into PI
2.053 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.054 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.055 * [backup-simplify]: Simplify (* 1/2 0) into 0
2.055 * [backup-simplify]: Simplify (- 0) into 0
2.055 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.057 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.058 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
2.059 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
2.059 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
2.059 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.059 * [taylor]: Taking taylor expansion of k in k
2.059 * [backup-simplify]: Simplify 0 into 0
2.059 * [backup-simplify]: Simplify 1 into 1
2.060 * [backup-simplify]: Simplify (/ 1 1) into 1
2.060 * [backup-simplify]: Simplify (sqrt 0) into 0
2.061 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.063 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
2.063 * [backup-simplify]: Simplify 0 into 0
2.064 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
2.065 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
2.067 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.067 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
2.068 * [backup-simplify]: Simplify (- 0) into 0
2.068 * [backup-simplify]: Simplify (+ 0 0) into 0
2.070 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.071 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
2.073 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.075 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0
2.075 * [taylor]: Taking taylor expansion of 0 in k
2.075 * [backup-simplify]: Simplify 0 into 0
2.076 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
2.077 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.079 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.079 * [backup-simplify]: Simplify (+ 0 0) into 0
2.080 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
2.080 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.081 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.082 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
2.085 * [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)))))))
2.091 * [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)))))))
2.092 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.093 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
2.094 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
2.096 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
2.097 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
2.097 * [backup-simplify]: Simplify (- 0) into 0
2.097 * [backup-simplify]: Simplify (+ 0 0) into 0
2.098 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.099 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.102 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.103 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.103 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
2.104 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0
2.104 * [taylor]: Taking taylor expansion of 0 in k
2.104 * [backup-simplify]: Simplify 0 into 0
2.104 * [backup-simplify]: Simplify 0 into 0
2.105 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
2.107 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.107 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
2.108 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.110 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
2.110 * [backup-simplify]: Simplify (+ 0 0) into 0
2.111 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
2.111 * [backup-simplify]: Simplify (- 0) into 0
2.111 * [backup-simplify]: Simplify (+ 0 0) into 0
2.112 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.115 * [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)))))
2.120 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
2.124 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
2.126 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.127 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
2.133 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
2.134 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
2.134 * [backup-simplify]: Simplify (- 0) into 0
2.135 * [backup-simplify]: Simplify (+ 0 0) into 0
2.136 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.138 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.141 * [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
2.141 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.142 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
2.144 * [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
2.144 * [taylor]: Taking taylor expansion of 0 in k
2.144 * [backup-simplify]: Simplify 0 into 0
2.144 * [backup-simplify]: Simplify 0 into 0
2.144 * [backup-simplify]: Simplify 0 into 0
2.145 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.149 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.151 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
2.153 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.159 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
2.160 * [backup-simplify]: Simplify (+ 0 0) into 0
2.161 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
2.161 * [backup-simplify]: Simplify (- 0) into 0
2.162 * [backup-simplify]: Simplify (+ 0 0) into 0
2.164 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.171 * [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)))))))
2.184 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
2.191 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
2.202 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
2.202 * [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)))))
2.202 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
2.202 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
2.202 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.202 * [taylor]: Taking taylor expansion of k in k
2.202 * [backup-simplify]: Simplify 0 into 0
2.202 * [backup-simplify]: Simplify 1 into 1
2.203 * [backup-simplify]: Simplify (sqrt 0) into 0
2.204 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.204 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
2.204 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
2.204 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
2.204 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
2.204 * [taylor]: Taking taylor expansion of 1/2 in k
2.204 * [backup-simplify]: Simplify 1/2 into 1/2
2.204 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.204 * [taylor]: Taking taylor expansion of 1/2 in k
2.204 * [backup-simplify]: Simplify 1/2 into 1/2
2.204 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.204 * [taylor]: Taking taylor expansion of k in k
2.204 * [backup-simplify]: Simplify 0 into 0
2.204 * [backup-simplify]: Simplify 1 into 1
2.206 * [backup-simplify]: Simplify (/ 1 1) into 1
2.206 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
2.206 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
2.206 * [taylor]: Taking taylor expansion of 2 in k
2.206 * [backup-simplify]: Simplify 2 into 2
2.206 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.206 * [taylor]: Taking taylor expansion of PI in k
2.206 * [backup-simplify]: Simplify PI into PI
2.206 * [taylor]: Taking taylor expansion of n in k
2.206 * [backup-simplify]: Simplify n into n
2.206 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.206 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
2.206 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
2.207 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.207 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.208 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.208 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
2.208 * [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))))
2.208 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
2.208 * [taylor]: Taking taylor expansion of (sqrt k) in n
2.208 * [taylor]: Taking taylor expansion of k in n
2.208 * [backup-simplify]: Simplify k into k
2.208 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
2.208 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
2.208 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
2.208 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.208 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.208 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
2.208 * [taylor]: Taking taylor expansion of 1/2 in n
2.209 * [backup-simplify]: Simplify 1/2 into 1/2
2.209 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.209 * [taylor]: Taking taylor expansion of 1/2 in n
2.209 * [backup-simplify]: Simplify 1/2 into 1/2
2.209 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.209 * [taylor]: Taking taylor expansion of k in n
2.209 * [backup-simplify]: Simplify k into k
2.209 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.209 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.209 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.209 * [taylor]: Taking taylor expansion of 2 in n
2.209 * [backup-simplify]: Simplify 2 into 2
2.209 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.209 * [taylor]: Taking taylor expansion of PI in n
2.209 * [backup-simplify]: Simplify PI into PI
2.209 * [taylor]: Taking taylor expansion of n in n
2.209 * [backup-simplify]: Simplify 0 into 0
2.209 * [backup-simplify]: Simplify 1 into 1
2.209 * [backup-simplify]: Simplify (/ PI 1) into PI
2.210 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.211 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.211 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.211 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
2.211 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
2.213 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.214 * [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)))
2.215 * [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))))
2.215 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
2.215 * [taylor]: Taking taylor expansion of (sqrt k) in n
2.215 * [taylor]: Taking taylor expansion of k in n
2.215 * [backup-simplify]: Simplify k into k
2.215 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
2.216 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
2.216 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
2.216 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.216 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.216 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
2.216 * [taylor]: Taking taylor expansion of 1/2 in n
2.216 * [backup-simplify]: Simplify 1/2 into 1/2
2.216 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.216 * [taylor]: Taking taylor expansion of 1/2 in n
2.216 * [backup-simplify]: Simplify 1/2 into 1/2
2.216 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.216 * [taylor]: Taking taylor expansion of k in n
2.216 * [backup-simplify]: Simplify k into k
2.216 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.216 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.216 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.216 * [taylor]: Taking taylor expansion of 2 in n
2.216 * [backup-simplify]: Simplify 2 into 2
2.216 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.216 * [taylor]: Taking taylor expansion of PI in n
2.216 * [backup-simplify]: Simplify PI into PI
2.216 * [taylor]: Taking taylor expansion of n in n
2.216 * [backup-simplify]: Simplify 0 into 0
2.216 * [backup-simplify]: Simplify 1 into 1
2.217 * [backup-simplify]: Simplify (/ PI 1) into PI
2.217 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.218 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.218 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.218 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
2.219 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
2.220 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.221 * [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)))
2.223 * [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))))
2.224 * [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))
2.224 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k
2.224 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
2.224 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
2.224 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
2.224 * [taylor]: Taking taylor expansion of 1/2 in k
2.224 * [backup-simplify]: Simplify 1/2 into 1/2
2.224 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.224 * [taylor]: Taking taylor expansion of 1/2 in k
2.224 * [backup-simplify]: Simplify 1/2 into 1/2
2.224 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.224 * [taylor]: Taking taylor expansion of k in k
2.224 * [backup-simplify]: Simplify 0 into 0
2.224 * [backup-simplify]: Simplify 1 into 1
2.225 * [backup-simplify]: Simplify (/ 1 1) into 1
2.225 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
2.225 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.225 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.225 * [taylor]: Taking taylor expansion of 2 in k
2.225 * [backup-simplify]: Simplify 2 into 2
2.225 * [taylor]: Taking taylor expansion of PI in k
2.225 * [backup-simplify]: Simplify PI into PI
2.225 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.227 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.227 * [taylor]: Taking taylor expansion of (log n) in k
2.227 * [taylor]: Taking taylor expansion of n in k
2.227 * [backup-simplify]: Simplify n into n
2.227 * [backup-simplify]: Simplify (log n) into (log n)
2.227 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.227 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.228 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.228 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.229 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
2.230 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
2.231 * [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))))
2.231 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.231 * [taylor]: Taking taylor expansion of k in k
2.231 * [backup-simplify]: Simplify 0 into 0
2.231 * [backup-simplify]: Simplify 1 into 1
2.232 * [backup-simplify]: Simplify (sqrt 0) into 0
2.233 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.234 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0
2.234 * [backup-simplify]: Simplify 0 into 0
2.235 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.236 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.238 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.238 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.238 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
2.239 * [backup-simplify]: Simplify (- 0) into 0
2.239 * [backup-simplify]: Simplify (+ 0 0) into 0
2.240 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.242 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
2.243 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.245 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0
2.245 * [taylor]: Taking taylor expansion of 0 in k
2.245 * [backup-simplify]: Simplify 0 into 0
2.245 * [backup-simplify]: Simplify 0 into 0
2.246 * [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))))))
2.247 * [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))))))
2.248 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.249 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.253 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
2.253 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.254 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
2.254 * [backup-simplify]: Simplify (- 0) into 0
2.254 * [backup-simplify]: Simplify (+ 0 0) into 0
2.256 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.257 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
2.260 * [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
2.261 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
2.263 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0
2.263 * [taylor]: Taking taylor expansion of 0 in k
2.263 * [backup-simplify]: Simplify 0 into 0
2.263 * [backup-simplify]: Simplify 0 into 0
2.263 * [backup-simplify]: Simplify 0 into 0
2.266 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.268 * [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))))))
2.269 * [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))))))
2.270 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.271 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.277 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
2.278 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.279 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
2.279 * [backup-simplify]: Simplify (- 0) into 0
2.280 * [backup-simplify]: Simplify (+ 0 0) into 0
2.282 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.284 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
2.287 * [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
2.288 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
2.290 * [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
2.290 * [taylor]: Taking taylor expansion of 0 in k
2.290 * [backup-simplify]: Simplify 0 into 0
2.290 * [backup-simplify]: Simplify 0 into 0
2.290 * [backup-simplify]: Simplify 0 into 0
2.290 * [backup-simplify]: Simplify 0 into 0
2.295 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.297 * [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))))))
2.298 * [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))))))
2.303 * [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))))))))
2.304 * [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)))
2.304 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0
2.304 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
2.304 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
2.304 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
2.304 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
2.304 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
2.304 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.304 * [taylor]: Taking taylor expansion of 1/2 in k
2.304 * [backup-simplify]: Simplify 1/2 into 1/2
2.304 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.304 * [taylor]: Taking taylor expansion of k in k
2.304 * [backup-simplify]: Simplify 0 into 0
2.304 * [backup-simplify]: Simplify 1 into 1
2.305 * [backup-simplify]: Simplify (/ 1 1) into 1
2.305 * [taylor]: Taking taylor expansion of 1/2 in k
2.305 * [backup-simplify]: Simplify 1/2 into 1/2
2.305 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
2.305 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
2.305 * [taylor]: Taking taylor expansion of -2 in k
2.305 * [backup-simplify]: Simplify -2 into -2
2.305 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.305 * [taylor]: Taking taylor expansion of PI in k
2.305 * [backup-simplify]: Simplify PI into PI
2.305 * [taylor]: Taking taylor expansion of n in k
2.305 * [backup-simplify]: Simplify n into n
2.305 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.305 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
2.305 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
2.306 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.306 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.307 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
2.307 * [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)))
2.307 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.307 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.307 * [taylor]: Taking taylor expansion of -1 in k
2.307 * [backup-simplify]: Simplify -1 into -1
2.307 * [taylor]: Taking taylor expansion of k in k
2.307 * [backup-simplify]: Simplify 0 into 0
2.307 * [backup-simplify]: Simplify 1 into 1
2.307 * [backup-simplify]: Simplify (/ -1 1) into -1
2.308 * [backup-simplify]: Simplify (sqrt 0) into 0
2.309 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.310 * [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))))
2.310 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
2.310 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
2.310 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
2.310 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
2.310 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
2.310 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.310 * [taylor]: Taking taylor expansion of 1/2 in n
2.310 * [backup-simplify]: Simplify 1/2 into 1/2
2.310 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.310 * [taylor]: Taking taylor expansion of k in n
2.310 * [backup-simplify]: Simplify k into k
2.310 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.310 * [taylor]: Taking taylor expansion of 1/2 in n
2.310 * [backup-simplify]: Simplify 1/2 into 1/2
2.310 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.310 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.310 * [taylor]: Taking taylor expansion of -2 in n
2.310 * [backup-simplify]: Simplify -2 into -2
2.310 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.310 * [taylor]: Taking taylor expansion of PI in n
2.310 * [backup-simplify]: Simplify PI into PI
2.310 * [taylor]: Taking taylor expansion of n in n
2.310 * [backup-simplify]: Simplify 0 into 0
2.310 * [backup-simplify]: Simplify 1 into 1
2.311 * [backup-simplify]: Simplify (/ PI 1) into PI
2.311 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.313 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.313 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.313 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
2.314 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.315 * [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)))
2.317 * [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))))
2.317 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.317 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.317 * [taylor]: Taking taylor expansion of -1 in n
2.317 * [backup-simplify]: Simplify -1 into -1
2.317 * [taylor]: Taking taylor expansion of k in n
2.317 * [backup-simplify]: Simplify k into k
2.317 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.317 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.317 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.317 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.319 * [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)))
2.319 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
2.319 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
2.319 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
2.319 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
2.319 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
2.319 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.319 * [taylor]: Taking taylor expansion of 1/2 in n
2.319 * [backup-simplify]: Simplify 1/2 into 1/2
2.319 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.319 * [taylor]: Taking taylor expansion of k in n
2.319 * [backup-simplify]: Simplify k into k
2.319 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.319 * [taylor]: Taking taylor expansion of 1/2 in n
2.319 * [backup-simplify]: Simplify 1/2 into 1/2
2.319 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.320 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.320 * [taylor]: Taking taylor expansion of -2 in n
2.320 * [backup-simplify]: Simplify -2 into -2
2.320 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.320 * [taylor]: Taking taylor expansion of PI in n
2.320 * [backup-simplify]: Simplify PI into PI
2.320 * [taylor]: Taking taylor expansion of n in n
2.320 * [backup-simplify]: Simplify 0 into 0
2.320 * [backup-simplify]: Simplify 1 into 1
2.321 * [backup-simplify]: Simplify (/ PI 1) into PI
2.321 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.322 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.323 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.323 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
2.324 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.325 * [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)))
2.326 * [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))))
2.327 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.327 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.327 * [taylor]: Taking taylor expansion of -1 in n
2.327 * [backup-simplify]: Simplify -1 into -1
2.327 * [taylor]: Taking taylor expansion of k in n
2.327 * [backup-simplify]: Simplify k into k
2.327 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.327 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.327 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.327 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.328 * [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)))
2.328 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k
2.329 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
2.329 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
2.329 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
2.329 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.329 * [taylor]: Taking taylor expansion of 1/2 in k
2.329 * [backup-simplify]: Simplify 1/2 into 1/2
2.329 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.329 * [taylor]: Taking taylor expansion of k in k
2.329 * [backup-simplify]: Simplify 0 into 0
2.329 * [backup-simplify]: Simplify 1 into 1
2.329 * [backup-simplify]: Simplify (/ 1 1) into 1
2.329 * [taylor]: Taking taylor expansion of 1/2 in k
2.329 * [backup-simplify]: Simplify 1/2 into 1/2
2.329 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
2.329 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
2.329 * [taylor]: Taking taylor expansion of (* -2 PI) in k
2.329 * [taylor]: Taking taylor expansion of -2 in k
2.329 * [backup-simplify]: Simplify -2 into -2
2.329 * [taylor]: Taking taylor expansion of PI in k
2.329 * [backup-simplify]: Simplify PI into PI
2.330 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.331 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.331 * [taylor]: Taking taylor expansion of (log n) in k
2.331 * [taylor]: Taking taylor expansion of n in k
2.331 * [backup-simplify]: Simplify n into n
2.331 * [backup-simplify]: Simplify (log n) into (log n)
2.332 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.332 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.332 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.334 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
2.335 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
2.336 * [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))))
2.336 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.336 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.336 * [taylor]: Taking taylor expansion of -1 in k
2.336 * [backup-simplify]: Simplify -1 into -1
2.336 * [taylor]: Taking taylor expansion of k in k
2.336 * [backup-simplify]: Simplify 0 into 0
2.336 * [backup-simplify]: Simplify 1 into 1
2.336 * [backup-simplify]: Simplify (/ -1 1) into -1
2.337 * [backup-simplify]: Simplify (sqrt 0) into 0
2.338 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.340 * [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)))))
2.341 * [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)))))
2.342 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.343 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.345 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
2.345 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.345 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
2.346 * [backup-simplify]: Simplify (+ 0 0) into 0
2.347 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.348 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
2.350 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.352 * [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
2.352 * [taylor]: Taking taylor expansion of 0 in k
2.352 * [backup-simplify]: Simplify 0 into 0
2.352 * [backup-simplify]: Simplify 0 into 0
2.355 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
2.359 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.361 * [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))))))
2.362 * [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))))))
2.363 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.364 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.368 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
2.368 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.369 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
2.369 * [backup-simplify]: Simplify (+ 0 0) into 0
2.371 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.372 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
2.375 * [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
2.375 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.376 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
2.377 * [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
2.377 * [taylor]: Taking taylor expansion of 0 in k
2.377 * [backup-simplify]: Simplify 0 into 0
2.377 * [backup-simplify]: Simplify 0 into 0
2.377 * [backup-simplify]: Simplify 0 into 0
2.379 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.383 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.387 * [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))))))
2.388 * [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))))))
2.392 * [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)))))))))))
2.393 * * * [progress]: simplifying candidates
2.393 * * * * [progress]: [ 1 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
2.393 * * * * [progress]: [ 2 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
2.393 * * * * [progress]: [ 3 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
2.393 * * * * [progress]: [ 4 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* (* n 2) PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
2.393 * * * * [progress]: [ 5 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
2.393 * * * * [progress]: [ 6 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
2.393 * * * * [progress]: [ 7 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
2.393 * * * * [progress]: [ 8 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (/ k 2))) (sqrt k)))>
2.393 * * * * [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)))>
2.393 * * * * [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)))>
2.393 * * * * [progress]: [ 11 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.393 * * * * [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)))>
2.394 * * * * [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)))>
2.394 * * * * [progress]: [ 14 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.394 * * * * [progress]: [ 15 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k)))>
2.394 * * * * [progress]: [ 16 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* (* n 2) PI) 1/2) (pow (* (* n 2) PI) (- (/ k 2)))) (sqrt k)))>
2.394 * * * * [progress]: [ 17 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n 2) (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))) (sqrt k)))>
2.394 * * * * [progress]: [ 18 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (sqrt k)))>
2.394 * * * * [progress]: [ 19 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
2.394 * * * * [progress]: [ 20 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
2.394 * * * * [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)))>
2.394 * * * * [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)))>
2.394 * * * * [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)))>
2.394 * * * * [progress]: [ 24 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (sqrt k)))>
2.394 * * * * [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)))>
2.394 * * * * [progress]: [ 26 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* (* n 2) PI) (- 1/2 (/ k 2))))) (sqrt k)))>
2.394 * * * * [progress]: [ 27 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.395 * * * * [progress]: [ 28 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.395 * * * * [progress]: [ 29 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* (* n 2) PI) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.395 * * * * [progress]: [ 30 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (+ (log n) (log 2)) (log PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.395 * * * * [progress]: [ 31 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log (* n 2)) (log PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.395 * * * * [progress]: [ 32 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.395 * * * * [progress]: [ 33 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.395 * * * * [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)))>
2.395 * * * * [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)))>
2.395 * * * * [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)))>
2.395 * * * * [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)))>
2.395 * * * * [progress]: [ 38 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.395 * * * * [progress]: [ 39 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* (* n 2) PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.395 * * * * [progress]: [ 40 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (* (cbrt PI) (cbrt PI))) (cbrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.395 * * * * [progress]: [ 41 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.395 * * * * [progress]: [ 42 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (* n 2) 1) PI) (- 1/2 (/ k 2))) (sqrt k)))>
2.395 * * * * [progress]: [ 43 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.396 * * * * [progress]: [ 44 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.396 * * * * [progress]: [ 45 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* PI (* n 2)) (- 1/2 (/ k 2))) (sqrt k)))>
2.396 * * * * [progress]: [ 46 / 127 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)) 1))>
2.396 * * * * [progress]: [ 47 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (+ (log n) (log 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.396 * * * * [progress]: [ 48 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log (* n 2)) (log PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.396 * * * * [progress]: [ 49 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.396 * * * * [progress]: [ 50 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* (* n 2) PI)) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.396 * * * * [progress]: [ 51 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
2.396 * * * * [progress]: [ 52 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
2.396 * * * * [progress]: [ 53 / 127 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
2.396 * * * * [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)))))>
2.396 * * * * [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)))))>
2.396 * * * * [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)))))>
2.396 * * * * [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)))))>
2.396 * * * * [progress]: [ 58 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (- (sqrt k))))>
2.397 * * * * [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)))))>
2.397 * * * * [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)))))>
2.397 * * * * [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)))))>
2.397 * * * * [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))))>
2.397 * * * * [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)))))>
2.397 * * * * [progress]: [ 64 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) 1) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))>
2.397 * * * * [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)))))>
2.397 * * * * [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)))))>
2.397 * * * * [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)))))>
2.397 * * * * [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))))>
2.397 * * * * [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)))))>
2.397 * * * * [progress]: [ 70 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) 1/2) 1) (/ (pow (* (* n 2) PI) (- (/ k 2))) (sqrt k))))>
2.397 * * * * [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)))))>
2.397 * * * * [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)))))>
2.397 * * * * [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)))))>
2.398 * * * * [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))))>
2.398 * * * * [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)))))>
2.398 * * * * [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))))>
2.398 * * * * [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)))))>
2.398 * * * * [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)))))>
2.398 * * * * [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)))))>
2.398 * * * * [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))))>
2.398 * * * * [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)))))>
2.398 * * * * [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))))>
2.398 * * * * [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)))))>
2.398 * * * * [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)))))>
2.398 * * * * [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)))))>
2.398 * * * * [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))))>
2.398 * * * * [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)))))>
2.399 * * * * [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))))>
2.399 * * * * [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)))))>
2.399 * * * * [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)))))>
2.399 * * * * [progress]: [ 91 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.399 * * * * [progress]: [ 92 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))>
2.399 * * * * [progress]: [ 93 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.399 * * * * [progress]: [ 94 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))>
2.399 * * * * [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)))))>
2.399 * * * * [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)))))>
2.399 * * * * [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)))))>
2.399 * * * * [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))))>
2.399 * * * * [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)))))>
2.399 * * * * [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))))>
2.399 * * * * [progress]: [ 101 / 127 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))))>
2.399 * * * * [progress]: [ 102 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (/ 1 (sqrt k))))>
2.399 * * * * [progress]: [ 103 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))>
2.400 * * * * [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))))>
2.400 * * * * [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))))>
2.400 * * * * [progress]: [ 106 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.400 * * * * [progress]: [ 107 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt 1)) (sqrt k)))>
2.400 * * * * [progress]: [ 108 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.400 * * * * [progress]: [ 109 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) 1) (sqrt k)))>
2.400 * * * * [progress]: [ 110 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) 1/2) (/ (sqrt k) (pow (* (* n 2) PI) (- (/ k 2))))))>
2.400 * * * * [progress]: [ 111 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) 1/2) (/ (sqrt k) (pow (* (* n 2) PI) (- (/ k 2))))))>
2.400 * * * * [progress]: [ 112 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n 2) (- 1/2 (/ k 2))) (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))))>
2.400 * * * * [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)))))))>
2.400 * * * * [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)))))))>
2.400 * * * * [progress]: [ 115 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (- 1/2 (/ k 2))))))>
2.400 * * * * [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)))))>
2.400 * * * * [progress]: [ 117 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) 1/2) (* (sqrt k) (pow (* (* n 2) PI) (/ k 2)))))>
2.400 * * * * [progress]: [ 118 / 127 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))))>
2.401 * * * * [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)))>
2.401 * * * * [progress]: [ 120 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k)))>
2.401 * * * * [progress]: [ 121 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k)))>
2.401 * * * * [progress]: [ 122 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.401 * * * * [progress]: [ 123 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.401 * * * * [progress]: [ 124 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.401 * * * * [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)))))))))))))))))))))))>
2.401 * * * * [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)))))))))>
2.401 * * * * [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))))))))))))>
2.404 * [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)))))))))))
2.410 * * [simplify]: iteration 0: 271 enodes
2.512 * * [simplify]: iteration 1: 662 enodes
2.700 * * [simplify]: iteration 2: 2001 enodes
3.197 * * [simplify]: iteration complete: 2001 enodes
3.197 * * [simplify]: Extracting #0: cost 99 inf + 0
3.197 * * [simplify]: Extracting #1: cost 342 inf + 1
3.199 * * [simplify]: Extracting #2: cost 590 inf + 1931
3.204 * * [simplify]: Extracting #3: cost 627 inf + 25636
3.223 * * [simplify]: Extracting #4: cost 438 inf + 90869
3.266 * * [simplify]: Extracting #5: cost 214 inf + 189941
3.334 * * [simplify]: Extracting #6: cost 112 inf + 249014
3.398 * * [simplify]: Extracting #7: cost 30 inf + 300427
3.482 * * [simplify]: Extracting #8: cost 3 inf + 322021
3.563 * * [simplify]: Extracting #9: cost 0 inf + 324899
3.639 * * [simplify]: Extracting #10: cost 0 inf + 324779
3.748 * [simplify]: Simplified to:
  (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n)))
  (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n)))
  (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n)))
  (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* (* 2 PI) n))
  (pow (* (* 2 PI) n) (/ k 2))
  (pow (* (* 2 PI) n) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* 2 PI) n) (sqrt (- 1/2 (/ k 2))))
  (* (* 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) (- (/ k 2)))
  (sqrt (* (* 2 PI) n))
  (pow (* (* 2 PI) n) (- (/ k 2)))
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n)))
  (exp (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (* (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (* (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))
  (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2)))
  (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2)))
  (real->posit16 (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (log (* (* 2 PI) n))
  (log (* (* 2 PI) n))
  (log (* (* 2 PI) n))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* (* (* n (* n n)) 8) PI) (* PI PI))
  (* (* (* (* PI PI) PI) (* n 2)) (* (* n 2) (* n 2)))
  (* (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) (cbrt PI)) (* n 2))
  (* (* (sqrt PI) 2) n)
  (* n 2)
  (* 2 PI)
  (real->posit16 (* (* 2 PI) n))
  (- (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* 2 PI) n))) (log (sqrt k)))
  (exp (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)))
  (/ (* (/ (* (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) k) (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt k))
  (* (cbrt (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)))
  (* (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)) (* (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k))))
  (sqrt (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)))
  (- (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (- (sqrt k))
  (/ (/ (sqrt (* (* 2 PI) n)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt k))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt k))
  (/ (/ (sqrt (* (* 2 PI) n)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (sqrt (* (* 2 PI) n)) (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt k))
  (/ (sqrt (* (* 2 PI) n)) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* 2 PI) n))
  (/ (pow (* (* 2 PI) n) (- (/ 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))) (fabs (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)))
  (/ (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)))
  (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))
  (* (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))
  (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) (fabs (cbrt k)))
  (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))
  (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))
  (/ (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (fabs (cbrt k)))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  1
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  1
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (cbrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (sqrt (cbrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (sqrt (sqrt k)))
  (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (sqrt k))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (sqrt (sqrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (sqrt (sqrt k)))
  (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2)))
  (/ (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (fabs (cbrt k)))
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))
  (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))
  (/ (sqrt k) (pow (* (* 2 PI) n) (- (/ k 2))))
  (/ (sqrt k) (pow (* (* 2 PI) n) (- (/ k 2))))
  (/ (sqrt k) (pow PI (- 1/2 (/ k 2))))
  (/ (sqrt k) (cbrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (pow (* (* 2 PI) n) (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* (* 2 PI) n) (- 1/4 (/ (/ k 2) 2))))
  (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
  (real->posit16 (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)))
  (- (+ (+ (+ (* 1/4 (* (exp (* (log (* (* 2 PI) n)) 1/2)) (* (* (* k k) (log n)) (log (* 2 PI))))) (* (exp (* (log (* (* 2 PI) n)) 1/2)) (* (* (* (log n) (log n)) (* k k)) 1/8))) (exp (* (log (* (* 2 PI) n)) 1/2))) (* (* (* 1/8 (* (log (* 2 PI)) (log (* 2 PI)))) (exp (* (log (* (* 2 PI) n)) 1/2))) (* k k))) (* 1/2 (* k (+ (* (exp (* (log (* (* 2 PI) n)) 1/2)) (log n)) (* (log (* 2 PI)) (exp (* (log (* (* 2 PI) n)) 1/2)))))))
  (exp (* (log (* (* 2 PI) n)) (- 1/2 (* k 1/2))))
  (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n)))))
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (- (+ (- (* (* (log (* 2 PI)) (exp (* (log (* (* 2 PI) n)) 1/2))) (* (* (* k k) (log n)) +nan.0)) (* (log (* 2 PI)) (* (exp (* (log (* (* 2 PI) n)) 1/2)) (* (* k k) +nan.0)))) (+ (- (* (exp (* (log (* (* 2 PI) n)) 1/2)) (* +nan.0 (* (* (log n) (log n)) (* k k)))) (* (exp (* (log (* (* 2 PI) n)) 1/2)) (* +nan.0 k))) (+ (- (* (exp (* (log (* (* 2 PI) n)) 1/2)) +nan.0) (* (* (log (* 2 PI)) (log (* 2 PI))) (* (exp (* (log (* (* 2 PI) n)) 1/2)) (* (* k k) +nan.0)))) (+ (+ (* (exp (* (log (* (* 2 PI) n)) 1/2)) (* (* (* k k) (log n)) +nan.0)) (- (* (exp (* (log (* (* 2 PI) n)) 1/2)) (* (* k k) +nan.0)))) (- (* +nan.0 (* (* (log (* 2 PI)) k) (exp (* (log (* (* 2 PI) n)) 1/2)))) (* (* (exp (* (log (* (* 2 PI) n)) 1/2)) (* +nan.0 k)) (log n))))))))
  (+ (/ (- (* +nan.0 (exp (* (log (* (* 2 PI) n)) (- 1/2 (* k 1/2)))))) (* (* k k) k)) (* +nan.0 (- (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* k 1/2)))) k) (/ (exp (* (log (* (* 2 PI) n)) (- 1/2 (* k 1/2)))) (* k k)))))
  (+ (* (/ (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n))))) k) (- +nan.0)) (* +nan.0 (- (/ (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n))))) (* k k)) (exp (* (- 1/2 (* k 1/2)) (- (log (* PI -2)) (log (/ -1 n))))))))
3.766 * * * [progress]: adding candidates to table
4.374 * * [progress]: iteration 2 / 4
4.374 * * * [progress]: picking best candidate
4.399 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
4.399 * * * [progress]: localizing error
4.436 * * * [progress]: generating rewritten candidates
4.436 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2)
4.455 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1)
4.472 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1)
4.481 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
4.546 * * * [progress]: generating series expansions
4.546 * * * * [progress]: [ 1 / 4 ] generating series at (2 2)
4.547 * [backup-simplify]: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
4.547 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
4.547 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
4.547 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
4.547 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
4.547 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
4.547 * [taylor]: Taking taylor expansion of 1/2 in k
4.547 * [backup-simplify]: Simplify 1/2 into 1/2
4.547 * [taylor]: Taking taylor expansion of (- 1 k) in k
4.547 * [taylor]: Taking taylor expansion of 1 in k
4.547 * [backup-simplify]: Simplify 1 into 1
4.547 * [taylor]: Taking taylor expansion of k in k
4.547 * [backup-simplify]: Simplify 0 into 0
4.547 * [backup-simplify]: Simplify 1 into 1
4.547 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
4.548 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
4.548 * [taylor]: Taking taylor expansion of 2 in k
4.548 * [backup-simplify]: Simplify 2 into 2
4.548 * [taylor]: Taking taylor expansion of (* n PI) in k
4.548 * [taylor]: Taking taylor expansion of n in k
4.548 * [backup-simplify]: Simplify n into n
4.548 * [taylor]: Taking taylor expansion of PI in k
4.548 * [backup-simplify]: Simplify PI into PI
4.548 * [backup-simplify]: Simplify (* n PI) into (* n PI)
4.548 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
4.548 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
4.548 * [backup-simplify]: Simplify (- 0) into 0
4.549 * [backup-simplify]: Simplify (+ 1 0) into 1
4.550 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
4.550 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
4.550 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
4.550 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
4.550 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
4.550 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
4.550 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
4.550 * [taylor]: Taking taylor expansion of 1/2 in n
4.550 * [backup-simplify]: Simplify 1/2 into 1/2
4.550 * [taylor]: Taking taylor expansion of (- 1 k) in n
4.550 * [taylor]: Taking taylor expansion of 1 in n
4.550 * [backup-simplify]: Simplify 1 into 1
4.550 * [taylor]: Taking taylor expansion of k in n
4.550 * [backup-simplify]: Simplify k into k
4.550 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
4.550 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
4.550 * [taylor]: Taking taylor expansion of 2 in n
4.550 * [backup-simplify]: Simplify 2 into 2
4.550 * [taylor]: Taking taylor expansion of (* n PI) in n
4.550 * [taylor]: Taking taylor expansion of n in n
4.550 * [backup-simplify]: Simplify 0 into 0
4.550 * [backup-simplify]: Simplify 1 into 1
4.550 * [taylor]: Taking taylor expansion of PI in n
4.550 * [backup-simplify]: Simplify PI into PI
4.551 * [backup-simplify]: Simplify (* 0 PI) into 0
4.551 * [backup-simplify]: Simplify (* 2 0) into 0
4.553 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.555 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
4.556 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.556 * [backup-simplify]: Simplify (- k) into (- k)
4.556 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
4.556 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
4.562 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
4.563 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
4.564 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
4.564 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
4.564 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
4.564 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
4.564 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
4.564 * [taylor]: Taking taylor expansion of 1/2 in n
4.564 * [backup-simplify]: Simplify 1/2 into 1/2
4.564 * [taylor]: Taking taylor expansion of (- 1 k) in n
4.564 * [taylor]: Taking taylor expansion of 1 in n
4.565 * [backup-simplify]: Simplify 1 into 1
4.565 * [taylor]: Taking taylor expansion of k in n
4.565 * [backup-simplify]: Simplify k into k
4.565 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
4.565 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
4.565 * [taylor]: Taking taylor expansion of 2 in n
4.565 * [backup-simplify]: Simplify 2 into 2
4.565 * [taylor]: Taking taylor expansion of (* n PI) in n
4.565 * [taylor]: Taking taylor expansion of n in n
4.565 * [backup-simplify]: Simplify 0 into 0
4.565 * [backup-simplify]: Simplify 1 into 1
4.565 * [taylor]: Taking taylor expansion of PI in n
4.565 * [backup-simplify]: Simplify PI into PI
4.565 * [backup-simplify]: Simplify (* 0 PI) into 0
4.566 * [backup-simplify]: Simplify (* 2 0) into 0
4.567 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.569 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
4.570 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.570 * [backup-simplify]: Simplify (- k) into (- k)
4.570 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
4.570 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
4.571 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
4.572 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
4.573 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
4.573 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
4.573 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
4.573 * [taylor]: Taking taylor expansion of 1/2 in k
4.573 * [backup-simplify]: Simplify 1/2 into 1/2
4.573 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
4.573 * [taylor]: Taking taylor expansion of (- 1 k) in k
4.573 * [taylor]: Taking taylor expansion of 1 in k
4.573 * [backup-simplify]: Simplify 1 into 1
4.573 * [taylor]: Taking taylor expansion of k in k
4.574 * [backup-simplify]: Simplify 0 into 0
4.574 * [backup-simplify]: Simplify 1 into 1
4.574 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
4.574 * [taylor]: Taking taylor expansion of (log n) in k
4.574 * [taylor]: Taking taylor expansion of n in k
4.574 * [backup-simplify]: Simplify n into n
4.574 * [backup-simplify]: Simplify (log n) into (log n)
4.574 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
4.574 * [taylor]: Taking taylor expansion of (* 2 PI) in k
4.574 * [taylor]: Taking taylor expansion of 2 in k
4.574 * [backup-simplify]: Simplify 2 into 2
4.574 * [taylor]: Taking taylor expansion of PI in k
4.574 * [backup-simplify]: Simplify PI into PI
4.574 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
4.575 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.576 * [backup-simplify]: Simplify (- 0) into 0
4.576 * [backup-simplify]: Simplify (+ 1 0) into 1
4.577 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
4.578 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
4.579 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
4.581 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
4.582 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
4.584 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
4.586 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
4.588 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
4.589 * [backup-simplify]: Simplify (- 0) into 0
4.589 * [backup-simplify]: Simplify (+ 0 0) into 0
4.590 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
4.591 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
4.593 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
4.595 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
4.595 * [taylor]: Taking taylor expansion of 0 in k
4.595 * [backup-simplify]: Simplify 0 into 0
4.595 * [backup-simplify]: Simplify 0 into 0
4.596 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
4.597 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
4.599 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
4.599 * [backup-simplify]: Simplify (+ 0 0) into 0
4.599 * [backup-simplify]: Simplify (- 1) into -1
4.600 * [backup-simplify]: Simplify (+ 0 -1) into -1
4.601 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
4.604 * [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)))))
4.607 * [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)))))))
4.610 * [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)))))))
4.612 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
4.613 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
4.616 * [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
4.617 * [backup-simplify]: Simplify (- 0) into 0
4.617 * [backup-simplify]: Simplify (+ 0 0) into 0
4.618 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
4.620 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
4.622 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
4.624 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
4.624 * [taylor]: Taking taylor expansion of 0 in k
4.624 * [backup-simplify]: Simplify 0 into 0
4.624 * [backup-simplify]: Simplify 0 into 0
4.624 * [backup-simplify]: Simplify 0 into 0
4.626 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
4.627 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
4.631 * [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
4.631 * [backup-simplify]: Simplify (+ 0 0) into 0
4.631 * [backup-simplify]: Simplify (- 0) into 0
4.632 * [backup-simplify]: Simplify (+ 0 0) into 0
4.634 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
4.636 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
4.640 * [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)))))
4.646 * [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)))))
4.656 * [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)))))
4.657 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
4.657 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
4.657 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
4.657 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
4.657 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
4.657 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
4.657 * [taylor]: Taking taylor expansion of 1/2 in k
4.657 * [backup-simplify]: Simplify 1/2 into 1/2
4.657 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
4.657 * [taylor]: Taking taylor expansion of 1 in k
4.657 * [backup-simplify]: Simplify 1 into 1
4.657 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.657 * [taylor]: Taking taylor expansion of k in k
4.657 * [backup-simplify]: Simplify 0 into 0
4.657 * [backup-simplify]: Simplify 1 into 1
4.658 * [backup-simplify]: Simplify (/ 1 1) into 1
4.658 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
4.658 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
4.658 * [taylor]: Taking taylor expansion of 2 in k
4.658 * [backup-simplify]: Simplify 2 into 2
4.658 * [taylor]: Taking taylor expansion of (/ PI n) in k
4.658 * [taylor]: Taking taylor expansion of PI in k
4.658 * [backup-simplify]: Simplify PI into PI
4.658 * [taylor]: Taking taylor expansion of n in k
4.658 * [backup-simplify]: Simplify n into n
4.658 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
4.658 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
4.658 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
4.659 * [backup-simplify]: Simplify (- 1) into -1
4.659 * [backup-simplify]: Simplify (+ 0 -1) into -1
4.659 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
4.660 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
4.660 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
4.660 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
4.660 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
4.660 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
4.660 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
4.660 * [taylor]: Taking taylor expansion of 1/2 in n
4.660 * [backup-simplify]: Simplify 1/2 into 1/2
4.660 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
4.660 * [taylor]: Taking taylor expansion of 1 in n
4.660 * [backup-simplify]: Simplify 1 into 1
4.660 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.660 * [taylor]: Taking taylor expansion of k in n
4.660 * [backup-simplify]: Simplify k into k
4.660 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.660 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
4.660 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
4.660 * [taylor]: Taking taylor expansion of 2 in n
4.660 * [backup-simplify]: Simplify 2 into 2
4.660 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.660 * [taylor]: Taking taylor expansion of PI in n
4.660 * [backup-simplify]: Simplify PI into PI
4.660 * [taylor]: Taking taylor expansion of n in n
4.660 * [backup-simplify]: Simplify 0 into 0
4.660 * [backup-simplify]: Simplify 1 into 1
4.661 * [backup-simplify]: Simplify (/ PI 1) into PI
4.662 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
4.663 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.663 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
4.663 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
4.663 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
4.664 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
4.665 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
4.667 * [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)))))
4.667 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
4.667 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
4.667 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
4.667 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
4.667 * [taylor]: Taking taylor expansion of 1/2 in n
4.667 * [backup-simplify]: Simplify 1/2 into 1/2
4.667 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
4.667 * [taylor]: Taking taylor expansion of 1 in n
4.667 * [backup-simplify]: Simplify 1 into 1
4.667 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.667 * [taylor]: Taking taylor expansion of k in n
4.667 * [backup-simplify]: Simplify k into k
4.667 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.667 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
4.667 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
4.667 * [taylor]: Taking taylor expansion of 2 in n
4.667 * [backup-simplify]: Simplify 2 into 2
4.667 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.667 * [taylor]: Taking taylor expansion of PI in n
4.667 * [backup-simplify]: Simplify PI into PI
4.667 * [taylor]: Taking taylor expansion of n in n
4.667 * [backup-simplify]: Simplify 0 into 0
4.667 * [backup-simplify]: Simplify 1 into 1
4.668 * [backup-simplify]: Simplify (/ PI 1) into PI
4.668 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
4.670 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.670 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
4.670 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
4.670 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
4.671 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
4.672 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
4.674 * [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)))))
4.674 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
4.674 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
4.674 * [taylor]: Taking taylor expansion of 1/2 in k
4.674 * [backup-simplify]: Simplify 1/2 into 1/2
4.674 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
4.674 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
4.674 * [taylor]: Taking taylor expansion of 1 in k
4.674 * [backup-simplify]: Simplify 1 into 1
4.674 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.674 * [taylor]: Taking taylor expansion of k in k
4.674 * [backup-simplify]: Simplify 0 into 0
4.674 * [backup-simplify]: Simplify 1 into 1
4.675 * [backup-simplify]: Simplify (/ 1 1) into 1
4.675 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
4.675 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
4.675 * [taylor]: Taking taylor expansion of (* 2 PI) in k
4.675 * [taylor]: Taking taylor expansion of 2 in k
4.675 * [backup-simplify]: Simplify 2 into 2
4.675 * [taylor]: Taking taylor expansion of PI in k
4.675 * [backup-simplify]: Simplify PI into PI
4.675 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
4.676 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.676 * [taylor]: Taking taylor expansion of (log n) in k
4.676 * [taylor]: Taking taylor expansion of n in k
4.676 * [backup-simplify]: Simplify n into n
4.676 * [backup-simplify]: Simplify (log n) into (log n)
4.677 * [backup-simplify]: Simplify (- 1) into -1
4.677 * [backup-simplify]: Simplify (+ 0 -1) into -1
4.677 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
4.678 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
4.680 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
4.681 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
4.682 * [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)))))
4.683 * [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)))))
4.684 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
4.685 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
4.687 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
4.687 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
4.687 * [backup-simplify]: Simplify (- 0) into 0
4.688 * [backup-simplify]: Simplify (+ 0 0) into 0
4.688 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
4.690 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
4.691 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
4.693 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
4.693 * [taylor]: Taking taylor expansion of 0 in k
4.693 * [backup-simplify]: Simplify 0 into 0
4.693 * [backup-simplify]: Simplify 0 into 0
4.693 * [backup-simplify]: Simplify 0 into 0
4.694 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.696 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
4.699 * [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
4.700 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.700 * [backup-simplify]: Simplify (- 0) into 0
4.700 * [backup-simplify]: Simplify (+ 0 0) into 0
4.701 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
4.703 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
4.705 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
4.707 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
4.707 * [taylor]: Taking taylor expansion of 0 in k
4.707 * [backup-simplify]: Simplify 0 into 0
4.707 * [backup-simplify]: Simplify 0 into 0
4.707 * [backup-simplify]: Simplify 0 into 0
4.707 * [backup-simplify]: Simplify 0 into 0
4.711 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.713 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
4.718 * [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
4.719 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.719 * [backup-simplify]: Simplify (- 0) into 0
4.719 * [backup-simplify]: Simplify (+ 0 0) into 0
4.721 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
4.722 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
4.724 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
4.727 * [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
4.727 * [taylor]: Taking taylor expansion of 0 in k
4.727 * [backup-simplify]: Simplify 0 into 0
4.727 * [backup-simplify]: Simplify 0 into 0
4.727 * [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))))))
4.728 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
4.728 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
4.728 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
4.728 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
4.728 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
4.728 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
4.728 * [taylor]: Taking taylor expansion of 1/2 in k
4.728 * [backup-simplify]: Simplify 1/2 into 1/2
4.728 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
4.728 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.728 * [taylor]: Taking taylor expansion of k in k
4.728 * [backup-simplify]: Simplify 0 into 0
4.728 * [backup-simplify]: Simplify 1 into 1
4.728 * [backup-simplify]: Simplify (/ 1 1) into 1
4.728 * [taylor]: Taking taylor expansion of 1 in k
4.728 * [backup-simplify]: Simplify 1 into 1
4.728 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
4.728 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
4.728 * [taylor]: Taking taylor expansion of -2 in k
4.728 * [backup-simplify]: Simplify -2 into -2
4.728 * [taylor]: Taking taylor expansion of (/ PI n) in k
4.728 * [taylor]: Taking taylor expansion of PI in k
4.729 * [backup-simplify]: Simplify PI into PI
4.729 * [taylor]: Taking taylor expansion of n in k
4.729 * [backup-simplify]: Simplify n into n
4.729 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
4.729 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
4.729 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
4.729 * [backup-simplify]: Simplify (+ 1 0) into 1
4.729 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
4.729 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
4.729 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
4.729 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
4.729 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
4.729 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
4.729 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
4.729 * [taylor]: Taking taylor expansion of 1/2 in n
4.729 * [backup-simplify]: Simplify 1/2 into 1/2
4.730 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
4.730 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.730 * [taylor]: Taking taylor expansion of k in n
4.730 * [backup-simplify]: Simplify k into k
4.730 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.730 * [taylor]: Taking taylor expansion of 1 in n
4.730 * [backup-simplify]: Simplify 1 into 1
4.730 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
4.730 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
4.730 * [taylor]: Taking taylor expansion of -2 in n
4.730 * [backup-simplify]: Simplify -2 into -2
4.730 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.730 * [taylor]: Taking taylor expansion of PI in n
4.730 * [backup-simplify]: Simplify PI into PI
4.730 * [taylor]: Taking taylor expansion of n in n
4.730 * [backup-simplify]: Simplify 0 into 0
4.730 * [backup-simplify]: Simplify 1 into 1
4.730 * [backup-simplify]: Simplify (/ PI 1) into PI
4.730 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
4.731 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
4.731 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
4.731 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
4.732 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
4.733 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
4.733 * [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)))))
4.733 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
4.734 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
4.734 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
4.734 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
4.734 * [taylor]: Taking taylor expansion of 1/2 in n
4.734 * [backup-simplify]: Simplify 1/2 into 1/2
4.734 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
4.734 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.734 * [taylor]: Taking taylor expansion of k in n
4.734 * [backup-simplify]: Simplify k into k
4.734 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.734 * [taylor]: Taking taylor expansion of 1 in n
4.734 * [backup-simplify]: Simplify 1 into 1
4.734 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
4.734 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
4.734 * [taylor]: Taking taylor expansion of -2 in n
4.734 * [backup-simplify]: Simplify -2 into -2
4.734 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.734 * [taylor]: Taking taylor expansion of PI in n
4.734 * [backup-simplify]: Simplify PI into PI
4.734 * [taylor]: Taking taylor expansion of n in n
4.734 * [backup-simplify]: Simplify 0 into 0
4.734 * [backup-simplify]: Simplify 1 into 1
4.734 * [backup-simplify]: Simplify (/ PI 1) into PI
4.734 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
4.735 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
4.735 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
4.735 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
4.736 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
4.737 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
4.738 * [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)))))
4.738 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
4.738 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
4.738 * [taylor]: Taking taylor expansion of 1/2 in k
4.738 * [backup-simplify]: Simplify 1/2 into 1/2
4.738 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
4.738 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
4.738 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.738 * [taylor]: Taking taylor expansion of k in k
4.738 * [backup-simplify]: Simplify 0 into 0
4.738 * [backup-simplify]: Simplify 1 into 1
4.738 * [backup-simplify]: Simplify (/ 1 1) into 1
4.738 * [taylor]: Taking taylor expansion of 1 in k
4.738 * [backup-simplify]: Simplify 1 into 1
4.738 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
4.738 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
4.738 * [taylor]: Taking taylor expansion of (* -2 PI) in k
4.738 * [taylor]: Taking taylor expansion of -2 in k
4.738 * [backup-simplify]: Simplify -2 into -2
4.738 * [taylor]: Taking taylor expansion of PI in k
4.738 * [backup-simplify]: Simplify PI into PI
4.739 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
4.739 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
4.739 * [taylor]: Taking taylor expansion of (log n) in k
4.739 * [taylor]: Taking taylor expansion of n in k
4.739 * [backup-simplify]: Simplify n into n
4.739 * [backup-simplify]: Simplify (log n) into (log n)
4.740 * [backup-simplify]: Simplify (+ 1 0) into 1
4.740 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
4.740 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
4.741 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
4.742 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
4.743 * [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)))))
4.743 * [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)))))
4.744 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
4.744 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
4.745 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
4.745 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
4.746 * [backup-simplify]: Simplify (+ 0 0) into 0
4.746 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
4.747 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
4.748 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
4.749 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
4.749 * [taylor]: Taking taylor expansion of 0 in k
4.749 * [backup-simplify]: Simplify 0 into 0
4.749 * [backup-simplify]: Simplify 0 into 0
4.749 * [backup-simplify]: Simplify 0 into 0
4.749 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.750 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
4.752 * [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
4.752 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.752 * [backup-simplify]: Simplify (+ 0 0) into 0
4.753 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
4.754 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
4.755 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
4.758 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
4.758 * [taylor]: Taking taylor expansion of 0 in k
4.758 * [backup-simplify]: Simplify 0 into 0
4.758 * [backup-simplify]: Simplify 0 into 0
4.758 * [backup-simplify]: Simplify 0 into 0
4.758 * [backup-simplify]: Simplify 0 into 0
4.759 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.761 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
4.767 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
4.767 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
4.767 * [backup-simplify]: Simplify (+ 0 0) into 0
4.769 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
4.770 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
4.772 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
4.775 * [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
4.775 * [taylor]: Taking taylor expansion of 0 in k
4.775 * [backup-simplify]: Simplify 0 into 0
4.775 * [backup-simplify]: Simplify 0 into 0
4.777 * [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))))))
4.777 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1)
4.777 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
4.777 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
4.777 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
4.777 * [taylor]: Taking taylor expansion of 2 in n
4.777 * [backup-simplify]: Simplify 2 into 2
4.777 * [taylor]: Taking taylor expansion of (* n PI) in n
4.777 * [taylor]: Taking taylor expansion of n in n
4.777 * [backup-simplify]: Simplify 0 into 0
4.777 * [backup-simplify]: Simplify 1 into 1
4.777 * [taylor]: Taking taylor expansion of PI in n
4.777 * [backup-simplify]: Simplify PI into PI
4.777 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
4.778 * [taylor]: Taking taylor expansion of 2 in n
4.778 * [backup-simplify]: Simplify 2 into 2
4.778 * [taylor]: Taking taylor expansion of (* n PI) in n
4.778 * [taylor]: Taking taylor expansion of n in n
4.778 * [backup-simplify]: Simplify 0 into 0
4.778 * [backup-simplify]: Simplify 1 into 1
4.778 * [taylor]: Taking taylor expansion of PI in n
4.778 * [backup-simplify]: Simplify PI into PI
4.778 * [backup-simplify]: Simplify (* 0 PI) into 0
4.779 * [backup-simplify]: Simplify (* 2 0) into 0
4.779 * [backup-simplify]: Simplify 0 into 0
4.780 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.782 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
4.783 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
4.784 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
4.785 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
4.785 * [backup-simplify]: Simplify 0 into 0
4.786 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
4.787 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
4.787 * [backup-simplify]: Simplify 0 into 0
4.789 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
4.790 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
4.790 * [backup-simplify]: Simplify 0 into 0
4.792 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
4.794 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
4.794 * [backup-simplify]: Simplify 0 into 0
4.796 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
4.798 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
4.798 * [backup-simplify]: Simplify 0 into 0
4.800 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
4.802 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
4.802 * [backup-simplify]: Simplify 0 into 0
4.803 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
4.804 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n))
4.804 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
4.804 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
4.804 * [taylor]: Taking taylor expansion of 2 in n
4.804 * [backup-simplify]: Simplify 2 into 2
4.804 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.804 * [taylor]: Taking taylor expansion of PI in n
4.804 * [backup-simplify]: Simplify PI into PI
4.804 * [taylor]: Taking taylor expansion of n in n
4.804 * [backup-simplify]: Simplify 0 into 0
4.804 * [backup-simplify]: Simplify 1 into 1
4.805 * [backup-simplify]: Simplify (/ PI 1) into PI
4.805 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
4.805 * [taylor]: Taking taylor expansion of 2 in n
4.805 * [backup-simplify]: Simplify 2 into 2
4.805 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.805 * [taylor]: Taking taylor expansion of PI in n
4.805 * [backup-simplify]: Simplify PI into PI
4.805 * [taylor]: Taking taylor expansion of n in n
4.805 * [backup-simplify]: Simplify 0 into 0
4.805 * [backup-simplify]: Simplify 1 into 1
4.806 * [backup-simplify]: Simplify (/ PI 1) into PI
4.806 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
4.807 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
4.808 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
4.808 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
4.809 * [backup-simplify]: Simplify 0 into 0
4.810 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.811 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
4.811 * [backup-simplify]: Simplify 0 into 0
4.813 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.814 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
4.814 * [backup-simplify]: Simplify 0 into 0
4.815 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.816 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
4.816 * [backup-simplify]: Simplify 0 into 0
4.817 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.818 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
4.818 * [backup-simplify]: Simplify 0 into 0
4.819 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.820 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
4.820 * [backup-simplify]: Simplify 0 into 0
4.820 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
4.821 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n))
4.821 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
4.821 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
4.821 * [taylor]: Taking taylor expansion of -2 in n
4.821 * [backup-simplify]: Simplify -2 into -2
4.821 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.821 * [taylor]: Taking taylor expansion of PI in n
4.821 * [backup-simplify]: Simplify PI into PI
4.821 * [taylor]: Taking taylor expansion of n in n
4.821 * [backup-simplify]: Simplify 0 into 0
4.821 * [backup-simplify]: Simplify 1 into 1
4.821 * [backup-simplify]: Simplify (/ PI 1) into PI
4.821 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
4.821 * [taylor]: Taking taylor expansion of -2 in n
4.821 * [backup-simplify]: Simplify -2 into -2
4.821 * [taylor]: Taking taylor expansion of (/ PI n) in n
4.821 * [taylor]: Taking taylor expansion of PI in n
4.821 * [backup-simplify]: Simplify PI into PI
4.821 * [taylor]: Taking taylor expansion of n in n
4.821 * [backup-simplify]: Simplify 0 into 0
4.821 * [backup-simplify]: Simplify 1 into 1
4.822 * [backup-simplify]: Simplify (/ PI 1) into PI
4.822 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
4.823 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
4.823 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
4.824 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
4.824 * [backup-simplify]: Simplify 0 into 0
4.824 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.825 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
4.825 * [backup-simplify]: Simplify 0 into 0
4.826 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.826 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
4.826 * [backup-simplify]: Simplify 0 into 0
4.827 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.828 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
4.828 * [backup-simplify]: Simplify 0 into 0
4.828 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.829 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
4.829 * [backup-simplify]: Simplify 0 into 0
4.830 * [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
4.831 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
4.831 * [backup-simplify]: Simplify 0 into 0
4.831 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
4.832 * * * * [progress]: [ 3 / 4 ] generating series at (2 1)
4.832 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k))
4.832 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0
4.832 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
4.832 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.832 * [taylor]: Taking taylor expansion of k in k
4.832 * [backup-simplify]: Simplify 0 into 0
4.832 * [backup-simplify]: Simplify 1 into 1
4.832 * [backup-simplify]: Simplify (/ 1 1) into 1
4.834 * [backup-simplify]: Simplify (sqrt 0) into 0
4.835 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
4.835 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
4.835 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.835 * [taylor]: Taking taylor expansion of k in k
4.835 * [backup-simplify]: Simplify 0 into 0
4.835 * [backup-simplify]: Simplify 1 into 1
4.835 * [backup-simplify]: Simplify (/ 1 1) into 1
4.836 * [backup-simplify]: Simplify (sqrt 0) into 0
4.836 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
4.837 * [backup-simplify]: Simplify 0 into 0
4.837 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.837 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
4.839 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
4.839 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.839 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.842 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
4.842 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.842 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
4.842 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k)
4.842 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0
4.842 * [taylor]: Taking taylor expansion of (sqrt k) in k
4.842 * [taylor]: Taking taylor expansion of k in k
4.842 * [backup-simplify]: Simplify 0 into 0
4.842 * [backup-simplify]: Simplify 1 into 1
4.842 * [backup-simplify]: Simplify (sqrt 0) into 0
4.843 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
4.843 * [taylor]: Taking taylor expansion of (sqrt k) in k
4.843 * [taylor]: Taking taylor expansion of k in k
4.843 * [backup-simplify]: Simplify 0 into 0
4.843 * [backup-simplify]: Simplify 1 into 1
4.843 * [backup-simplify]: Simplify (sqrt 0) into 0
4.844 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
4.844 * [backup-simplify]: Simplify 0 into 0
4.844 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.846 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
4.846 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.849 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
4.849 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.850 * [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))))))))
4.850 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k)))
4.850 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0
4.850 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
4.850 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
4.850 * [taylor]: Taking taylor expansion of (/ -1 k) in k
4.850 * [taylor]: Taking taylor expansion of -1 in k
4.850 * [backup-simplify]: Simplify -1 into -1
4.850 * [taylor]: Taking taylor expansion of k in k
4.850 * [backup-simplify]: Simplify 0 into 0
4.850 * [backup-simplify]: Simplify 1 into 1
4.851 * [backup-simplify]: Simplify (/ -1 1) into -1
4.851 * [backup-simplify]: Simplify (sqrt 0) into 0
4.852 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
4.853 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
4.853 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
4.853 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
4.853 * [taylor]: Taking taylor expansion of (/ -1 k) in k
4.853 * [taylor]: Taking taylor expansion of -1 in k
4.853 * [backup-simplify]: Simplify -1 into -1
4.853 * [taylor]: Taking taylor expansion of k in k
4.853 * [backup-simplify]: Simplify 0 into 0
4.853 * [backup-simplify]: Simplify 1 into 1
4.853 * [backup-simplify]: Simplify (/ -1 1) into -1
4.854 * [backup-simplify]: Simplify (sqrt 0) into 0
4.856 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
4.856 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
4.856 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.857 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
4.860 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
4.862 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
4.862 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
4.863 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.867 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
4.869 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
4.869 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
4.870 * [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)))))
4.870 * * * * [progress]: [ 4 / 4 ] generating series at (2)
4.870 * [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)))
4.870 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0
4.871 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
4.871 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
4.871 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
4.871 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
4.871 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
4.871 * [taylor]: Taking taylor expansion of 1/2 in n
4.871 * [backup-simplify]: Simplify 1/2 into 1/2
4.871 * [taylor]: Taking taylor expansion of (- 1 k) in n
4.871 * [taylor]: Taking taylor expansion of 1 in n
4.871 * [backup-simplify]: Simplify 1 into 1
4.871 * [taylor]: Taking taylor expansion of k in n
4.871 * [backup-simplify]: Simplify k into k
4.871 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
4.871 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
4.871 * [taylor]: Taking taylor expansion of 2 in n
4.871 * [backup-simplify]: Simplify 2 into 2
4.871 * [taylor]: Taking taylor expansion of (* n PI) in n
4.871 * [taylor]: Taking taylor expansion of n in n
4.871 * [backup-simplify]: Simplify 0 into 0
4.871 * [backup-simplify]: Simplify 1 into 1
4.871 * [taylor]: Taking taylor expansion of PI in n
4.871 * [backup-simplify]: Simplify PI into PI
4.871 * [backup-simplify]: Simplify (* 0 PI) into 0
4.871 * [backup-simplify]: Simplify (* 2 0) into 0
4.872 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.873 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
4.874 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.874 * [backup-simplify]: Simplify (- k) into (- k)
4.874 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
4.874 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
4.875 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
4.876 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
4.876 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
4.876 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
4.876 * [taylor]: Taking taylor expansion of (/ 1 k) in n
4.876 * [taylor]: Taking taylor expansion of k in n
4.876 * [backup-simplify]: Simplify k into k
4.876 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
4.876 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
4.877 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
4.877 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
4.877 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
4.877 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
4.877 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
4.877 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
4.877 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
4.877 * [taylor]: Taking taylor expansion of 1/2 in k
4.877 * [backup-simplify]: Simplify 1/2 into 1/2
4.877 * [taylor]: Taking taylor expansion of (- 1 k) in k
4.877 * [taylor]: Taking taylor expansion of 1 in k
4.877 * [backup-simplify]: Simplify 1 into 1
4.877 * [taylor]: Taking taylor expansion of k in k
4.877 * [backup-simplify]: Simplify 0 into 0
4.877 * [backup-simplify]: Simplify 1 into 1
4.877 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
4.877 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
4.877 * [taylor]: Taking taylor expansion of 2 in k
4.877 * [backup-simplify]: Simplify 2 into 2
4.877 * [taylor]: Taking taylor expansion of (* n PI) in k
4.877 * [taylor]: Taking taylor expansion of n in k
4.877 * [backup-simplify]: Simplify n into n
4.877 * [taylor]: Taking taylor expansion of PI in k
4.877 * [backup-simplify]: Simplify PI into PI
4.877 * [backup-simplify]: Simplify (* n PI) into (* n PI)
4.877 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
4.877 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
4.877 * [backup-simplify]: Simplify (- 0) into 0
4.878 * [backup-simplify]: Simplify (+ 1 0) into 1
4.878 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
4.878 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
4.878 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
4.878 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
4.878 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.878 * [taylor]: Taking taylor expansion of k in k
4.878 * [backup-simplify]: Simplify 0 into 0
4.878 * [backup-simplify]: Simplify 1 into 1
4.878 * [backup-simplify]: Simplify (/ 1 1) into 1
4.879 * [backup-simplify]: Simplify (sqrt 0) into 0
4.879 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
4.879 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
4.879 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
4.879 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
4.879 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
4.879 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
4.879 * [taylor]: Taking taylor expansion of 1/2 in k
4.879 * [backup-simplify]: Simplify 1/2 into 1/2
4.879 * [taylor]: Taking taylor expansion of (- 1 k) in k
4.879 * [taylor]: Taking taylor expansion of 1 in k
4.879 * [backup-simplify]: Simplify 1 into 1
4.879 * [taylor]: Taking taylor expansion of k in k
4.879 * [backup-simplify]: Simplify 0 into 0
4.880 * [backup-simplify]: Simplify 1 into 1
4.880 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
4.880 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
4.880 * [taylor]: Taking taylor expansion of 2 in k
4.880 * [backup-simplify]: Simplify 2 into 2
4.880 * [taylor]: Taking taylor expansion of (* n PI) in k
4.880 * [taylor]: Taking taylor expansion of n in k
4.880 * [backup-simplify]: Simplify n into n
4.880 * [taylor]: Taking taylor expansion of PI in k
4.880 * [backup-simplify]: Simplify PI into PI
4.880 * [backup-simplify]: Simplify (* n PI) into (* n PI)
4.880 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
4.880 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
4.880 * [backup-simplify]: Simplify (- 0) into 0
4.880 * [backup-simplify]: Simplify (+ 1 0) into 1
4.881 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
4.881 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
4.881 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
4.881 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
4.881 * [taylor]: Taking taylor expansion of (/ 1 k) in k
4.881 * [taylor]: Taking taylor expansion of k in k
4.881 * [backup-simplify]: Simplify 0 into 0
4.881 * [backup-simplify]: Simplify 1 into 1
4.881 * [backup-simplify]: Simplify (/ 1 1) into 1
4.881 * [backup-simplify]: Simplify (sqrt 0) into 0
4.882 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
4.882 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0
4.882 * [taylor]: Taking taylor expansion of 0 in n
4.882 * [backup-simplify]: Simplify 0 into 0
4.882 * [backup-simplify]: Simplify 0 into 0
4.883 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
4.883 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
4.883 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
4.884 * [backup-simplify]: Simplify (- 1) into -1
4.884 * [backup-simplify]: Simplify (+ 0 -1) into -1
4.884 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
4.885 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
4.885 * [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)))))
4.885 * [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)))))
4.885 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
4.885 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
4.885 * [taylor]: Taking taylor expansion of +nan.0 in n
4.885 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.885 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
4.885 * [taylor]: Taking taylor expansion of (sqrt 2) in n
4.885 * [taylor]: Taking taylor expansion of 2 in n
4.885 * [backup-simplify]: Simplify 2 into 2
4.885 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
4.886 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
4.886 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
4.886 * [taylor]: Taking taylor expansion of (* n PI) in n
4.886 * [taylor]: Taking taylor expansion of n in n
4.886 * [backup-simplify]: Simplify 0 into 0
4.886 * [backup-simplify]: Simplify 1 into 1
4.886 * [taylor]: Taking taylor expansion of PI in n
4.886 * [backup-simplify]: Simplify PI into PI
4.886 * [backup-simplify]: Simplify (* 0 PI) into 0
4.887 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.887 * [backup-simplify]: Simplify (sqrt 0) into 0
4.888 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
4.888 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
4.889 * [backup-simplify]: Simplify (* +nan.0 0) into 0
4.889 * [backup-simplify]: Simplify (- 0) into 0
4.889 * [backup-simplify]: Simplify 0 into 0
4.889 * [backup-simplify]: Simplify 0 into 0
4.889 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
4.891 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
4.892 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
4.892 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
4.893 * [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
4.893 * [backup-simplify]: Simplify (- 0) into 0
4.894 * [backup-simplify]: Simplify (+ 0 0) into 0
4.894 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
4.895 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
4.896 * [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)))
4.896 * [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)))))))
4.896 * [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
4.896 * [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
4.896 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
4.896 * [taylor]: Taking taylor expansion of +nan.0 in n
4.896 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.896 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
4.896 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
4.896 * [taylor]: Taking taylor expansion of (sqrt 2) in n
4.896 * [taylor]: Taking taylor expansion of 2 in n
4.896 * [backup-simplify]: Simplify 2 into 2
4.897 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
4.897 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
4.897 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
4.897 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
4.897 * [taylor]: Taking taylor expansion of 2 in n
4.897 * [backup-simplify]: Simplify 2 into 2
4.897 * [taylor]: Taking taylor expansion of (* n PI) in n
4.897 * [taylor]: Taking taylor expansion of n in n
4.897 * [backup-simplify]: Simplify 0 into 0
4.897 * [backup-simplify]: Simplify 1 into 1
4.897 * [taylor]: Taking taylor expansion of PI in n
4.897 * [backup-simplify]: Simplify PI into PI
4.897 * [backup-simplify]: Simplify (* 0 PI) into 0
4.898 * [backup-simplify]: Simplify (* 2 0) into 0
4.899 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.900 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
4.900 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.900 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
4.900 * [taylor]: Taking taylor expansion of (* n PI) in n
4.900 * [taylor]: Taking taylor expansion of n in n
4.900 * [backup-simplify]: Simplify 0 into 0
4.900 * [backup-simplify]: Simplify 1 into 1
4.900 * [taylor]: Taking taylor expansion of PI in n
4.900 * [backup-simplify]: Simplify PI into PI
4.901 * [backup-simplify]: Simplify (* 0 PI) into 0
4.902 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.902 * [backup-simplify]: Simplify (sqrt 0) into 0
4.903 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
4.903 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
4.903 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
4.903 * [taylor]: Taking taylor expansion of +nan.0 in n
4.903 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.903 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
4.903 * [taylor]: Taking taylor expansion of (sqrt 2) in n
4.903 * [taylor]: Taking taylor expansion of 2 in n
4.903 * [backup-simplify]: Simplify 2 into 2
4.904 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
4.904 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
4.904 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
4.904 * [taylor]: Taking taylor expansion of (* n PI) in n
4.904 * [taylor]: Taking taylor expansion of n in n
4.904 * [backup-simplify]: Simplify 0 into 0
4.904 * [backup-simplify]: Simplify 1 into 1
4.904 * [taylor]: Taking taylor expansion of PI in n
4.904 * [backup-simplify]: Simplify PI into PI
4.905 * [backup-simplify]: Simplify (* 0 PI) into 0
4.907 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.907 * [backup-simplify]: Simplify (sqrt 0) into 0
4.909 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
4.910 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
4.912 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
4.913 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
4.914 * [backup-simplify]: Simplify (* +nan.0 0) into 0
4.914 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
4.915 * [backup-simplify]: Simplify (* +nan.0 0) into 0
4.915 * [backup-simplify]: Simplify (- 0) into 0
4.916 * [backup-simplify]: Simplify (+ 0 0) into 0
4.916 * [backup-simplify]: Simplify (- 0) into 0
4.916 * [backup-simplify]: Simplify 0 into 0
4.919 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
4.925 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
4.929 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
4.931 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI)))
4.931 * [backup-simplify]: Simplify 0 into 0
4.932 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
4.937 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
4.938 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
4.939 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
4.942 * [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
4.942 * [backup-simplify]: Simplify (- 0) into 0
4.943 * [backup-simplify]: Simplify (+ 0 0) into 0
4.947 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
4.948 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0
4.950 * [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)))
4.952 * [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)))))))))
4.952 * [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
4.952 * [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
4.952 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
4.952 * [taylor]: Taking taylor expansion of +nan.0 in n
4.952 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.952 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
4.952 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
4.952 * [taylor]: Taking taylor expansion of (sqrt 2) in n
4.952 * [taylor]: Taking taylor expansion of 2 in n
4.952 * [backup-simplify]: Simplify 2 into 2
4.952 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
4.953 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
4.953 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
4.953 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
4.953 * [taylor]: Taking taylor expansion of 2 in n
4.953 * [backup-simplify]: Simplify 2 into 2
4.953 * [taylor]: Taking taylor expansion of (* n PI) in n
4.953 * [taylor]: Taking taylor expansion of n in n
4.953 * [backup-simplify]: Simplify 0 into 0
4.953 * [backup-simplify]: Simplify 1 into 1
4.953 * [taylor]: Taking taylor expansion of PI in n
4.953 * [backup-simplify]: Simplify PI into PI
4.954 * [backup-simplify]: Simplify (* 0 PI) into 0
4.954 * [backup-simplify]: Simplify (* 2 0) into 0
4.956 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.958 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
4.959 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.959 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
4.959 * [taylor]: Taking taylor expansion of (* n PI) in n
4.959 * [taylor]: Taking taylor expansion of n in n
4.959 * [backup-simplify]: Simplify 0 into 0
4.959 * [backup-simplify]: Simplify 1 into 1
4.959 * [taylor]: Taking taylor expansion of PI in n
4.959 * [backup-simplify]: Simplify PI into PI
4.960 * [backup-simplify]: Simplify (* 0 PI) into 0
4.961 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.962 * [backup-simplify]: Simplify (sqrt 0) into 0
4.963 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
4.963 * [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
4.963 * [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
4.963 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
4.963 * [taylor]: Taking taylor expansion of +nan.0 in n
4.963 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.963 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
4.963 * [taylor]: Taking taylor expansion of (sqrt 2) in n
4.964 * [taylor]: Taking taylor expansion of 2 in n
4.964 * [backup-simplify]: Simplify 2 into 2
4.964 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
4.965 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
4.965 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
4.965 * [taylor]: Taking taylor expansion of (* n PI) in n
4.965 * [taylor]: Taking taylor expansion of n in n
4.965 * [backup-simplify]: Simplify 0 into 0
4.965 * [backup-simplify]: Simplify 1 into 1
4.965 * [taylor]: Taking taylor expansion of PI in n
4.965 * [backup-simplify]: Simplify PI into PI
4.966 * [backup-simplify]: Simplify (* 0 PI) into 0
4.967 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.968 * [backup-simplify]: Simplify (sqrt 0) into 0
4.969 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
4.969 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n
4.969 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n
4.969 * [taylor]: Taking taylor expansion of +nan.0 in n
4.969 * [backup-simplify]: Simplify +nan.0 into +nan.0
4.969 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n
4.969 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n
4.969 * [taylor]: Taking taylor expansion of (sqrt 2) in n
4.969 * [taylor]: Taking taylor expansion of 2 in n
4.969 * [backup-simplify]: Simplify 2 into 2
4.970 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
4.970 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
4.970 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
4.970 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
4.970 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
4.970 * [taylor]: Taking taylor expansion of 2 in n
4.970 * [backup-simplify]: Simplify 2 into 2
4.970 * [taylor]: Taking taylor expansion of (* n PI) in n
4.970 * [taylor]: Taking taylor expansion of n in n
4.970 * [backup-simplify]: Simplify 0 into 0
4.970 * [backup-simplify]: Simplify 1 into 1
4.970 * [taylor]: Taking taylor expansion of PI in n
4.971 * [backup-simplify]: Simplify PI into PI
4.971 * [backup-simplify]: Simplify (* 0 PI) into 0
4.971 * [backup-simplify]: Simplify (* 2 0) into 0
4.973 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.974 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
4.975 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
4.977 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
4.977 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
4.977 * [taylor]: Taking taylor expansion of (* n PI) in n
4.977 * [taylor]: Taking taylor expansion of n in n
4.977 * [backup-simplify]: Simplify 0 into 0
4.977 * [backup-simplify]: Simplify 1 into 1
4.977 * [taylor]: Taking taylor expansion of PI in n
4.977 * [backup-simplify]: Simplify PI into PI
4.978 * [backup-simplify]: Simplify (* 0 PI) into 0
4.979 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
4.980 * [backup-simplify]: Simplify (sqrt 0) into 0
4.981 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
4.983 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
4.984 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
4.986 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
4.986 * [backup-simplify]: Simplify (* +nan.0 0) into 0
4.987 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
4.987 * [backup-simplify]: Simplify (* +nan.0 0) into 0
4.989 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
4.991 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
4.993 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2)
4.995 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2))
4.996 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0
4.997 * [backup-simplify]: Simplify (* +nan.0 0) into 0
4.997 * [backup-simplify]: Simplify (- 0) into 0
4.997 * [backup-simplify]: Simplify (+ 0 0) into 0
4.998 * [backup-simplify]: Simplify (- 0) into 0
4.998 * [backup-simplify]: Simplify (+ 0 0) into 0
4.999 * [backup-simplify]: Simplify (- 0) into 0
4.999 * [backup-simplify]: Simplify 0 into 0
5.000 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.001 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.003 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.004 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.006 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
5.009 * [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))))))))
5.016 * [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))))))))
5.019 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
5.025 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
5.029 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
5.039 * [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))))))))))
5.048 * [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)))))))
5.056 * [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)))))))
5.058 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.063 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
5.064 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0
5.070 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
5.079 * [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))))
5.083 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
5.087 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
5.105 * [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)))))))))))))
5.106 * [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))
5.106 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0
5.106 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
5.106 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
5.107 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.107 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.107 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
5.107 * [taylor]: Taking taylor expansion of 1/2 in n
5.107 * [backup-simplify]: Simplify 1/2 into 1/2
5.107 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.107 * [taylor]: Taking taylor expansion of 1 in n
5.107 * [backup-simplify]: Simplify 1 into 1
5.107 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.107 * [taylor]: Taking taylor expansion of k in n
5.107 * [backup-simplify]: Simplify k into k
5.107 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.107 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.107 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.107 * [taylor]: Taking taylor expansion of 2 in n
5.107 * [backup-simplify]: Simplify 2 into 2
5.107 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.107 * [taylor]: Taking taylor expansion of PI in n
5.107 * [backup-simplify]: Simplify PI into PI
5.107 * [taylor]: Taking taylor expansion of n in n
5.107 * [backup-simplify]: Simplify 0 into 0
5.107 * [backup-simplify]: Simplify 1 into 1
5.108 * [backup-simplify]: Simplify (/ PI 1) into PI
5.108 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.109 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.109 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.109 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.110 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
5.111 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.111 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.112 * [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)))))
5.112 * [taylor]: Taking taylor expansion of (sqrt k) in n
5.112 * [taylor]: Taking taylor expansion of k in n
5.112 * [backup-simplify]: Simplify k into k
5.112 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
5.112 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
5.112 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
5.112 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
5.112 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
5.112 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
5.112 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
5.112 * [taylor]: Taking taylor expansion of 1/2 in k
5.112 * [backup-simplify]: Simplify 1/2 into 1/2
5.112 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
5.112 * [taylor]: Taking taylor expansion of 1 in k
5.113 * [backup-simplify]: Simplify 1 into 1
5.113 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.113 * [taylor]: Taking taylor expansion of k in k
5.113 * [backup-simplify]: Simplify 0 into 0
5.113 * [backup-simplify]: Simplify 1 into 1
5.113 * [backup-simplify]: Simplify (/ 1 1) into 1
5.113 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
5.113 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
5.113 * [taylor]: Taking taylor expansion of 2 in k
5.113 * [backup-simplify]: Simplify 2 into 2
5.113 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.113 * [taylor]: Taking taylor expansion of PI in k
5.113 * [backup-simplify]: Simplify PI into PI
5.113 * [taylor]: Taking taylor expansion of n in k
5.113 * [backup-simplify]: Simplify n into n
5.113 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.113 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
5.113 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
5.113 * [backup-simplify]: Simplify (- 1) into -1
5.114 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.114 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
5.114 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
5.114 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
5.114 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.114 * [taylor]: Taking taylor expansion of k in k
5.114 * [backup-simplify]: Simplify 0 into 0
5.114 * [backup-simplify]: Simplify 1 into 1
5.114 * [backup-simplify]: Simplify (sqrt 0) into 0
5.115 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.115 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
5.115 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
5.115 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
5.115 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
5.115 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
5.115 * [taylor]: Taking taylor expansion of 1/2 in k
5.115 * [backup-simplify]: Simplify 1/2 into 1/2
5.115 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
5.115 * [taylor]: Taking taylor expansion of 1 in k
5.115 * [backup-simplify]: Simplify 1 into 1
5.115 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.115 * [taylor]: Taking taylor expansion of k in k
5.115 * [backup-simplify]: Simplify 0 into 0
5.115 * [backup-simplify]: Simplify 1 into 1
5.116 * [backup-simplify]: Simplify (/ 1 1) into 1
5.116 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
5.116 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
5.116 * [taylor]: Taking taylor expansion of 2 in k
5.116 * [backup-simplify]: Simplify 2 into 2
5.116 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.116 * [taylor]: Taking taylor expansion of PI in k
5.116 * [backup-simplify]: Simplify PI into PI
5.116 * [taylor]: Taking taylor expansion of n in k
5.116 * [backup-simplify]: Simplify n into n
5.116 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.116 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
5.116 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
5.116 * [backup-simplify]: Simplify (- 1) into -1
5.117 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.117 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
5.117 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
5.117 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
5.117 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.117 * [taylor]: Taking taylor expansion of k in k
5.117 * [backup-simplify]: Simplify 0 into 0
5.117 * [backup-simplify]: Simplify 1 into 1
5.117 * [backup-simplify]: Simplify (sqrt 0) into 0
5.118 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.119 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0
5.119 * [taylor]: Taking taylor expansion of 0 in n
5.119 * [backup-simplify]: Simplify 0 into 0
5.119 * [backup-simplify]: Simplify 0 into 0
5.119 * [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))))))))
5.119 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
5.119 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
5.119 * [taylor]: Taking taylor expansion of +nan.0 in n
5.119 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.119 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
5.119 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
5.119 * [taylor]: Taking taylor expansion of 1/2 in n
5.119 * [backup-simplify]: Simplify 1/2 into 1/2
5.119 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
5.119 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.119 * [taylor]: Taking taylor expansion of 1 in n
5.119 * [backup-simplify]: Simplify 1 into 1
5.119 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.119 * [taylor]: Taking taylor expansion of k in n
5.119 * [backup-simplify]: Simplify k into k
5.119 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.119 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.119 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.119 * [taylor]: Taking taylor expansion of 2 in n
5.119 * [backup-simplify]: Simplify 2 into 2
5.119 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.119 * [taylor]: Taking taylor expansion of PI in n
5.119 * [backup-simplify]: Simplify PI into PI
5.119 * [taylor]: Taking taylor expansion of n in n
5.119 * [backup-simplify]: Simplify 0 into 0
5.119 * [backup-simplify]: Simplify 1 into 1
5.120 * [backup-simplify]: Simplify (/ PI 1) into PI
5.120 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.121 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.121 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.121 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.122 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.122 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
5.123 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.124 * [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)))))
5.125 * [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))))))
5.125 * [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)))))))
5.126 * [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)))))))
5.126 * [backup-simplify]: Simplify 0 into 0
5.128 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.128 * [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))))))))
5.128 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
5.128 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
5.128 * [taylor]: Taking taylor expansion of +nan.0 in n
5.128 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.129 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
5.129 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
5.129 * [taylor]: Taking taylor expansion of 1/2 in n
5.129 * [backup-simplify]: Simplify 1/2 into 1/2
5.129 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
5.129 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.129 * [taylor]: Taking taylor expansion of 1 in n
5.129 * [backup-simplify]: Simplify 1 into 1
5.129 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.129 * [taylor]: Taking taylor expansion of k in n
5.129 * [backup-simplify]: Simplify k into k
5.129 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.129 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.129 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.129 * [taylor]: Taking taylor expansion of 2 in n
5.129 * [backup-simplify]: Simplify 2 into 2
5.129 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.129 * [taylor]: Taking taylor expansion of PI in n
5.129 * [backup-simplify]: Simplify PI into PI
5.129 * [taylor]: Taking taylor expansion of n in n
5.129 * [backup-simplify]: Simplify 0 into 0
5.129 * [backup-simplify]: Simplify 1 into 1
5.129 * [backup-simplify]: Simplify (/ PI 1) into PI
5.129 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.130 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.130 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.130 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.131 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.132 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
5.133 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.133 * [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)))))
5.134 * [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))))))
5.135 * [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)))))))
5.136 * [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)))))))
5.137 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.137 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.138 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.138 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.139 * [backup-simplify]: Simplify (- 0) into 0
5.139 * [backup-simplify]: Simplify (+ 0 0) into 0
5.140 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.140 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
5.141 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0
5.143 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.144 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
5.144 * [backup-simplify]: Simplify (- 0) into 0
5.144 * [backup-simplify]: Simplify 0 into 0
5.144 * [backup-simplify]: Simplify 0 into 0
5.146 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.147 * [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))))))))
5.147 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
5.147 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
5.147 * [taylor]: Taking taylor expansion of +nan.0 in n
5.147 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.147 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
5.147 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
5.147 * [taylor]: Taking taylor expansion of 1/2 in n
5.147 * [backup-simplify]: Simplify 1/2 into 1/2
5.147 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
5.147 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.147 * [taylor]: Taking taylor expansion of 1 in n
5.147 * [backup-simplify]: Simplify 1 into 1
5.147 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.147 * [taylor]: Taking taylor expansion of k in n
5.147 * [backup-simplify]: Simplify k into k
5.147 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.147 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.147 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.147 * [taylor]: Taking taylor expansion of 2 in n
5.147 * [backup-simplify]: Simplify 2 into 2
5.147 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.147 * [taylor]: Taking taylor expansion of PI in n
5.147 * [backup-simplify]: Simplify PI into PI
5.147 * [taylor]: Taking taylor expansion of n in n
5.147 * [backup-simplify]: Simplify 0 into 0
5.147 * [backup-simplify]: Simplify 1 into 1
5.148 * [backup-simplify]: Simplify (/ PI 1) into PI
5.148 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.149 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.149 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.149 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.150 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.150 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
5.151 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.152 * [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)))))
5.153 * [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))))))
5.153 * [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)))))))
5.154 * [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)))))))
5.157 * [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))))))))
5.157 * [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)))
5.157 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0
5.157 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
5.157 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
5.157 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
5.157 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
5.157 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
5.157 * [taylor]: Taking taylor expansion of 1/2 in n
5.157 * [backup-simplify]: Simplify 1/2 into 1/2
5.157 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.157 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.157 * [taylor]: Taking taylor expansion of k in n
5.157 * [backup-simplify]: Simplify k into k
5.157 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.157 * [taylor]: Taking taylor expansion of 1 in n
5.157 * [backup-simplify]: Simplify 1 into 1
5.157 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.157 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.157 * [taylor]: Taking taylor expansion of -2 in n
5.157 * [backup-simplify]: Simplify -2 into -2
5.157 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.157 * [taylor]: Taking taylor expansion of PI in n
5.157 * [backup-simplify]: Simplify PI into PI
5.157 * [taylor]: Taking taylor expansion of n in n
5.157 * [backup-simplify]: Simplify 0 into 0
5.158 * [backup-simplify]: Simplify 1 into 1
5.158 * [backup-simplify]: Simplify (/ PI 1) into PI
5.158 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.159 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.159 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.159 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
5.160 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.160 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.161 * [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)))))
5.161 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
5.161 * [taylor]: Taking taylor expansion of (/ -1 k) in n
5.161 * [taylor]: Taking taylor expansion of -1 in n
5.161 * [backup-simplify]: Simplify -1 into -1
5.161 * [taylor]: Taking taylor expansion of k in n
5.161 * [backup-simplify]: Simplify k into k
5.161 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
5.161 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
5.161 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
5.161 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
5.162 * [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)))
5.162 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
5.162 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
5.162 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
5.162 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
5.162 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
5.162 * [taylor]: Taking taylor expansion of 1/2 in k
5.162 * [backup-simplify]: Simplify 1/2 into 1/2
5.162 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.162 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.162 * [taylor]: Taking taylor expansion of k in k
5.162 * [backup-simplify]: Simplify 0 into 0
5.162 * [backup-simplify]: Simplify 1 into 1
5.163 * [backup-simplify]: Simplify (/ 1 1) into 1
5.163 * [taylor]: Taking taylor expansion of 1 in k
5.163 * [backup-simplify]: Simplify 1 into 1
5.163 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
5.163 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
5.163 * [taylor]: Taking taylor expansion of -2 in k
5.163 * [backup-simplify]: Simplify -2 into -2
5.163 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.163 * [taylor]: Taking taylor expansion of PI in k
5.163 * [backup-simplify]: Simplify PI into PI
5.163 * [taylor]: Taking taylor expansion of n in k
5.163 * [backup-simplify]: Simplify n into n
5.163 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.163 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
5.163 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
5.163 * [backup-simplify]: Simplify (+ 1 0) into 1
5.164 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.164 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
5.164 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
5.164 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.164 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.164 * [taylor]: Taking taylor expansion of -1 in k
5.164 * [backup-simplify]: Simplify -1 into -1
5.164 * [taylor]: Taking taylor expansion of k in k
5.164 * [backup-simplify]: Simplify 0 into 0
5.164 * [backup-simplify]: Simplify 1 into 1
5.164 * [backup-simplify]: Simplify (/ -1 1) into -1
5.164 * [backup-simplify]: Simplify (sqrt 0) into 0
5.165 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.165 * [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)))))
5.165 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
5.165 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
5.165 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
5.165 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
5.165 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
5.166 * [taylor]: Taking taylor expansion of 1/2 in k
5.166 * [backup-simplify]: Simplify 1/2 into 1/2
5.166 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.166 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.166 * [taylor]: Taking taylor expansion of k in k
5.166 * [backup-simplify]: Simplify 0 into 0
5.166 * [backup-simplify]: Simplify 1 into 1
5.166 * [backup-simplify]: Simplify (/ 1 1) into 1
5.166 * [taylor]: Taking taylor expansion of 1 in k
5.166 * [backup-simplify]: Simplify 1 into 1
5.166 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
5.166 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
5.166 * [taylor]: Taking taylor expansion of -2 in k
5.166 * [backup-simplify]: Simplify -2 into -2
5.166 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.166 * [taylor]: Taking taylor expansion of PI in k
5.166 * [backup-simplify]: Simplify PI into PI
5.166 * [taylor]: Taking taylor expansion of n in k
5.166 * [backup-simplify]: Simplify n into n
5.166 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.167 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
5.167 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
5.167 * [backup-simplify]: Simplify (+ 1 0) into 1
5.168 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.168 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
5.168 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
5.168 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.168 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.168 * [taylor]: Taking taylor expansion of -1 in k
5.168 * [backup-simplify]: Simplify -1 into -1
5.168 * [taylor]: Taking taylor expansion of k in k
5.168 * [backup-simplify]: Simplify 0 into 0
5.168 * [backup-simplify]: Simplify 1 into 1
5.169 * [backup-simplify]: Simplify (/ -1 1) into -1
5.169 * [backup-simplify]: Simplify (sqrt 0) into 0
5.170 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.171 * [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)))))
5.171 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
5.171 * [taylor]: Taking taylor expansion of +nan.0 in n
5.171 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.171 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
5.171 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
5.171 * [taylor]: Taking taylor expansion of 1/2 in n
5.171 * [backup-simplify]: Simplify 1/2 into 1/2
5.171 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
5.171 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.171 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.171 * [taylor]: Taking taylor expansion of -2 in n
5.171 * [backup-simplify]: Simplify -2 into -2
5.171 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.171 * [taylor]: Taking taylor expansion of PI in n
5.171 * [backup-simplify]: Simplify PI into PI
5.171 * [taylor]: Taking taylor expansion of n in n
5.171 * [backup-simplify]: Simplify 0 into 0
5.171 * [backup-simplify]: Simplify 1 into 1
5.172 * [backup-simplify]: Simplify (/ PI 1) into PI
5.172 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.173 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.173 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.173 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.174 * [taylor]: Taking taylor expansion of k in n
5.174 * [backup-simplify]: Simplify k into k
5.174 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.174 * [taylor]: Taking taylor expansion of 1 in n
5.174 * [backup-simplify]: Simplify 1 into 1
5.175 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.175 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.176 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
5.178 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.179 * [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)))))
5.180 * [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))))))
5.181 * [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))))))
5.182 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
5.185 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.186 * [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))))))
5.187 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
5.187 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
5.187 * [taylor]: Taking taylor expansion of +nan.0 in n
5.187 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.187 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
5.187 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
5.187 * [taylor]: Taking taylor expansion of 1/2 in n
5.187 * [backup-simplify]: Simplify 1/2 into 1/2
5.187 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
5.187 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.187 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.187 * [taylor]: Taking taylor expansion of -2 in n
5.187 * [backup-simplify]: Simplify -2 into -2
5.187 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.187 * [taylor]: Taking taylor expansion of PI in n
5.187 * [backup-simplify]: Simplify PI into PI
5.187 * [taylor]: Taking taylor expansion of n in n
5.187 * [backup-simplify]: Simplify 0 into 0
5.187 * [backup-simplify]: Simplify 1 into 1
5.188 * [backup-simplify]: Simplify (/ PI 1) into PI
5.188 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.189 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.189 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.189 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.189 * [taylor]: Taking taylor expansion of k in n
5.189 * [backup-simplify]: Simplify k into k
5.189 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.189 * [taylor]: Taking taylor expansion of 1 in n
5.189 * [backup-simplify]: Simplify 1 into 1
5.191 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.191 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.192 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
5.193 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.195 * [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)))))
5.196 * [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))))))
5.197 * [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)))))))
5.199 * [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)))))))
5.200 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.201 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.201 * [backup-simplify]: Simplify (+ 0 0) into 0
5.202 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.203 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.208 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
5.209 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0
5.211 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0
5.213 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.215 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0
5.215 * [backup-simplify]: Simplify 0 into 0
5.216 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.221 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.222 * [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))))))
5.222 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
5.222 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
5.223 * [taylor]: Taking taylor expansion of +nan.0 in n
5.223 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.223 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
5.223 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
5.223 * [taylor]: Taking taylor expansion of 1/2 in n
5.223 * [backup-simplify]: Simplify 1/2 into 1/2
5.223 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
5.223 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.223 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.223 * [taylor]: Taking taylor expansion of -2 in n
5.223 * [backup-simplify]: Simplify -2 into -2
5.223 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.223 * [taylor]: Taking taylor expansion of PI in n
5.223 * [backup-simplify]: Simplify PI into PI
5.223 * [taylor]: Taking taylor expansion of n in n
5.223 * [backup-simplify]: Simplify 0 into 0
5.223 * [backup-simplify]: Simplify 1 into 1
5.224 * [backup-simplify]: Simplify (/ PI 1) into PI
5.224 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.225 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.225 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.225 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.225 * [taylor]: Taking taylor expansion of k in n
5.225 * [backup-simplify]: Simplify k into k
5.225 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.225 * [taylor]: Taking taylor expansion of 1 in n
5.226 * [backup-simplify]: Simplify 1 into 1
5.227 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.227 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.229 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
5.230 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.231 * [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)))))
5.233 * [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))))))
5.234 * [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)))))))
5.235 * [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)))))))
5.240 * [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))))))))))))
5.240 * * * [progress]: simplifying candidates
5.241 * * * * [progress]: [ 1 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
5.241 * * * * [progress]: [ 2 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
5.241 * * * * [progress]: [ 3 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
5.241 * * * * [progress]: [ 4 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
5.241 * * * * [progress]: [ 5 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
5.241 * * * * [progress]: [ 6 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
5.241 * * * * [progress]: [ 7 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
5.241 * * * * [progress]: [ 8 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))))>
5.241 * * * * [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)))))>
5.241 * * * * [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)))))>
5.241 * * * * [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)))))>
5.241 * * * * [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)))))>
5.243 * * * * [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))))>
5.243 * * * * [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)))))>
5.243 * * * * [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)))))>
5.243 * * * * [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))))>
5.243 * * * * [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)))))>
5.243 * * * * [progress]: [ 18 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
5.243 * * * * [progress]: [ 19 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (- 1 k) 2))))>
5.243 * * * * [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)))))>
5.243 * * * * [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)))))>
5.243 * * * * [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))))>
5.243 * * * * [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)))))>
5.244 * * * * [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)))))>
5.244 * * * * [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))))>
5.244 * * * * [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)))))>
5.244 * * * * [progress]: [ 27 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
5.244 * * * * [progress]: [ 28 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (- 1 k) 2))))>
5.244 * * * * [progress]: [ 29 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
5.244 * * * * [progress]: [ 30 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (- 1 k)) (/ 1 2))))>
5.244 * * * * [progress]: [ 31 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))))>
5.244 * * * * [progress]: [ 32 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (- 1 k) 2)) 1)))>
5.244 * * * * [progress]: [ 33 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.244 * * * * [progress]: [ 34 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (log (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.244 * * * * [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))))))>
5.244 * * * * [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))))))>
5.245 * * * * [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))))))>
5.245 * * * * [progress]: [ 38 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.245 * * * * [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)))))>
5.245 * * * * [progress]: [ 40 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (posit16->real (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.245 * * * * [progress]: [ 41 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
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5.245 * * * * [progress]: [ 44 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (+ (+ (log 2) (log PI)) (log n))) (/ (- 1 k) 2))))>
5.245 * * * * [progress]: [ 45 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (+ (log (* 2 PI)) (log n))) (/ (- 1 k) 2))))>
5.245 * * * * [progress]: [ 46 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (log (* (* 2 PI) n))) (/ (- 1 k) 2))))>
5.245 * * * * [progress]: [ 47 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (log (exp (* (* 2 PI) n))) (/ (- 1 k) 2))))>
5.245 * * * * [progress]: [ 48 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))) (/ (- 1 k) 2))))>
5.245 * * * * [progress]: [ 49 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))) (/ (- 1 k) 2))))>
5.246 * * * * [progress]: [ 50 / 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))))>
5.246 * * * * [progress]: [ 51 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))) (/ (- 1 k) 2))))>
5.246 * * * * [progress]: [ 52 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (sqrt (* (* 2 PI) n)) (sqrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
5.246 * * * * [progress]: [ 53 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 1 (* (* 2 PI) n)) (/ (- 1 k) 2))))>
5.246 * * * * [progress]: [ 54 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1 k) 2))))>
5.246 * * * * [progress]: [ 55 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (sqrt n)) (sqrt n)) (/ (- 1 k) 2))))>
5.246 * * * * [progress]: [ 56 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) 1) n) (/ (- 1 k) 2))))>
5.246 * * * * [progress]: [ 57 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* PI n)) (/ (- 1 k) 2))))>
5.246 * * * * [progress]: [ 58 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (posit16->real (real->posit16 (* (* 2 PI) n))) (/ (- 1 k) 2))))>
5.246 * * * * [progress]: [ 59 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))>
5.246 * * * * [progress]: [ 60 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) -1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.246 * * * * [progress]: [ 61 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.246 * * * * [progress]: [ 62 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) (- 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.246 * * * * [progress]: [ 63 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow k (- (/ 1 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.246 * * * * [progress]: [ 64 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (/ 1 (sqrt k)) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.247 * * * * [progress]: [ 65 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (- (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.247 * * * * [progress]: [ 66 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (- 0 (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.247 * * * * [progress]: [ 67 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (- (log 1) (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.247 * * * * [progress]: [ 68 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (log (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.247 * * * * [progress]: [ 69 / 188 ] simplifiying candidate #<alt (λ (k n) (* (log (exp (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.247 * * * * [progress]: [ 70 / 188 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.247 * * * * [progress]: [ 71 / 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))))>
5.247 * * * * [progress]: [ 72 / 188 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.247 * * * * [progress]: [ 73 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.247 * * * * [progress]: [ 74 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (- 1) (- (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.247 * * * * [progress]: [ 75 / 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))))>
5.247 * * * * [progress]: [ 76 / 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))))>
5.247 * * * * [progress]: [ 77 / 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))))>
5.247 * * * * [progress]: [ 78 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (/ (cbrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.248 * * * * [progress]: [ 79 / 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))))>
5.248 * * * * [progress]: [ 80 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.248 * * * * [progress]: [ 81 / 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))))>
5.248 * * * * [progress]: [ 82 / 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))))>
5.248 * * * * [progress]: [ 83 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.248 * * * * [progress]: [ 84 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt 1)) (/ (sqrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.248 * * * * [progress]: [ 85 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.248 * * * * [progress]: [ 86 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) 1) (/ (sqrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.248 * * * * [progress]: [ 87 / 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))))>
5.248 * * * * [progress]: [ 88 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1 (sqrt (cbrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.248 * * * * [progress]: [ 89 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.248 * * * * [progress]: [ 90 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt 1)) (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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5.248 * * * * [progress]: [ 92 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 1) (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.249 * * * * [progress]: [ 93 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* 1 (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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5.249 * * * * [progress]: [ 96 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.249 * * * * [progress]: [ 97 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.249 * * * * [progress]: [ 98 / 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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5.249 * * * * [progress]: [ 102 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt k) (cbrt 1))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.249 * * * * [progress]: [ 103 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt k) (sqrt 1))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.249 * * * * [progress]: [ 104 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt k) 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.249 * * * * [progress]: [ 105 / 188 ] simplifiying candidate #<alt (λ (k n) (* (posit16->real (real->posit16 (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.249 * * * * [progress]: [ 106 / 188 ] simplifiying candidate #<alt (λ (k n) (pow (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1))>
5.249 * * * * [progress]: [ 107 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
5.250 * * * * [progress]: [ 108 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
5.250 * * * * [progress]: [ 109 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
5.250 * * * * [progress]: [ 110 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
5.250 * * * * [progress]: [ 111 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.250 * * * * [progress]: [ 112 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
5.250 * * * * [progress]: [ 113 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
5.250 * * * * [progress]: [ 114 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
5.250 * * * * [progress]: [ 115 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
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5.250 * * * * [progress]: [ 117 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
5.250 * * * * [progress]: [ 118 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
5.250 * * * * [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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5.251 * * * * [progress]: [ 122 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
5.251 * * * * [progress]: [ 123 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
5.251 * * * * [progress]: [ 124 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
5.251 * * * * [progress]: [ 125 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
5.251 * * * * [progress]: [ 126 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.251 * * * * [progress]: [ 127 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.251 * * * * [progress]: [ 128 / 188 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.251 * * * * [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))))))>
5.251 * * * * [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))))))>
5.251 * * * * [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))))))>
5.251 * * * * [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))))))>
5.251 * * * * [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))))))>
5.251 * * * * [progress]: [ 134 / 188 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ 1 2))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))))>
5.251 * * * * [progress]: [ 135 / 188 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.251 * * * * [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))))))>
5.252 * * * * [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)))))>
5.252 * * * * [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))))))>
5.252 * * * * [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)))))>
5.252 * * * * [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))))))>
5.252 * * * * [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)))))>
5.252 * * * * [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))))))>
5.252 * * * * [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)))))>
5.252 * * * * [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))))))>
5.252 * * * * [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)))))>
5.252 * * * * [progress]: [ 146 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))))>
5.252 * * * * [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)))))>
5.252 * * * * [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)))))>
5.252 * * * * [progress]: [ 149 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.253 * * * * [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))))>
5.253 * * * * [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)))))>
5.253 * * * * [progress]: [ 152 / 188 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (sqrt k))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.253 * * * * [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)))))>
5.253 * * * * [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)))))>
5.253 * * * * [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)))))>
5.253 * * * * [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)))))>
5.253 * * * * [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)))))>
5.253 * * * * [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)))))>
5.253 * * * * [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)))))>
5.253 * * * * [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)))))>
5.253 * * * * [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)))))>
5.253 * * * * [progress]: [ 162 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt 1)) (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.253 * * * * [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)))))>
5.254 * * * * [progress]: [ 164 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) 1) (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.254 * * * * [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)))))>
5.254 * * * * [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)))))>
5.254 * * * * [progress]: [ 167 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.254 * * * * [progress]: [ 168 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.254 * * * * [progress]: [ 169 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.254 * * * * [progress]: [ 170 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.254 * * * * [progress]: [ 171 / 188 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.254 * * * * [progress]: [ 172 / 188 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.254 * * * * [progress]: [ 173 / 188 ] simplifiying candidate #<alt (λ (k n) (/ (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))) (pow (* (* 2 PI) n) (/ k 2))))>
5.254 * * * * [progress]: [ 174 / 188 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt k)))>
5.254 * * * * [progress]: [ 175 / 188 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.254 * * * * [progress]: [ 176 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
5.254 * * * * [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)))))))>
5.255 * * * * [progress]: [ 178 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))))>
5.255 * * * * [progress]: [ 179 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))>
5.255 * * * * [progress]: [ 180 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
5.255 * * * * [progress]: [ 181 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
5.255 * * * * [progress]: [ 182 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
5.255 * * * * [progress]: [ 183 / 188 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.255 * * * * [progress]: [ 184 / 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))))>
5.255 * * * * [progress]: [ 185 / 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))))>
5.255 * * * * [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))))))))))))))>
5.255 * * * * [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)))))))))>
5.255 * * * * [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)))))))))))))>
5.259 * [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)))
  (* (* 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))
  (- 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)))
  (+ (- (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))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
  (- (+ (* +nan.0 (* (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))))))))))))
5.265 * * [simplify]: iteration 0: 345 enodes
5.460 * * [simplify]: iteration 1: 930 enodes
5.694 * * [simplify]: iteration 2: 2001 enodes
6.120 * * [simplify]: iteration complete: 2001 enodes
6.121 * * [simplify]: Extracting #0: cost 96 inf + 0
6.122 * * [simplify]: Extracting #1: cost 330 inf + 3
6.126 * * [simplify]: Extracting #2: cost 579 inf + 6154
6.139 * * [simplify]: Extracting #3: cost 533 inf + 43676
6.173 * * [simplify]: Extracting #4: cost 344 inf + 117720
6.221 * * [simplify]: Extracting #5: cost 155 inf + 185076
6.281 * * [simplify]: Extracting #6: cost 63 inf + 220369
6.699 * * [simplify]: Extracting #7: cost 15 inf + 248942
6.742 * * [simplify]: Extracting #8: cost 0 inf + 258292
6.821 * * [simplify]: Extracting #9: cost 0 inf + 256272
6.861 * [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)) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* n (* 2 PI)) (+ (sqrt k) 1))
  (pow (* n (* 2 PI)) (/ (+ (sqrt k) 1) (* (cbrt 2) (cbrt 2))))
  (pow (* n (* 2 PI)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* n (* 2 PI)) (+ (sqrt k) 1))
  (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 (* 2 PI) (/ (- 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)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (log (* n (* 2 PI)))
  (log (* n (* 2 PI)))
  (log (* n (* 2 PI)))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* (* (* (* PI PI) PI) (* 2 4)) (* n n)) n)
  (* (* (* 2 PI) (* (* 2 PI) (* 2 PI))) (* (* n n) n))
  (* (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)))
  (* (* (cbrt n) (cbrt n)) (* 2 PI))
  (* (* 2 PI) (sqrt n))
  (* 2 PI)
  (* PI n)
  (real->posit16 (* n (* 2 PI)))
  -1/2
  -1
  -1/2
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (exp (/ 1 (sqrt k)))
  (/ 1 (* k (sqrt k)))
  (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
  (cbrt (/ 1 (sqrt k)))
  (* (/ (/ 1 (sqrt k)) (sqrt k)) (/ 1 (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)))
  (- (- (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)) (* (/ (- 1 k) 2) (log (* n (* 2 PI))))))
  (exp (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (/ (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 3) (* k (sqrt k)))
  (* (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 3) (* (/ (/ 1 (sqrt k)) (sqrt k)) (/ 1 (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 (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k))))
  (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k))))
  (* (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 (* 2 PI) (/ (- 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))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (/ 1 (sqrt k))))
  (* (sqrt (/ 1 (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (/ (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)))
  (- (+ (+ (* (* (log (* 2 PI)) (* (* (log n) (* k k)) (exp (* (log (* n (* 2 PI))) 1/2)))) 1/4) (* (* (exp (* (log (* n (* 2 PI))) 1/2)) (* (* (log n) (log n)) (* k k))) 1/8)) (+ (exp (* (log (* n (* 2 PI))) 1/2)) (* 1/8 (* (* (* (exp (* (log (* n (* 2 PI))) 1/2)) (* k k)) (log (* 2 PI))) (log (* 2 PI)))))) (* 1/2 (* k (+ (* (exp (* (log (* n (* 2 PI))) 1/2)) (log n)) (* (log (* 2 PI)) (exp (* (log (* n (* 2 PI))) 1/2)))))))
  (exp (* (* 1/2 (- 1 k)) (log (* n (* 2 PI)))))
  (exp (* (* 1/2 (- (log (* PI -2)) (log (/ -1 n)))) (- 1 k)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (- (+ (- (* (* k k) +nan.0) +nan.0) (* k +nan.0)))
  (+ (/ (- +nan.0) (* k k)) (- (/ +nan.0 k) (/ +nan.0 (* (* k k) k))))
  (- (- (/ +nan.0 (* k k)) (- (/ +nan.0 k) +nan.0)))
  (+ (* (* +nan.0 (sqrt 2)) (- (* (* PI n) k))) (+ (- (* (* +nan.0 (sqrt 2)) (* PI n)) (* +nan.0 (* (* (* (* PI n) k) (sqrt 2)) (log (* 2 PI))))) (* (* +nan.0 (sqrt 2)) (- (* (* PI n) (* k (log n))) (* (* PI n) (* PI n))))))
  (+ (* (- +nan.0) (/ (exp (* (* 1/2 (- 1 k)) (log (* n (* 2 PI))))) k)) (- (/ (* +nan.0 (exp (* (* 1/2 (- 1 k)) (log (* n (* 2 PI)))))) (* k k)) (* (/ +nan.0 (* k k)) (/ (exp (* (* 1/2 (- 1 k)) (log (* n (* 2 PI))))) k))))
  (- (- (* +nan.0 (/ (exp (* (* 1/2 (- (log (* PI -2)) (log (/ -1 n)))) (- 1 k))) k)) (* +nan.0 (+ (- (exp (* (* 1/2 (- (log (* PI -2)) (log (/ -1 n)))) (- 1 k)))) (/ (exp (* (* 1/2 (- (log (* PI -2)) (log (/ -1 n)))) (- 1 k))) (* k k))))))
6.873 * * * [progress]: adding candidates to table
7.605 * * [progress]: iteration 3 / 4
7.605 * * * [progress]: picking best candidate
7.644 * * * * [pick]: Picked  #<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))))>
7.645 * * * [progress]: localizing error
7.684 * * * [progress]: generating rewritten candidates
7.684 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1)
7.712 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1)
7.744 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1)
7.767 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1)
7.782 * * * [progress]: generating series expansions
7.782 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1)
7.782 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k))))
7.782 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0
7.782 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k
7.782 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k
7.782 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k
7.782 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k
7.782 * [taylor]: Taking taylor expansion of 1/2 in k
7.782 * [backup-simplify]: Simplify 1/2 into 1/2
7.782 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
7.782 * [taylor]: Taking taylor expansion of 1/2 in k
7.782 * [backup-simplify]: Simplify 1/2 into 1/2
7.782 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
7.782 * [taylor]: Taking taylor expansion of 1/2 in k
7.782 * [backup-simplify]: Simplify 1/2 into 1/2
7.782 * [taylor]: Taking taylor expansion of k in k
7.782 * [backup-simplify]: Simplify 0 into 0
7.782 * [backup-simplify]: Simplify 1 into 1
7.782 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
7.782 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
7.782 * [taylor]: Taking taylor expansion of 2 in k
7.782 * [backup-simplify]: Simplify 2 into 2
7.783 * [taylor]: Taking taylor expansion of (* n PI) in k
7.783 * [taylor]: Taking taylor expansion of n in k
7.783 * [backup-simplify]: Simplify n into n
7.783 * [taylor]: Taking taylor expansion of PI in k
7.783 * [backup-simplify]: Simplify PI into PI
7.783 * [backup-simplify]: Simplify (* n PI) into (* n PI)
7.783 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
7.783 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
7.783 * [backup-simplify]: Simplify (* 1/2 0) into 0
7.783 * [backup-simplify]: Simplify (- 0) into 0
7.784 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
7.784 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
7.784 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
7.784 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
7.784 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
7.784 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
7.784 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
7.784 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
7.784 * [taylor]: Taking taylor expansion of 1/2 in n
7.784 * [backup-simplify]: Simplify 1/2 into 1/2
7.784 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
7.784 * [taylor]: Taking taylor expansion of 1/2 in n
7.784 * [backup-simplify]: Simplify 1/2 into 1/2
7.784 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
7.784 * [taylor]: Taking taylor expansion of 1/2 in n
7.784 * [backup-simplify]: Simplify 1/2 into 1/2
7.784 * [taylor]: Taking taylor expansion of k in n
7.784 * [backup-simplify]: Simplify k into k
7.784 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
7.784 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
7.784 * [taylor]: Taking taylor expansion of 2 in n
7.784 * [backup-simplify]: Simplify 2 into 2
7.784 * [taylor]: Taking taylor expansion of (* n PI) in n
7.784 * [taylor]: Taking taylor expansion of n in n
7.784 * [backup-simplify]: Simplify 0 into 0
7.784 * [backup-simplify]: Simplify 1 into 1
7.785 * [taylor]: Taking taylor expansion of PI in n
7.785 * [backup-simplify]: Simplify PI into PI
7.785 * [backup-simplify]: Simplify (* 0 PI) into 0
7.785 * [backup-simplify]: Simplify (* 2 0) into 0
7.786 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.787 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
7.788 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.788 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
7.788 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
7.788 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
7.788 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
7.789 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.790 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
7.790 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
7.790 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
7.791 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
7.791 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
7.791 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
7.791 * [taylor]: Taking taylor expansion of 1/2 in n
7.791 * [backup-simplify]: Simplify 1/2 into 1/2
7.791 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
7.791 * [taylor]: Taking taylor expansion of 1/2 in n
7.791 * [backup-simplify]: Simplify 1/2 into 1/2
7.791 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
7.791 * [taylor]: Taking taylor expansion of 1/2 in n
7.791 * [backup-simplify]: Simplify 1/2 into 1/2
7.791 * [taylor]: Taking taylor expansion of k in n
7.791 * [backup-simplify]: Simplify k into k
7.791 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
7.791 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
7.791 * [taylor]: Taking taylor expansion of 2 in n
7.791 * [backup-simplify]: Simplify 2 into 2
7.791 * [taylor]: Taking taylor expansion of (* n PI) in n
7.791 * [taylor]: Taking taylor expansion of n in n
7.791 * [backup-simplify]: Simplify 0 into 0
7.791 * [backup-simplify]: Simplify 1 into 1
7.791 * [taylor]: Taking taylor expansion of PI in n
7.791 * [backup-simplify]: Simplify PI into PI
7.794 * [backup-simplify]: Simplify (* 0 PI) into 0
7.794 * [backup-simplify]: Simplify (* 2 0) into 0
7.795 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.796 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
7.797 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.797 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
7.797 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
7.797 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
7.797 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
7.798 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.799 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
7.799 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
7.799 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k
7.799 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
7.799 * [taylor]: Taking taylor expansion of 1/2 in k
7.799 * [backup-simplify]: Simplify 1/2 into 1/2
7.799 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
7.800 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 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 (* 1/2 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 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 n) (log (* 2 PI))) in k
7.800 * [taylor]: Taking taylor expansion of (log n) in k
7.800 * [taylor]: Taking taylor expansion of n in k
7.800 * [backup-simplify]: Simplify n into n
7.800 * [backup-simplify]: Simplify (log n) into (log n)
7.800 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
7.800 * [taylor]: Taking taylor expansion of (* 2 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 PI in k
7.800 * [backup-simplify]: Simplify PI into PI
7.800 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.801 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.801 * [backup-simplify]: Simplify (* 1/2 0) into 0
7.801 * [backup-simplify]: Simplify (- 0) into 0
7.802 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
7.802 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.803 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
7.804 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI))))
7.804 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
7.805 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
7.806 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
7.806 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
7.808 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.808 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
7.808 * [backup-simplify]: Simplify (- 0) into 0
7.809 * [backup-simplify]: Simplify (+ 0 0) into 0
7.809 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0
7.810 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.811 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
7.812 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.812 * [taylor]: Taking taylor expansion of 0 in k
7.812 * [backup-simplify]: Simplify 0 into 0
7.812 * [backup-simplify]: Simplify 0 into 0
7.812 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
7.813 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
7.814 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.814 * [backup-simplify]: Simplify (+ 0 0) into 0
7.815 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
7.815 * [backup-simplify]: Simplify (- 1/2) into -1/2
7.815 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
7.816 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
7.818 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI)))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))))
7.820 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
7.823 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
7.824 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
7.825 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
7.827 * [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
7.827 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
7.828 * [backup-simplify]: Simplify (- 0) into 0
7.828 * [backup-simplify]: Simplify (+ 0 0) into 0
7.828 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0
7.829 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.830 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
7.832 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.832 * [taylor]: Taking taylor expansion of 0 in k
7.832 * [backup-simplify]: Simplify 0 into 0
7.832 * [backup-simplify]: Simplify 0 into 0
7.832 * [backup-simplify]: Simplify 0 into 0
7.833 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
7.834 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
7.836 * [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
7.836 * [backup-simplify]: Simplify (+ 0 0) into 0
7.836 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
7.837 * [backup-simplify]: Simplify (- 0) into 0
7.837 * [backup-simplify]: Simplify (+ 0 0) into 0
7.838 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
7.840 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI))))))) into 0
7.843 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
7.846 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
7.851 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
7.852 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (/ (- 1/2 (/ (/ 1 k) 2)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))))
7.852 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
7.852 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k
7.852 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k
7.852 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k
7.852 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k
7.852 * [taylor]: Taking taylor expansion of 1/2 in k
7.852 * [backup-simplify]: Simplify 1/2 into 1/2
7.852 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
7.852 * [taylor]: Taking taylor expansion of 1/2 in k
7.852 * [backup-simplify]: Simplify 1/2 into 1/2
7.852 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
7.852 * [taylor]: Taking taylor expansion of 1/2 in k
7.852 * [backup-simplify]: Simplify 1/2 into 1/2
7.852 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.852 * [taylor]: Taking taylor expansion of k in k
7.852 * [backup-simplify]: Simplify 0 into 0
7.852 * [backup-simplify]: Simplify 1 into 1
7.852 * [backup-simplify]: Simplify (/ 1 1) into 1
7.852 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
7.852 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
7.852 * [taylor]: Taking taylor expansion of 2 in k
7.852 * [backup-simplify]: Simplify 2 into 2
7.852 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.852 * [taylor]: Taking taylor expansion of PI in k
7.852 * [backup-simplify]: Simplify PI into PI
7.852 * [taylor]: Taking taylor expansion of n in k
7.852 * [backup-simplify]: Simplify n into n
7.852 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.852 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
7.852 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
7.853 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.853 * [backup-simplify]: Simplify (- 1/2) into -1/2
7.853 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
7.853 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4
7.854 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
7.854 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))))
7.854 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
7.854 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
7.854 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
7.854 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
7.854 * [taylor]: Taking taylor expansion of 1/2 in n
7.854 * [backup-simplify]: Simplify 1/2 into 1/2
7.854 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
7.854 * [taylor]: Taking taylor expansion of 1/2 in n
7.854 * [backup-simplify]: Simplify 1/2 into 1/2
7.854 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
7.854 * [taylor]: Taking taylor expansion of 1/2 in n
7.854 * [backup-simplify]: Simplify 1/2 into 1/2
7.854 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.854 * [taylor]: Taking taylor expansion of k in n
7.854 * [backup-simplify]: Simplify k into k
7.854 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.854 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
7.854 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
7.854 * [taylor]: Taking taylor expansion of 2 in n
7.854 * [backup-simplify]: Simplify 2 into 2
7.854 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.854 * [taylor]: Taking taylor expansion of PI in n
7.854 * [backup-simplify]: Simplify PI into PI
7.854 * [taylor]: Taking taylor expansion of n in n
7.854 * [backup-simplify]: Simplify 0 into 0
7.854 * [backup-simplify]: Simplify 1 into 1
7.854 * [backup-simplify]: Simplify (/ PI 1) into PI
7.855 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.855 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.855 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
7.856 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
7.856 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
7.856 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
7.857 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.857 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
7.858 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
7.858 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
7.858 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
7.858 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
7.858 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
7.858 * [taylor]: Taking taylor expansion of 1/2 in n
7.858 * [backup-simplify]: Simplify 1/2 into 1/2
7.858 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
7.858 * [taylor]: Taking taylor expansion of 1/2 in n
7.858 * [backup-simplify]: Simplify 1/2 into 1/2
7.858 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
7.858 * [taylor]: Taking taylor expansion of 1/2 in n
7.858 * [backup-simplify]: Simplify 1/2 into 1/2
7.858 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.858 * [taylor]: Taking taylor expansion of k in n
7.858 * [backup-simplify]: Simplify k into k
7.858 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.858 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
7.858 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
7.858 * [taylor]: Taking taylor expansion of 2 in n
7.858 * [backup-simplify]: Simplify 2 into 2
7.858 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.858 * [taylor]: Taking taylor expansion of PI in n
7.858 * [backup-simplify]: Simplify PI into PI
7.858 * [taylor]: Taking taylor expansion of n in n
7.859 * [backup-simplify]: Simplify 0 into 0
7.859 * [backup-simplify]: Simplify 1 into 1
7.859 * [backup-simplify]: Simplify (/ PI 1) into PI
7.859 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.860 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.860 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
7.860 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
7.860 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
7.860 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
7.861 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.862 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
7.862 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
7.863 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k
7.863 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
7.863 * [taylor]: Taking taylor expansion of 1/2 in k
7.863 * [backup-simplify]: Simplify 1/2 into 1/2
7.863 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
7.863 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
7.863 * [taylor]: Taking taylor expansion of 1/2 in k
7.863 * [backup-simplify]: Simplify 1/2 into 1/2
7.863 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
7.863 * [taylor]: Taking taylor expansion of 1/2 in k
7.863 * [backup-simplify]: Simplify 1/2 into 1/2
7.863 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.863 * [taylor]: Taking taylor expansion of k in k
7.863 * [backup-simplify]: Simplify 0 into 0
7.863 * [backup-simplify]: Simplify 1 into 1
7.863 * [backup-simplify]: Simplify (/ 1 1) into 1
7.863 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
7.863 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
7.863 * [taylor]: Taking taylor expansion of (* 2 PI) in k
7.863 * [taylor]: Taking taylor expansion of 2 in k
7.863 * [backup-simplify]: Simplify 2 into 2
7.863 * [taylor]: Taking taylor expansion of PI in k
7.863 * [backup-simplify]: Simplify PI into PI
7.863 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.864 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.864 * [taylor]: Taking taylor expansion of (log n) in k
7.864 * [taylor]: Taking taylor expansion of n in k
7.864 * [backup-simplify]: Simplify n into n
7.864 * [backup-simplify]: Simplify (log n) into (log n)
7.865 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.865 * [backup-simplify]: Simplify (- 1/2) into -1/2
7.865 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
7.865 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.866 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
7.867 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
7.867 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
7.868 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
7.869 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
7.870 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.870 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
7.871 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.871 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.871 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
7.872 * [backup-simplify]: Simplify (- 0) into 0
7.872 * [backup-simplify]: Simplify (+ 0 0) into 0
7.872 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
7.873 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.874 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
7.875 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.875 * [taylor]: Taking taylor expansion of 0 in k
7.875 * [backup-simplify]: Simplify 0 into 0
7.875 * [backup-simplify]: Simplify 0 into 0
7.875 * [backup-simplify]: Simplify 0 into 0
7.876 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.876 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
7.878 * [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
7.879 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.879 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
7.880 * [backup-simplify]: Simplify (- 0) into 0
7.880 * [backup-simplify]: Simplify (+ 0 0) into 0
7.880 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
7.884 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.885 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
7.886 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.886 * [taylor]: Taking taylor expansion of 0 in k
7.886 * [backup-simplify]: Simplify 0 into 0
7.886 * [backup-simplify]: Simplify 0 into 0
7.886 * [backup-simplify]: Simplify 0 into 0
7.886 * [backup-simplify]: Simplify 0 into 0
7.887 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.888 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.891 * [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
7.891 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.892 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
7.892 * [backup-simplify]: Simplify (- 0) into 0
7.892 * [backup-simplify]: Simplify (+ 0 0) into 0
7.893 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0
7.894 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
7.895 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
7.897 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 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
7.897 * [taylor]: Taking taylor expansion of 0 in k
7.897 * [backup-simplify]: Simplify 0 into 0
7.897 * [backup-simplify]: Simplify 0 into 0
7.898 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))
7.898 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)))
7.898 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0
7.898 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
7.898 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k
7.898 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k
7.898 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
7.898 * [taylor]: Taking taylor expansion of 1/2 in k
7.898 * [backup-simplify]: Simplify 1/2 into 1/2
7.898 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
7.898 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
7.898 * [taylor]: Taking taylor expansion of 1/2 in k
7.898 * [backup-simplify]: Simplify 1/2 into 1/2
7.898 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.898 * [taylor]: Taking taylor expansion of k in k
7.898 * [backup-simplify]: Simplify 0 into 0
7.898 * [backup-simplify]: Simplify 1 into 1
7.898 * [backup-simplify]: Simplify (/ 1 1) into 1
7.898 * [taylor]: Taking taylor expansion of 1/2 in k
7.898 * [backup-simplify]: Simplify 1/2 into 1/2
7.898 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
7.898 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
7.898 * [taylor]: Taking taylor expansion of -2 in k
7.899 * [backup-simplify]: Simplify -2 into -2
7.899 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.899 * [taylor]: Taking taylor expansion of PI in k
7.899 * [backup-simplify]: Simplify PI into PI
7.899 * [taylor]: Taking taylor expansion of n in k
7.899 * [backup-simplify]: Simplify n into n
7.899 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.899 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
7.899 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
7.899 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.900 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
7.900 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
7.900 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
7.901 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
7.901 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
7.901 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
7.901 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
7.901 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
7.901 * [taylor]: Taking taylor expansion of 1/2 in n
7.901 * [backup-simplify]: Simplify 1/2 into 1/2
7.901 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
7.901 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
7.901 * [taylor]: Taking taylor expansion of 1/2 in n
7.901 * [backup-simplify]: Simplify 1/2 into 1/2
7.901 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.901 * [taylor]: Taking taylor expansion of k in n
7.901 * [backup-simplify]: Simplify k into k
7.901 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.901 * [taylor]: Taking taylor expansion of 1/2 in n
7.901 * [backup-simplify]: Simplify 1/2 into 1/2
7.901 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
7.901 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
7.901 * [taylor]: Taking taylor expansion of -2 in n
7.901 * [backup-simplify]: Simplify -2 into -2
7.901 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.901 * [taylor]: Taking taylor expansion of PI in n
7.901 * [backup-simplify]: Simplify PI into PI
7.901 * [taylor]: Taking taylor expansion of n in n
7.901 * [backup-simplify]: Simplify 0 into 0
7.901 * [backup-simplify]: Simplify 1 into 1
7.902 * [backup-simplify]: Simplify (/ PI 1) into PI
7.902 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.903 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
7.904 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
7.904 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
7.904 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
7.905 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.907 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
7.908 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
7.908 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
7.908 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
7.908 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
7.908 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
7.908 * [taylor]: Taking taylor expansion of 1/2 in n
7.908 * [backup-simplify]: Simplify 1/2 into 1/2
7.908 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
7.908 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
7.908 * [taylor]: Taking taylor expansion of 1/2 in n
7.908 * [backup-simplify]: Simplify 1/2 into 1/2
7.908 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.908 * [taylor]: Taking taylor expansion of k in n
7.908 * [backup-simplify]: Simplify k into k
7.908 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.908 * [taylor]: Taking taylor expansion of 1/2 in n
7.908 * [backup-simplify]: Simplify 1/2 into 1/2
7.908 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
7.908 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
7.908 * [taylor]: Taking taylor expansion of -2 in n
7.908 * [backup-simplify]: Simplify -2 into -2
7.909 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.909 * [taylor]: Taking taylor expansion of PI in n
7.909 * [backup-simplify]: Simplify PI into PI
7.909 * [taylor]: Taking taylor expansion of n in n
7.909 * [backup-simplify]: Simplify 0 into 0
7.909 * [backup-simplify]: Simplify 1 into 1
7.909 * [backup-simplify]: Simplify (/ PI 1) into PI
7.910 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.911 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
7.911 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
7.911 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
7.911 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
7.913 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.914 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
7.915 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
7.915 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k
7.915 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
7.915 * [taylor]: Taking taylor expansion of 1/2 in k
7.915 * [backup-simplify]: Simplify 1/2 into 1/2
7.915 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
7.916 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
7.916 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
7.916 * [taylor]: Taking taylor expansion of 1/2 in k
7.916 * [backup-simplify]: Simplify 1/2 into 1/2
7.916 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.916 * [taylor]: Taking taylor expansion of k in k
7.916 * [backup-simplify]: Simplify 0 into 0
7.916 * [backup-simplify]: Simplify 1 into 1
7.917 * [backup-simplify]: Simplify (/ 1 1) into 1
7.917 * [taylor]: Taking taylor expansion of 1/2 in k
7.917 * [backup-simplify]: Simplify 1/2 into 1/2
7.917 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
7.917 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
7.917 * [taylor]: Taking taylor expansion of (* -2 PI) in k
7.917 * [taylor]: Taking taylor expansion of -2 in k
7.917 * [backup-simplify]: Simplify -2 into -2
7.917 * [taylor]: Taking taylor expansion of PI in k
7.917 * [backup-simplify]: Simplify PI into PI
7.917 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
7.918 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
7.918 * [taylor]: Taking taylor expansion of (log n) in k
7.918 * [taylor]: Taking taylor expansion of n in k
7.919 * [backup-simplify]: Simplify n into n
7.919 * [backup-simplify]: Simplify (log n) into (log n)
7.919 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
7.919 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
7.920 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.921 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
7.922 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
7.923 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n)))
7.924 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
7.926 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
7.927 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.928 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
7.929 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
7.930 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.930 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
7.931 * [backup-simplify]: Simplify (+ 0 0) into 0
7.931 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
7.933 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.934 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
7.936 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.936 * [taylor]: Taking taylor expansion of 0 in k
7.936 * [backup-simplify]: Simplify 0 into 0
7.936 * [backup-simplify]: Simplify 0 into 0
7.936 * [backup-simplify]: Simplify 0 into 0
7.937 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.939 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
7.942 * [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
7.942 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.943 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
7.944 * [backup-simplify]: Simplify (+ 0 0) into 0
7.944 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
7.946 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.947 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
7.950 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.950 * [taylor]: Taking taylor expansion of 0 in k
7.950 * [backup-simplify]: Simplify 0 into 0
7.950 * [backup-simplify]: Simplify 0 into 0
7.950 * [backup-simplify]: Simplify 0 into 0
7.950 * [backup-simplify]: Simplify 0 into 0
7.952 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.953 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.959 * [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
7.959 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.960 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
7.960 * [backup-simplify]: Simplify (+ 0 0) into 0
7.961 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
7.961 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
7.963 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
7.964 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 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
7.964 * [taylor]: Taking taylor expansion of 0 in k
7.964 * [backup-simplify]: Simplify 0 into 0
7.964 * [backup-simplify]: Simplify 0 into 0
7.965 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))
7.965 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1)
7.965 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k))))
7.965 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0
7.965 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k
7.965 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k
7.965 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k
7.965 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k
7.965 * [taylor]: Taking taylor expansion of 1/2 in k
7.966 * [backup-simplify]: Simplify 1/2 into 1/2
7.966 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
7.966 * [taylor]: Taking taylor expansion of 1/2 in k
7.966 * [backup-simplify]: Simplify 1/2 into 1/2
7.966 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
7.966 * [taylor]: Taking taylor expansion of 1/2 in k
7.966 * [backup-simplify]: Simplify 1/2 into 1/2
7.966 * [taylor]: Taking taylor expansion of k in k
7.966 * [backup-simplify]: Simplify 0 into 0
7.966 * [backup-simplify]: Simplify 1 into 1
7.966 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
7.966 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
7.966 * [taylor]: Taking taylor expansion of 2 in k
7.966 * [backup-simplify]: Simplify 2 into 2
7.966 * [taylor]: Taking taylor expansion of (* n PI) in k
7.966 * [taylor]: Taking taylor expansion of n in k
7.966 * [backup-simplify]: Simplify n into n
7.966 * [taylor]: Taking taylor expansion of PI in k
7.966 * [backup-simplify]: Simplify PI into PI
7.966 * [backup-simplify]: Simplify (* n PI) into (* n PI)
7.966 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
7.966 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
7.966 * [backup-simplify]: Simplify (* 1/2 0) into 0
7.966 * [backup-simplify]: Simplify (- 0) into 0
7.967 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
7.967 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
7.967 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
7.967 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
7.967 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
7.967 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
7.967 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
7.967 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
7.967 * [taylor]: Taking taylor expansion of 1/2 in n
7.967 * [backup-simplify]: Simplify 1/2 into 1/2
7.967 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
7.967 * [taylor]: Taking taylor expansion of 1/2 in n
7.967 * [backup-simplify]: Simplify 1/2 into 1/2
7.967 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
7.967 * [taylor]: Taking taylor expansion of 1/2 in n
7.967 * [backup-simplify]: Simplify 1/2 into 1/2
7.967 * [taylor]: Taking taylor expansion of k in n
7.967 * [backup-simplify]: Simplify k into k
7.967 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
7.967 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
7.967 * [taylor]: Taking taylor expansion of 2 in n
7.967 * [backup-simplify]: Simplify 2 into 2
7.967 * [taylor]: Taking taylor expansion of (* n PI) in n
7.967 * [taylor]: Taking taylor expansion of n in n
7.967 * [backup-simplify]: Simplify 0 into 0
7.967 * [backup-simplify]: Simplify 1 into 1
7.967 * [taylor]: Taking taylor expansion of PI in n
7.967 * [backup-simplify]: Simplify PI into PI
7.968 * [backup-simplify]: Simplify (* 0 PI) into 0
7.968 * [backup-simplify]: Simplify (* 2 0) into 0
7.969 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.970 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
7.971 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.971 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
7.971 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
7.971 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
7.971 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
7.972 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.973 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
7.973 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
7.973 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
7.973 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
7.973 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
7.973 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
7.973 * [taylor]: Taking taylor expansion of 1/2 in n
7.973 * [backup-simplify]: Simplify 1/2 into 1/2
7.973 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
7.973 * [taylor]: Taking taylor expansion of 1/2 in n
7.973 * [backup-simplify]: Simplify 1/2 into 1/2
7.973 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
7.973 * [taylor]: Taking taylor expansion of 1/2 in n
7.973 * [backup-simplify]: Simplify 1/2 into 1/2
7.973 * [taylor]: Taking taylor expansion of k in n
7.974 * [backup-simplify]: Simplify k into k
7.974 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
7.974 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
7.974 * [taylor]: Taking taylor expansion of 2 in n
7.974 * [backup-simplify]: Simplify 2 into 2
7.974 * [taylor]: Taking taylor expansion of (* n PI) in n
7.974 * [taylor]: Taking taylor expansion of n in n
7.974 * [backup-simplify]: Simplify 0 into 0
7.974 * [backup-simplify]: Simplify 1 into 1
7.974 * [taylor]: Taking taylor expansion of PI in n
7.974 * [backup-simplify]: Simplify PI into PI
7.974 * [backup-simplify]: Simplify (* 0 PI) into 0
7.974 * [backup-simplify]: Simplify (* 2 0) into 0
7.975 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.976 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
7.977 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.977 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
7.977 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
7.977 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
7.977 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
7.978 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.979 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
7.979 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
7.980 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k
7.980 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
7.980 * [taylor]: Taking taylor expansion of 1/2 in k
7.980 * [backup-simplify]: Simplify 1/2 into 1/2
7.980 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
7.980 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
7.980 * [taylor]: Taking taylor expansion of 1/2 in k
7.980 * [backup-simplify]: Simplify 1/2 into 1/2
7.980 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
7.980 * [taylor]: Taking taylor expansion of 1/2 in k
7.980 * [backup-simplify]: Simplify 1/2 into 1/2
7.980 * [taylor]: Taking taylor expansion of k in k
7.980 * [backup-simplify]: Simplify 0 into 0
7.980 * [backup-simplify]: Simplify 1 into 1
7.980 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
7.980 * [taylor]: Taking taylor expansion of (log n) in k
7.980 * [taylor]: Taking taylor expansion of n in k
7.980 * [backup-simplify]: Simplify n into n
7.980 * [backup-simplify]: Simplify (log n) into (log n)
7.980 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
7.980 * [taylor]: Taking taylor expansion of (* 2 PI) in k
7.980 * [taylor]: Taking taylor expansion of 2 in k
7.980 * [backup-simplify]: Simplify 2 into 2
7.980 * [taylor]: Taking taylor expansion of PI in k
7.980 * [backup-simplify]: Simplify PI into PI
7.980 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
7.981 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
7.981 * [backup-simplify]: Simplify (* 1/2 0) into 0
7.981 * [backup-simplify]: Simplify (- 0) into 0
7.982 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
7.982 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.983 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
7.984 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI))))
7.984 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
7.985 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
7.986 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
7.986 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
7.987 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.988 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
7.988 * [backup-simplify]: Simplify (- 0) into 0
7.988 * [backup-simplify]: Simplify (+ 0 0) into 0
7.989 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0
7.989 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
7.990 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
7.991 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.991 * [taylor]: Taking taylor expansion of 0 in k
7.991 * [backup-simplify]: Simplify 0 into 0
7.991 * [backup-simplify]: Simplify 0 into 0
7.992 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
7.992 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
7.995 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
7.996 * [backup-simplify]: Simplify (+ 0 0) into 0
7.996 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
7.996 * [backup-simplify]: Simplify (- 1/2) into -1/2
7.997 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
7.998 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
7.999 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI)))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))))
8.001 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
8.003 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
8.004 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
8.005 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
8.006 * [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
8.007 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
8.007 * [backup-simplify]: Simplify (- 0) into 0
8.007 * [backup-simplify]: Simplify (+ 0 0) into 0
8.008 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0
8.009 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
8.010 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
8.011 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
8.011 * [taylor]: Taking taylor expansion of 0 in k
8.011 * [backup-simplify]: Simplify 0 into 0
8.011 * [backup-simplify]: Simplify 0 into 0
8.011 * [backup-simplify]: Simplify 0 into 0
8.013 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
8.013 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
8.015 * [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
8.015 * [backup-simplify]: Simplify (+ 0 0) into 0
8.016 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
8.016 * [backup-simplify]: Simplify (- 0) into 0
8.016 * [backup-simplify]: Simplify (+ 0 0) into 0
8.018 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
8.020 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI))))))) into 0
8.022 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
8.025 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
8.031 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
8.031 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (/ (- 1/2 (/ (/ 1 k) 2)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))))
8.031 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
8.031 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k
8.031 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k
8.031 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k
8.031 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k
8.031 * [taylor]: Taking taylor expansion of 1/2 in k
8.031 * [backup-simplify]: Simplify 1/2 into 1/2
8.031 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
8.031 * [taylor]: Taking taylor expansion of 1/2 in k
8.032 * [backup-simplify]: Simplify 1/2 into 1/2
8.032 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
8.032 * [taylor]: Taking taylor expansion of 1/2 in k
8.032 * [backup-simplify]: Simplify 1/2 into 1/2
8.032 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.032 * [taylor]: Taking taylor expansion of k in k
8.032 * [backup-simplify]: Simplify 0 into 0
8.032 * [backup-simplify]: Simplify 1 into 1
8.032 * [backup-simplify]: Simplify (/ 1 1) into 1
8.032 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
8.032 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
8.032 * [taylor]: Taking taylor expansion of 2 in k
8.032 * [backup-simplify]: Simplify 2 into 2
8.032 * [taylor]: Taking taylor expansion of (/ PI n) in k
8.032 * [taylor]: Taking taylor expansion of PI in k
8.032 * [backup-simplify]: Simplify PI into PI
8.032 * [taylor]: Taking taylor expansion of n in k
8.032 * [backup-simplify]: Simplify n into n
8.032 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
8.032 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
8.032 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
8.032 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
8.033 * [backup-simplify]: Simplify (- 1/2) into -1/2
8.033 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
8.033 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4
8.033 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
8.033 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))))
8.033 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
8.033 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
8.033 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
8.034 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
8.034 * [taylor]: Taking taylor expansion of 1/2 in n
8.034 * [backup-simplify]: Simplify 1/2 into 1/2
8.034 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
8.034 * [taylor]: Taking taylor expansion of 1/2 in n
8.034 * [backup-simplify]: Simplify 1/2 into 1/2
8.034 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
8.034 * [taylor]: Taking taylor expansion of 1/2 in n
8.034 * [backup-simplify]: Simplify 1/2 into 1/2
8.034 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.034 * [taylor]: Taking taylor expansion of k in n
8.034 * [backup-simplify]: Simplify k into k
8.034 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.034 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
8.034 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
8.034 * [taylor]: Taking taylor expansion of 2 in n
8.034 * [backup-simplify]: Simplify 2 into 2
8.034 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.034 * [taylor]: Taking taylor expansion of PI in n
8.034 * [backup-simplify]: Simplify PI into PI
8.034 * [taylor]: Taking taylor expansion of n in n
8.034 * [backup-simplify]: Simplify 0 into 0
8.034 * [backup-simplify]: Simplify 1 into 1
8.034 * [backup-simplify]: Simplify (/ PI 1) into PI
8.035 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.036 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.036 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
8.036 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
8.036 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
8.036 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
8.038 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
8.039 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
8.040 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
8.040 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
8.040 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
8.040 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
8.040 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
8.040 * [taylor]: Taking taylor expansion of 1/2 in n
8.040 * [backup-simplify]: Simplify 1/2 into 1/2
8.040 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
8.040 * [taylor]: Taking taylor expansion of 1/2 in n
8.040 * [backup-simplify]: Simplify 1/2 into 1/2
8.040 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
8.040 * [taylor]: Taking taylor expansion of 1/2 in n
8.040 * [backup-simplify]: Simplify 1/2 into 1/2
8.041 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.041 * [taylor]: Taking taylor expansion of k in n
8.041 * [backup-simplify]: Simplify k into k
8.041 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.041 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
8.041 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
8.041 * [taylor]: Taking taylor expansion of 2 in n
8.041 * [backup-simplify]: Simplify 2 into 2
8.041 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.041 * [taylor]: Taking taylor expansion of PI in n
8.041 * [backup-simplify]: Simplify PI into PI
8.041 * [taylor]: Taking taylor expansion of n in n
8.041 * [backup-simplify]: Simplify 0 into 0
8.041 * [backup-simplify]: Simplify 1 into 1
8.042 * [backup-simplify]: Simplify (/ PI 1) into PI
8.042 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.043 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.043 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
8.043 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
8.044 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
8.044 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
8.045 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
8.047 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
8.048 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
8.048 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k
8.048 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
8.048 * [taylor]: Taking taylor expansion of 1/2 in k
8.048 * [backup-simplify]: Simplify 1/2 into 1/2
8.048 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
8.048 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
8.048 * [taylor]: Taking taylor expansion of 1/2 in k
8.048 * [backup-simplify]: Simplify 1/2 into 1/2
8.048 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
8.048 * [taylor]: Taking taylor expansion of 1/2 in k
8.048 * [backup-simplify]: Simplify 1/2 into 1/2
8.048 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.048 * [taylor]: Taking taylor expansion of k in k
8.048 * [backup-simplify]: Simplify 0 into 0
8.049 * [backup-simplify]: Simplify 1 into 1
8.049 * [backup-simplify]: Simplify (/ 1 1) into 1
8.049 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
8.049 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
8.049 * [taylor]: Taking taylor expansion of (* 2 PI) in k
8.049 * [taylor]: Taking taylor expansion of 2 in k
8.049 * [backup-simplify]: Simplify 2 into 2
8.049 * [taylor]: Taking taylor expansion of PI in k
8.049 * [backup-simplify]: Simplify PI into PI
8.050 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.051 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
8.051 * [taylor]: Taking taylor expansion of (log n) in k
8.051 * [taylor]: Taking taylor expansion of n in k
8.051 * [backup-simplify]: Simplify n into n
8.051 * [backup-simplify]: Simplify (log n) into (log n)
8.051 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
8.052 * [backup-simplify]: Simplify (- 1/2) into -1/2
8.052 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
8.052 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
8.053 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
8.055 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
8.056 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
8.057 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
8.059 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
8.060 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.061 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
8.062 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
8.063 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
8.063 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
8.063 * [backup-simplify]: Simplify (- 0) into 0
8.063 * [backup-simplify]: Simplify (+ 0 0) into 0
8.064 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
8.065 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
8.065 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
8.067 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
8.067 * [taylor]: Taking taylor expansion of 0 in k
8.067 * [backup-simplify]: Simplify 0 into 0
8.067 * [backup-simplify]: Simplify 0 into 0
8.067 * [backup-simplify]: Simplify 0 into 0
8.068 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.068 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
8.070 * [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
8.070 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
8.071 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
8.071 * [backup-simplify]: Simplify (- 0) into 0
8.071 * [backup-simplify]: Simplify (+ 0 0) into 0
8.072 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
8.073 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
8.074 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
8.075 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
8.075 * [taylor]: Taking taylor expansion of 0 in k
8.075 * [backup-simplify]: Simplify 0 into 0
8.075 * [backup-simplify]: Simplify 0 into 0
8.075 * [backup-simplify]: Simplify 0 into 0
8.075 * [backup-simplify]: Simplify 0 into 0
8.076 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.077 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.080 * [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
8.080 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
8.081 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
8.081 * [backup-simplify]: Simplify (- 0) into 0
8.081 * [backup-simplify]: Simplify (+ 0 0) into 0
8.082 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0
8.083 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
8.085 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
8.088 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 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
8.088 * [taylor]: Taking taylor expansion of 0 in k
8.088 * [backup-simplify]: Simplify 0 into 0
8.088 * [backup-simplify]: Simplify 0 into 0
8.090 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))
8.090 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)))
8.090 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0
8.090 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
8.090 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k
8.090 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k
8.090 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
8.090 * [taylor]: Taking taylor expansion of 1/2 in k
8.090 * [backup-simplify]: Simplify 1/2 into 1/2
8.090 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
8.090 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
8.090 * [taylor]: Taking taylor expansion of 1/2 in k
8.090 * [backup-simplify]: Simplify 1/2 into 1/2
8.090 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.090 * [taylor]: Taking taylor expansion of k in k
8.090 * [backup-simplify]: Simplify 0 into 0
8.090 * [backup-simplify]: Simplify 1 into 1
8.091 * [backup-simplify]: Simplify (/ 1 1) into 1
8.091 * [taylor]: Taking taylor expansion of 1/2 in k
8.091 * [backup-simplify]: Simplify 1/2 into 1/2
8.091 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
8.091 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
8.091 * [taylor]: Taking taylor expansion of -2 in k
8.091 * [backup-simplify]: Simplify -2 into -2
8.091 * [taylor]: Taking taylor expansion of (/ PI n) in k
8.091 * [taylor]: Taking taylor expansion of PI in k
8.091 * [backup-simplify]: Simplify PI into PI
8.091 * [taylor]: Taking taylor expansion of n in k
8.091 * [backup-simplify]: Simplify n into n
8.091 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
8.091 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
8.091 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
8.092 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
8.092 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
8.093 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
8.093 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
8.093 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
8.093 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
8.093 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
8.093 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
8.093 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
8.093 * [taylor]: Taking taylor expansion of 1/2 in n
8.093 * [backup-simplify]: Simplify 1/2 into 1/2
8.093 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
8.093 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
8.093 * [taylor]: Taking taylor expansion of 1/2 in n
8.093 * [backup-simplify]: Simplify 1/2 into 1/2
8.093 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.093 * [taylor]: Taking taylor expansion of k in n
8.093 * [backup-simplify]: Simplify k into k
8.093 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.093 * [taylor]: Taking taylor expansion of 1/2 in n
8.093 * [backup-simplify]: Simplify 1/2 into 1/2
8.093 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
8.094 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
8.094 * [taylor]: Taking taylor expansion of -2 in n
8.094 * [backup-simplify]: Simplify -2 into -2
8.094 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.094 * [taylor]: Taking taylor expansion of PI in n
8.094 * [backup-simplify]: Simplify PI into PI
8.094 * [taylor]: Taking taylor expansion of n in n
8.094 * [backup-simplify]: Simplify 0 into 0
8.094 * [backup-simplify]: Simplify 1 into 1
8.094 * [backup-simplify]: Simplify (/ PI 1) into PI
8.095 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
8.096 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
8.096 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
8.096 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
8.096 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
8.097 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
8.101 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
8.101 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
8.102 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
8.102 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
8.102 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
8.102 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
8.102 * [taylor]: Taking taylor expansion of 1/2 in n
8.102 * [backup-simplify]: Simplify 1/2 into 1/2
8.102 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
8.102 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
8.102 * [taylor]: Taking taylor expansion of 1/2 in n
8.102 * [backup-simplify]: Simplify 1/2 into 1/2
8.102 * [taylor]: Taking taylor expansion of (/ 1 k) in n
8.102 * [taylor]: Taking taylor expansion of k in n
8.102 * [backup-simplify]: Simplify k into k
8.102 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
8.102 * [taylor]: Taking taylor expansion of 1/2 in n
8.102 * [backup-simplify]: Simplify 1/2 into 1/2
8.102 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
8.102 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
8.102 * [taylor]: Taking taylor expansion of -2 in n
8.102 * [backup-simplify]: Simplify -2 into -2
8.102 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.102 * [taylor]: Taking taylor expansion of PI in n
8.102 * [backup-simplify]: Simplify PI into PI
8.102 * [taylor]: Taking taylor expansion of n in n
8.102 * [backup-simplify]: Simplify 0 into 0
8.102 * [backup-simplify]: Simplify 1 into 1
8.102 * [backup-simplify]: Simplify (/ PI 1) into PI
8.103 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
8.103 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
8.103 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
8.103 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
8.103 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
8.104 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
8.105 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
8.106 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
8.106 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k
8.106 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
8.106 * [taylor]: Taking taylor expansion of 1/2 in k
8.106 * [backup-simplify]: Simplify 1/2 into 1/2
8.106 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
8.106 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
8.106 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
8.106 * [taylor]: Taking taylor expansion of 1/2 in k
8.106 * [backup-simplify]: Simplify 1/2 into 1/2
8.106 * [taylor]: Taking taylor expansion of (/ 1 k) in k
8.106 * [taylor]: Taking taylor expansion of k in k
8.106 * [backup-simplify]: Simplify 0 into 0
8.106 * [backup-simplify]: Simplify 1 into 1
8.106 * [backup-simplify]: Simplify (/ 1 1) into 1
8.106 * [taylor]: Taking taylor expansion of 1/2 in k
8.106 * [backup-simplify]: Simplify 1/2 into 1/2
8.106 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
8.106 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
8.106 * [taylor]: Taking taylor expansion of (* -2 PI) in k
8.106 * [taylor]: Taking taylor expansion of -2 in k
8.106 * [backup-simplify]: Simplify -2 into -2
8.106 * [taylor]: Taking taylor expansion of PI in k
8.106 * [backup-simplify]: Simplify PI into PI
8.107 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
8.107 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
8.107 * [taylor]: Taking taylor expansion of (log n) in k
8.107 * [taylor]: Taking taylor expansion of n in k
8.107 * [backup-simplify]: Simplify n into n
8.107 * [backup-simplify]: Simplify (log n) into (log n)
8.108 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
8.108 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
8.108 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
8.109 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
8.109 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
8.110 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n)))
8.111 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
8.112 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
8.112 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.113 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
8.114 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
8.114 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
8.114 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
8.114 * [backup-simplify]: Simplify (+ 0 0) into 0
8.115 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
8.116 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
8.116 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
8.117 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
8.117 * [taylor]: Taking taylor expansion of 0 in k
8.117 * [backup-simplify]: Simplify 0 into 0
8.117 * [backup-simplify]: Simplify 0 into 0
8.118 * [backup-simplify]: Simplify 0 into 0
8.118 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.119 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
8.121 * [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
8.121 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
8.121 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
8.122 * [backup-simplify]: Simplify (+ 0 0) into 0
8.122 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
8.123 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
8.124 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
8.125 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
8.125 * [taylor]: Taking taylor expansion of 0 in k
8.126 * [backup-simplify]: Simplify 0 into 0
8.126 * [backup-simplify]: Simplify 0 into 0
8.126 * [backup-simplify]: Simplify 0 into 0
8.126 * [backup-simplify]: Simplify 0 into 0
8.126 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.128 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.134 * [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
8.134 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
8.136 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
8.136 * [backup-simplify]: Simplify (+ 0 0) into 0
8.137 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
8.139 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
8.141 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
8.143 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 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
8.143 * [taylor]: Taking taylor expansion of 0 in k
8.143 * [backup-simplify]: Simplify 0 into 0
8.143 * [backup-simplify]: Simplify 0 into 0
8.145 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))
8.145 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1)
8.145 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI))
8.145 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
8.145 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
8.145 * [taylor]: Taking taylor expansion of 2 in n
8.145 * [backup-simplify]: Simplify 2 into 2
8.145 * [taylor]: Taking taylor expansion of (* n PI) in n
8.145 * [taylor]: Taking taylor expansion of n in n
8.145 * [backup-simplify]: Simplify 0 into 0
8.145 * [backup-simplify]: Simplify 1 into 1
8.145 * [taylor]: Taking taylor expansion of PI in n
8.145 * [backup-simplify]: Simplify PI into PI
8.145 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
8.145 * [taylor]: Taking taylor expansion of 2 in n
8.145 * [backup-simplify]: Simplify 2 into 2
8.145 * [taylor]: Taking taylor expansion of (* n PI) in n
8.145 * [taylor]: Taking taylor expansion of n in n
8.145 * [backup-simplify]: Simplify 0 into 0
8.145 * [backup-simplify]: Simplify 1 into 1
8.146 * [taylor]: Taking taylor expansion of PI in n
8.146 * [backup-simplify]: Simplify PI into PI
8.146 * [backup-simplify]: Simplify (* 0 PI) into 0
8.146 * [backup-simplify]: Simplify (* 2 0) into 0
8.147 * [backup-simplify]: Simplify 0 into 0
8.148 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.148 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
8.149 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.149 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
8.150 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
8.150 * [backup-simplify]: Simplify 0 into 0
8.151 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
8.151 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
8.151 * [backup-simplify]: Simplify 0 into 0
8.152 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.153 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
8.153 * [backup-simplify]: Simplify 0 into 0
8.154 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
8.155 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
8.155 * [backup-simplify]: Simplify 0 into 0
8.156 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
8.157 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
8.157 * [backup-simplify]: Simplify 0 into 0
8.158 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
8.159 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
8.159 * [backup-simplify]: Simplify 0 into 0
8.160 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
8.160 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n))
8.160 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
8.160 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
8.160 * [taylor]: Taking taylor expansion of 2 in n
8.160 * [backup-simplify]: Simplify 2 into 2
8.160 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.160 * [taylor]: Taking taylor expansion of PI in n
8.160 * [backup-simplify]: Simplify PI into PI
8.160 * [taylor]: Taking taylor expansion of n in n
8.160 * [backup-simplify]: Simplify 0 into 0
8.160 * [backup-simplify]: Simplify 1 into 1
8.160 * [backup-simplify]: Simplify (/ PI 1) into PI
8.160 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
8.160 * [taylor]: Taking taylor expansion of 2 in n
8.160 * [backup-simplify]: Simplify 2 into 2
8.160 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.160 * [taylor]: Taking taylor expansion of PI in n
8.160 * [backup-simplify]: Simplify PI into PI
8.160 * [taylor]: Taking taylor expansion of n in n
8.160 * [backup-simplify]: Simplify 0 into 0
8.160 * [backup-simplify]: Simplify 1 into 1
8.161 * [backup-simplify]: Simplify (/ PI 1) into PI
8.161 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.161 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.162 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.162 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
8.162 * [backup-simplify]: Simplify 0 into 0
8.163 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.163 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
8.163 * [backup-simplify]: Simplify 0 into 0
8.164 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.165 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.165 * [backup-simplify]: Simplify 0 into 0
8.165 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.166 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.166 * [backup-simplify]: Simplify 0 into 0
8.167 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.168 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
8.168 * [backup-simplify]: Simplify 0 into 0
8.168 * [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
8.169 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
8.169 * [backup-simplify]: Simplify 0 into 0
8.170 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
8.170 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n))
8.170 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
8.170 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
8.170 * [taylor]: Taking taylor expansion of -2 in n
8.170 * [backup-simplify]: Simplify -2 into -2
8.170 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.170 * [taylor]: Taking taylor expansion of PI in n
8.170 * [backup-simplify]: Simplify PI into PI
8.170 * [taylor]: Taking taylor expansion of n in n
8.170 * [backup-simplify]: Simplify 0 into 0
8.170 * [backup-simplify]: Simplify 1 into 1
8.170 * [backup-simplify]: Simplify (/ PI 1) into PI
8.170 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
8.170 * [taylor]: Taking taylor expansion of -2 in n
8.170 * [backup-simplify]: Simplify -2 into -2
8.170 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.170 * [taylor]: Taking taylor expansion of PI in n
8.170 * [backup-simplify]: Simplify PI into PI
8.171 * [taylor]: Taking taylor expansion of n in n
8.171 * [backup-simplify]: Simplify 0 into 0
8.171 * [backup-simplify]: Simplify 1 into 1
8.171 * [backup-simplify]: Simplify (/ PI 1) into PI
8.171 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
8.171 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
8.172 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.172 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
8.173 * [backup-simplify]: Simplify 0 into 0
8.173 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.174 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
8.174 * [backup-simplify]: Simplify 0 into 0
8.174 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.175 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.175 * [backup-simplify]: Simplify 0 into 0
8.176 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.177 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.177 * [backup-simplify]: Simplify 0 into 0
8.177 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.179 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
8.179 * [backup-simplify]: Simplify 0 into 0
8.180 * [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
8.182 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
8.182 * [backup-simplify]: Simplify 0 into 0
8.183 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
8.183 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1)
8.183 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI))
8.183 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
8.183 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
8.183 * [taylor]: Taking taylor expansion of 2 in n
8.183 * [backup-simplify]: Simplify 2 into 2
8.183 * [taylor]: Taking taylor expansion of (* n PI) in n
8.183 * [taylor]: Taking taylor expansion of n in n
8.183 * [backup-simplify]: Simplify 0 into 0
8.183 * [backup-simplify]: Simplify 1 into 1
8.183 * [taylor]: Taking taylor expansion of PI in n
8.183 * [backup-simplify]: Simplify PI into PI
8.183 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
8.183 * [taylor]: Taking taylor expansion of 2 in n
8.183 * [backup-simplify]: Simplify 2 into 2
8.183 * [taylor]: Taking taylor expansion of (* n PI) in n
8.183 * [taylor]: Taking taylor expansion of n in n
8.183 * [backup-simplify]: Simplify 0 into 0
8.183 * [backup-simplify]: Simplify 1 into 1
8.183 * [taylor]: Taking taylor expansion of PI in n
8.183 * [backup-simplify]: Simplify PI into PI
8.184 * [backup-simplify]: Simplify (* 0 PI) into 0
8.184 * [backup-simplify]: Simplify (* 2 0) into 0
8.184 * [backup-simplify]: Simplify 0 into 0
8.186 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
8.188 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
8.188 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.189 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
8.190 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
8.190 * [backup-simplify]: Simplify 0 into 0
8.191 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
8.192 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
8.192 * [backup-simplify]: Simplify 0 into 0
8.193 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.194 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
8.194 * [backup-simplify]: Simplify 0 into 0
8.194 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
8.195 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
8.195 * [backup-simplify]: Simplify 0 into 0
8.196 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
8.197 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
8.197 * [backup-simplify]: Simplify 0 into 0
8.198 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
8.201 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
8.202 * [backup-simplify]: Simplify 0 into 0
8.202 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
8.202 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n))
8.202 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
8.202 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
8.202 * [taylor]: Taking taylor expansion of 2 in n
8.202 * [backup-simplify]: Simplify 2 into 2
8.202 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.202 * [taylor]: Taking taylor expansion of PI in n
8.202 * [backup-simplify]: Simplify PI into PI
8.202 * [taylor]: Taking taylor expansion of n in n
8.202 * [backup-simplify]: Simplify 0 into 0
8.202 * [backup-simplify]: Simplify 1 into 1
8.203 * [backup-simplify]: Simplify (/ PI 1) into PI
8.203 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
8.203 * [taylor]: Taking taylor expansion of 2 in n
8.203 * [backup-simplify]: Simplify 2 into 2
8.203 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.203 * [taylor]: Taking taylor expansion of PI in n
8.203 * [backup-simplify]: Simplify PI into PI
8.203 * [taylor]: Taking taylor expansion of n in n
8.203 * [backup-simplify]: Simplify 0 into 0
8.203 * [backup-simplify]: Simplify 1 into 1
8.203 * [backup-simplify]: Simplify (/ PI 1) into PI
8.203 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.204 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
8.204 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.205 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
8.205 * [backup-simplify]: Simplify 0 into 0
8.205 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.206 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
8.206 * [backup-simplify]: Simplify 0 into 0
8.207 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.207 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.207 * [backup-simplify]: Simplify 0 into 0
8.208 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.209 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.209 * [backup-simplify]: Simplify 0 into 0
8.209 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.210 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
8.210 * [backup-simplify]: Simplify 0 into 0
8.211 * [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
8.212 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
8.212 * [backup-simplify]: Simplify 0 into 0
8.212 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
8.213 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n))
8.213 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
8.213 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
8.213 * [taylor]: Taking taylor expansion of -2 in n
8.213 * [backup-simplify]: Simplify -2 into -2
8.213 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.213 * [taylor]: Taking taylor expansion of PI in n
8.213 * [backup-simplify]: Simplify PI into PI
8.213 * [taylor]: Taking taylor expansion of n in n
8.213 * [backup-simplify]: Simplify 0 into 0
8.213 * [backup-simplify]: Simplify 1 into 1
8.213 * [backup-simplify]: Simplify (/ PI 1) into PI
8.213 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
8.213 * [taylor]: Taking taylor expansion of -2 in n
8.213 * [backup-simplify]: Simplify -2 into -2
8.213 * [taylor]: Taking taylor expansion of (/ PI n) in n
8.213 * [taylor]: Taking taylor expansion of PI in n
8.213 * [backup-simplify]: Simplify PI into PI
8.213 * [taylor]: Taking taylor expansion of n in n
8.213 * [backup-simplify]: Simplify 0 into 0
8.213 * [backup-simplify]: Simplify 1 into 1
8.213 * [backup-simplify]: Simplify (/ PI 1) into PI
8.214 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
8.214 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
8.215 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
8.215 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
8.215 * [backup-simplify]: Simplify 0 into 0
8.216 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.216 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
8.216 * [backup-simplify]: Simplify 0 into 0
8.217 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.218 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
8.218 * [backup-simplify]: Simplify 0 into 0
8.218 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.219 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
8.219 * [backup-simplify]: Simplify 0 into 0
8.220 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
8.221 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
8.221 * [backup-simplify]: Simplify 0 into 0
8.221 * [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
8.223 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
8.223 * [backup-simplify]: Simplify 0 into 0
8.223 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
8.223 * * * [progress]: simplifying candidates
8.223 * * * * [progress]: [ 1 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (exp (* (+ (+ (log n) (log 2)) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
8.224 * * * * [progress]: [ 2 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (exp (* (+ (log (* n 2)) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
8.224 * * * * [progress]: [ 3 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (exp (* (log (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
8.224 * * * * [progress]: [ 4 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (exp (* (log (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
8.224 * * * * [progress]: [ 5 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (* 1 (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
8.224 * * * * [progress]: [ 6 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (* 1 (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
8.224 * * * * [progress]: [ 7 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (* 1 (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
8.224 * * * * [progress]: [ 8 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (/ (pow (* (* n 2) PI) (/ 1/2 2)) (pow (* (* n 2) PI) (/ (/ k 2) 2))) (sqrt k))))>
8.224 * * * * [progress]: [ 9 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2)))) (cbrt (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
8.224 * * * * [progress]: [ 10 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (sqrt (/ (- 1/2 (/ k 2)) 2))) (sqrt (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
8.224 * * * * [progress]: [ 11 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2))) (sqrt k))))>
8.224 * * * * [progress]: [ 12 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))) (/ (cbrt (- 1/2 (/ k 2))) (sqrt 2))) (sqrt k))))>
8.225 * * * * [progress]: [ 13 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)) (/ (cbrt (- 1/2 (/ k 2))) 2)) (sqrt k))))>
8.225 * * * * [progress]: [ 14 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1/2 (/ k 2))) (cbrt 2))) (sqrt k))))>
8.225 * * * * [progress]: [ 15 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (sqrt k))))>
8.225 * * * * [progress]: [ 16 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) 1)) (/ (sqrt (- 1/2 (/ k 2))) 2)) (sqrt k))))>
8.225 * * * * [progress]: [ 17 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) (sqrt k))))>
8.225 * * * * [progress]: [ 18 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) (sqrt k))))>
8.225 * * * * [progress]: [ 19 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.225 * * * * [progress]: [ 20 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (cbrt 2))) (sqrt k))))>
8.225 * * * * [progress]: [ 21 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (sqrt k))))>
8.225 * * * * [progress]: [ 22 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1)) (/ (- (sqrt 1/2) (sqrt (/ k 2))) 2)) (sqrt k))))>
8.225 * * * * [progress]: [ 23 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (cbrt 2))) (sqrt k))))>
8.225 * * * * [progress]: [ 24 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (sqrt k))))>
8.225 * * * * [progress]: [ 25 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1)) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 2)) (sqrt k))))>
8.226 * * * * [progress]: [ 26 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) (sqrt k))))>
8.226 * * * * [progress]: [ 27 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) (sqrt k))))>
8.226 * * * * [progress]: [ 28 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.226 * * * * [progress]: [ 29 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) 1) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.226 * * * * [progress]: [ 30 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (/ 1 2)) (sqrt k))))>
8.226 * * * * [progress]: [ 31 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
8.226 * * * * [progress]: [ 32 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (sqrt k))))>
8.226 * * * * [progress]: [ 33 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (exp (log (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
8.226 * * * * [progress]: [ 34 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (log (exp (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
8.226 * * * * [progress]: [ 35 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (* (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
8.226 * * * * [progress]: [ 36 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (cbrt (* (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
8.226 * * * * [progress]: [ 37 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (* (sqrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
8.227 * * * * [progress]: [ 38 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (* 1 (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
8.227 * * * * [progress]: [ 39 / 130 ] 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) 2)) (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2))) (sqrt k))))>
8.227 * * * * [progress]: [ 40 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (posit16->real (real->posit16 (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
8.227 * * * * [progress]: [ 41 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (exp (* (+ (+ (log n) (log 2)) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.227 * * * * [progress]: [ 42 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (exp (* (+ (log (* n 2)) (log PI)) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.227 * * * * [progress]: [ 43 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (exp (* (log (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.227 * * * * [progress]: [ 44 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (exp (* (log (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.227 * * * * [progress]: [ 45 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (* 1 (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.227 * * * * [progress]: [ 46 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (* 1 (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.227 * * * * [progress]: [ 47 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (* 1 (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.227 * * * * [progress]: [ 48 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ (pow (* (* n 2) PI) (/ 1/2 2)) (pow (* (* n 2) PI) (/ (/ k 2) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.227 * * * * [progress]: [ 49 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2)))) (cbrt (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.227 * * * * [progress]: [ 50 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (sqrt (/ (- 1/2 (/ k 2)) 2))) (sqrt (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.228 * * * * [progress]: [ 51 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.228 * * * * [progress]: [ 52 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))) (/ (cbrt (- 1/2 (/ k 2))) (sqrt 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.228 * * * * [progress]: [ 53 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)) (/ (cbrt (- 1/2 (/ k 2))) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.228 * * * * [progress]: [ 54 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1/2 (/ k 2))) (cbrt 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.228 * * * * [progress]: [ 55 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.228 * * * * [progress]: [ 56 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) 1)) (/ (sqrt (- 1/2 (/ k 2))) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.228 * * * * [progress]: [ 57 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.228 * * * * [progress]: [ 58 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.228 * * * * [progress]: [ 59 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.228 * * * * [progress]: [ 60 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (cbrt 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.228 * * * * [progress]: [ 61 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.228 * * * * [progress]: [ 62 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1)) (/ (- (sqrt 1/2) (sqrt (/ k 2))) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.229 * * * * [progress]: [ 63 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (cbrt 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.229 * * * * [progress]: [ 64 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.229 * * * * [progress]: [ 65 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1)) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.229 * * * * [progress]: [ 66 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.229 * * * * [progress]: [ 67 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.229 * * * * [progress]: [ 68 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.229 * * * * [progress]: [ 69 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) 1) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.229 * * * * [progress]: [ 70 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (/ 1 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.229 * * * * [progress]: [ 71 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.229 * * * * [progress]: [ 72 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.229 * * * * [progress]: [ 73 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (exp (log (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.229 * * * * [progress]: [ 74 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (log (exp (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.229 * * * * [progress]: [ 75 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.230 * * * * [progress]: [ 76 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (cbrt (* (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.230 * * * * [progress]: [ 77 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (sqrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.230 * * * * [progress]: [ 78 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (* 1 (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.230 * * * * [progress]: [ 79 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.230 * * * * [progress]: [ 80 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (posit16->real (real->posit16 (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.230 * * * * [progress]: [ 81 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) 1) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.230 * * * * [progress]: [ 82 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) 1) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.230 * * * * [progress]: [ 83 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (pow (* (* n 2) PI) 1) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.230 * * * * [progress]: [ 84 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (exp (+ (+ (log n) (log 2)) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.230 * * * * [progress]: [ 85 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (exp (+ (log (* n 2)) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.230 * * * * [progress]: [ 86 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (exp (log (* (* n 2) PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.230 * * * * [progress]: [ 87 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (log (exp (* (* n 2) PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.230 * * * * [progress]: [ 88 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (cbrt (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.231 * * * * [progress]: [ 89 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (cbrt (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.231 * * * * [progress]: [ 90 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.231 * * * * [progress]: [ 91 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (cbrt (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.231 * * * * [progress]: [ 92 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.231 * * * * [progress]: [ 93 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* 1 (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.231 * * * * [progress]: [ 94 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* (* n 2) (* (cbrt PI) (cbrt PI))) (cbrt PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.231 * * * * [progress]: [ 95 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.231 * * * * [progress]: [ 96 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* (* n 2) 1) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.231 * * * * [progress]: [ 97 / 130 ] 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))))>
8.231 * * * * [progress]: [ 98 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (posit16->real (real->posit16 (* (* n 2) PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.231 * * * * [progress]: [ 99 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* PI (* n 2)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.231 * * * * [progress]: [ 100 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) 1) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.231 * * * * [progress]: [ 101 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) 1) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.232 * * * * [progress]: [ 102 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (pow (* (* n 2) PI) 1) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.232 * * * * [progress]: [ 103 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (exp (+ (+ (log n) (log 2)) (log PI))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.232 * * * * [progress]: [ 104 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (exp (+ (log (* n 2)) (log PI))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.232 * * * * [progress]: [ 105 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (exp (log (* (* n 2) PI))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.232 * * * * [progress]: [ 106 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (log (exp (* (* n 2) PI))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.232 * * * * [progress]: [ 107 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (cbrt (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.232 * * * * [progress]: [ 108 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (cbrt (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.232 * * * * [progress]: [ 109 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.232 * * * * [progress]: [ 110 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (cbrt (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.232 * * * * [progress]: [ 111 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.232 * * * * [progress]: [ 112 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 1 (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.232 * * * * [progress]: [ 113 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* (* n 2) (* (cbrt PI) (cbrt PI))) (cbrt PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.232 * * * * [progress]: [ 114 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.233 * * * * [progress]: [ 115 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* (* n 2) 1) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.233 * * * * [progress]: [ 116 / 130 ] 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))))>
8.233 * * * * [progress]: [ 117 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (posit16->real (real->posit16 (* (* n 2) PI))) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.233 * * * * [progress]: [ 118 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* PI (* n 2)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.233 * * * * [progress]: [ 119 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) (sqrt k))))>
8.233 * * * * [progress]: [ 120 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k))))>
8.233 * * * * [progress]: [ 121 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k))))>
8.233 * * * * [progress]: [ 122 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.233 * * * * [progress]: [ 123 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.233 * * * * [progress]: [ 124 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.233 * * * * [progress]: [ 125 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.233 * * * * [progress]: [ 126 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.233 * * * * [progress]: [ 127 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.233 * * * * [progress]: [ 128 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.234 * * * * [progress]: [ 129 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.234 * * * * [progress]: [ 130 / 130 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
8.236 * [simplify]: Simplifying:
  (* (+ (+ (log n) (log 2)) (log PI)) (/ (- 1/2 (/ k 2)) 2))
  (* (+ (log (* n 2)) (log PI)) (/ (- 1/2 (/ k 2)) 2))
  (* (log (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2))
  (* (log (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2))
  (* 1 (/ (- 1/2 (/ k 2)) 2))
  (* 1 (/ (- 1/2 (/ k 2)) 2))
  (* 1 (/ (- 1/2 (/ k 2)) 2))
  (pow (* (* n 2) PI) (/ 1/2 2))
  (pow (* (* n 2) PI) (/ (/ k 2) 2))
  (pow (* (* n 2) PI) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2))))
  (pow (* (* n 2) PI) (sqrt (/ (- 1/2 (/ k 2)) 2)))
  (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2)))
  (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1))
  (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2)))
  (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) 1))
  (pow (* (* n 2) PI) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ 1 (sqrt 2)))
  (pow (* (* n 2) PI) (/ 1 1))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2)))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2)))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1))
  (pow (* (* n 2) PI) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ 1 (sqrt 2)))
  (pow (* (* n 2) PI) (/ 1 1))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) (- 1/2 (/ k 2)))
  (pow (* n 2) (/ (- 1/2 (/ k 2)) 2))
  (pow PI (/ (- 1/2 (/ k 2)) 2))
  (log (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (exp (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))))
  (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (sqrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (sqrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2))
  (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2))
  (real->posit16 (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (+ (+ (log n) (log 2)) (log PI)) (/ (- 1/2 (/ k 2)) 2))
  (* (+ (log (* n 2)) (log PI)) (/ (- 1/2 (/ k 2)) 2))
  (* (log (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2))
  (* (log (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2))
  (* 1 (/ (- 1/2 (/ k 2)) 2))
  (* 1 (/ (- 1/2 (/ k 2)) 2))
  (* 1 (/ (- 1/2 (/ k 2)) 2))
  (pow (* (* n 2) PI) (/ 1/2 2))
  (pow (* (* n 2) PI) (/ (/ k 2) 2))
  (pow (* (* n 2) PI) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2))))
  (pow (* (* n 2) PI) (sqrt (/ (- 1/2 (/ k 2)) 2)))
  (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2)))
  (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1))
  (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2)))
  (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) 1))
  (pow (* (* n 2) PI) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ 1 (sqrt 2)))
  (pow (* (* n 2) PI) (/ 1 1))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2)))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2)))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1))
  (pow (* (* n 2) PI) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ 1 (sqrt 2)))
  (pow (* (* n 2) PI) (/ 1 1))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) (- 1/2 (/ k 2)))
  (pow (* n 2) (/ (- 1/2 (/ k 2)) 2))
  (pow PI (/ (- 1/2 (/ k 2)) 2))
  (log (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (exp (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))))
  (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (sqrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (sqrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2))
  (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2))
  (real->posit16 (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 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))
  (* (* 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))
  (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
  (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))
  (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
  (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
8.240 * * [simplify]: iteration 0: 165 enodes
8.312 * * [simplify]: iteration 1: 462 enodes
8.561 * * [simplify]: iteration 2: 1556 enodes
8.984 * * [simplify]: iteration 3: 2002 enodes
9.448 * * [simplify]: iteration complete: 2002 enodes
9.448 * * [simplify]: Extracting #0: cost 45 inf + 0
9.449 * * [simplify]: Extracting #1: cost 297 inf + 0
9.451 * * [simplify]: Extracting #2: cost 537 inf + 2810
9.457 * * [simplify]: Extracting #3: cost 525 inf + 35054
9.487 * * [simplify]: Extracting #4: cost 278 inf + 110482
9.536 * * [simplify]: Extracting #5: cost 81 inf + 191592
9.599 * * [simplify]: Extracting #6: cost 14 inf + 216308
9.667 * * [simplify]: Extracting #7: cost 0 inf + 220140
9.733 * * [simplify]: Extracting #8: cost 0 inf + 218820
9.786 * * [simplify]: Extracting #9: cost 0 inf + 218179
9.820 * [simplify]: Simplified to:
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (- 1/4 (/ k 4))
  (- 1/4 (/ k 4))
  (- 1/4 (/ k 4))
  (pow (* 2 (* PI n)) 1/4)
  (pow (* 2 (* PI n)) (/ k 4))
  (pow (* 2 (* PI n)) (* (cbrt (- 1/4 (/ k 4))) (cbrt (- 1/4 (/ k 4)))))
  (pow (* 2 (* PI n)) (sqrt (- 1/4 (/ k 4))))
  (pow (* 2 (* PI n)) (* (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2))))
  (pow (* 2 (* PI n)) (* (/ (cbrt (- 1/2 (/ k 2))) (sqrt 2)) (cbrt (- 1/2 (/ k 2)))))
  (pow (* 2 (* PI n)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* 2 (* PI n)) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* PI n)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2)))
  (pow (* 2 (* PI n)) (sqrt (- 1/2 (/ k 2))))
  (pow (* 2 (* PI n)) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* 2 (* PI n)) (/ 1 (sqrt 2)))
  (* 2 (* PI n))
  (pow (* 2 (* PI n)) (/ (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (cbrt 2)) (cbrt 2)))
  (pow (* 2 (* PI n)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2)))
  (pow (* 2 (* PI n)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* 2 (* PI n)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* PI n)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2)))
  (pow (* 2 (* PI n)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* 2 (* PI n)) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* 2 (* PI n)) (/ 1 (sqrt 2)))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))
  (pow (* 2 n) (- 1/4 (/ k 4)))
  (pow PI (- 1/4 (/ k 4)))
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (exp (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (* (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))) (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))))
  (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (* (* (pow (* 2 (* PI n)) (- 1/4 (/ k 4))) (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))) (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (sqrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (sqrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (pow (* 2 (* PI n)) (- 1/8 (/ k 8)))
  (pow (* 2 (* PI n)) (- 1/8 (/ k 8)))
  (real->posit16 (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (- 1/4 (/ k 4))
  (- 1/4 (/ k 4))
  (- 1/4 (/ k 4))
  (pow (* 2 (* PI n)) 1/4)
  (pow (* 2 (* PI n)) (/ k 4))
  (pow (* 2 (* PI n)) (* (cbrt (- 1/4 (/ k 4))) (cbrt (- 1/4 (/ k 4)))))
  (pow (* 2 (* PI n)) (sqrt (- 1/4 (/ k 4))))
  (pow (* 2 (* PI n)) (* (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2))))
  (pow (* 2 (* PI n)) (* (/ (cbrt (- 1/2 (/ k 2))) (sqrt 2)) (cbrt (- 1/2 (/ k 2)))))
  (pow (* 2 (* PI n)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* 2 (* PI n)) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* PI n)) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2)))
  (pow (* 2 (* PI n)) (sqrt (- 1/2 (/ k 2))))
  (pow (* 2 (* PI n)) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* 2 (* PI n)) (/ 1 (sqrt 2)))
  (* 2 (* PI n))
  (pow (* 2 (* PI n)) (/ (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (cbrt 2)) (cbrt 2)))
  (pow (* 2 (* PI n)) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2)))
  (pow (* 2 (* PI n)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* 2 (* PI n)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* 2 (* PI n)) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2)))
  (pow (* 2 (* PI n)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* 2 (* PI n)) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* 2 (* PI n)) (/ 1 (sqrt 2)))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))
  (pow (* 2 n) (- 1/4 (/ k 4)))
  (pow PI (- 1/4 (/ k 4)))
  (* (- 1/4 (/ k 4)) (log (* 2 (* PI n))))
  (exp (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (* (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))) (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))))
  (cbrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (* (* (pow (* 2 (* PI n)) (- 1/4 (/ k 4))) (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))) (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (sqrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (sqrt (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (pow (* 2 (* PI n)) (- 1/8 (/ k 8)))
  (pow (* 2 (* PI n)) (- 1/8 (/ k 8)))
  (real->posit16 (pow (* 2 (* PI n)) (- 1/4 (/ k 4))))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (log (* 2 (* PI n)))
  (log (* 2 (* PI n)))
  (log (* 2 (* PI n)))
  (exp (+ (* PI n) (* 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) (cbrt PI)) (* 2 n))
  (* (* n 2) (sqrt PI))
  (* 2 n)
  (* 2 PI)
  (real->posit16 (* 2 (* PI n)))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (log (* 2 (* PI n)))
  (log (* 2 (* PI n)))
  (log (* 2 (* PI n)))
  (exp (+ (* PI n) (* 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) (cbrt PI)) (* 2 n))
  (* (* n 2) (sqrt PI))
  (* 2 n)
  (* 2 PI)
  (real->posit16 (* 2 (* PI n)))
  (- (+ (+ (* (* (* 1/16 (log (* 2 PI))) (* (log n) (exp (* (log (* 2 (* PI n))) 1/4)))) (* k k)) (exp (* (log (* 2 (* PI n))) 1/4))) (* 1/32 (* (* k k) (+ (* (* (log n) (log n)) (exp (* (log (* 2 (* PI n))) 1/4))) (* (* (log (* 2 PI)) (log (* 2 PI))) (exp (* (log (* 2 (* PI n))) 1/4))))))) (* (* k (+ (* (log n) (exp (* (log (* 2 (* PI n))) 1/4))) (* (exp (* (log (* 2 (* PI n))) 1/4)) (log (* 2 PI))))) 1/4))
  (exp (* (- 1/2 (* k 1/2)) (* (log (* 2 (* PI n))) 1/2)))
  (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (* (- 1/2 (* k 1/2)) 1/2)))
  (- (+ (+ (* (* (* 1/16 (log (* 2 PI))) (* (log n) (exp (* (log (* 2 (* PI n))) 1/4)))) (* k k)) (exp (* (log (* 2 (* PI n))) 1/4))) (* 1/32 (* (* k k) (+ (* (* (log n) (log n)) (exp (* (log (* 2 (* PI n))) 1/4))) (* (* (log (* 2 PI)) (log (* 2 PI))) (exp (* (log (* 2 (* PI n))) 1/4))))))) (* (* k (+ (* (log n) (exp (* (log (* 2 (* PI n))) 1/4))) (* (exp (* (log (* 2 (* PI n))) 1/4)) (log (* 2 PI))))) 1/4))
  (exp (* (- 1/2 (* k 1/2)) (* (log (* 2 (* PI n))) 1/2)))
  (exp (* (- (log (* -2 PI)) (log (/ -1 n))) (* (- 1/2 (* k 1/2)) 1/2)))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (* 2 (* PI n))
9.841 * * * [progress]: adding candidates to table
10.674 * * [progress]: iteration 4 / 4
10.674 * * * [progress]: picking best candidate
10.709 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
10.709 * * * [progress]: localizing error
10.781 * * * [progress]: generating rewritten candidates
10.781 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1)
10.797 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1)
10.819 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1 1)
10.847 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2)
10.872 * * * [progress]: generating series expansions
10.872 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1)
10.872 * [backup-simplify]: Simplify (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k))))
10.873 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0
10.873 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k
10.873 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k
10.873 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k
10.873 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k
10.873 * [taylor]: Taking taylor expansion of 1/2 in k
10.873 * [backup-simplify]: Simplify 1/2 into 1/2
10.873 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
10.873 * [taylor]: Taking taylor expansion of 1/2 in k
10.873 * [backup-simplify]: Simplify 1/2 into 1/2
10.873 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
10.873 * [taylor]: Taking taylor expansion of 1/2 in k
10.873 * [backup-simplify]: Simplify 1/2 into 1/2
10.873 * [taylor]: Taking taylor expansion of k in k
10.873 * [backup-simplify]: Simplify 0 into 0
10.873 * [backup-simplify]: Simplify 1 into 1
10.873 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
10.873 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
10.873 * [taylor]: Taking taylor expansion of 2 in k
10.873 * [backup-simplify]: Simplify 2 into 2
10.873 * [taylor]: Taking taylor expansion of (* n PI) in k
10.873 * [taylor]: Taking taylor expansion of n in k
10.873 * [backup-simplify]: Simplify n into n
10.873 * [taylor]: Taking taylor expansion of PI in k
10.873 * [backup-simplify]: Simplify PI into PI
10.873 * [backup-simplify]: Simplify (* n PI) into (* n PI)
10.873 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
10.873 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
10.874 * [backup-simplify]: Simplify (* 1/2 0) into 0
10.875 * [backup-simplify]: Simplify (- 0) into 0
10.875 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
10.875 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
10.876 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
10.876 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
10.876 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
10.876 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
10.876 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
10.876 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
10.876 * [taylor]: Taking taylor expansion of 1/2 in n
10.876 * [backup-simplify]: Simplify 1/2 into 1/2
10.876 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
10.876 * [taylor]: Taking taylor expansion of 1/2 in n
10.876 * [backup-simplify]: Simplify 1/2 into 1/2
10.876 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
10.876 * [taylor]: Taking taylor expansion of 1/2 in n
10.876 * [backup-simplify]: Simplify 1/2 into 1/2
10.876 * [taylor]: Taking taylor expansion of k in n
10.876 * [backup-simplify]: Simplify k into k
10.876 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
10.876 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
10.876 * [taylor]: Taking taylor expansion of 2 in n
10.876 * [backup-simplify]: Simplify 2 into 2
10.876 * [taylor]: Taking taylor expansion of (* n PI) in n
10.876 * [taylor]: Taking taylor expansion of n in n
10.876 * [backup-simplify]: Simplify 0 into 0
10.876 * [backup-simplify]: Simplify 1 into 1
10.876 * [taylor]: Taking taylor expansion of PI in n
10.876 * [backup-simplify]: Simplify PI into PI
10.877 * [backup-simplify]: Simplify (* 0 PI) into 0
10.877 * [backup-simplify]: Simplify (* 2 0) into 0
10.879 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
10.881 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
10.882 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.882 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
10.882 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
10.882 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
10.882 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
10.884 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
10.885 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
10.886 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
10.886 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
10.886 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
10.886 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
10.886 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
10.886 * [taylor]: Taking taylor expansion of 1/2 in n
10.886 * [backup-simplify]: Simplify 1/2 into 1/2
10.886 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
10.886 * [taylor]: Taking taylor expansion of 1/2 in n
10.886 * [backup-simplify]: Simplify 1/2 into 1/2
10.887 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
10.887 * [taylor]: Taking taylor expansion of 1/2 in n
10.887 * [backup-simplify]: Simplify 1/2 into 1/2
10.887 * [taylor]: Taking taylor expansion of k in n
10.887 * [backup-simplify]: Simplify k into k
10.887 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
10.887 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
10.887 * [taylor]: Taking taylor expansion of 2 in n
10.887 * [backup-simplify]: Simplify 2 into 2
10.887 * [taylor]: Taking taylor expansion of (* n PI) in n
10.887 * [taylor]: Taking taylor expansion of n in n
10.887 * [backup-simplify]: Simplify 0 into 0
10.887 * [backup-simplify]: Simplify 1 into 1
10.887 * [taylor]: Taking taylor expansion of PI in n
10.887 * [backup-simplify]: Simplify PI into PI
10.887 * [backup-simplify]: Simplify (* 0 PI) into 0
10.888 * [backup-simplify]: Simplify (* 2 0) into 0
10.889 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
10.891 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
10.891 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.891 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
10.892 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
10.892 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
10.892 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
10.893 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
10.893 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
10.894 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
10.894 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k
10.894 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
10.894 * [taylor]: Taking taylor expansion of 1/2 in k
10.894 * [backup-simplify]: Simplify 1/2 into 1/2
10.894 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
10.894 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
10.894 * [taylor]: Taking taylor expansion of 1/2 in k
10.894 * [backup-simplify]: Simplify 1/2 into 1/2
10.894 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
10.894 * [taylor]: Taking taylor expansion of 1/2 in k
10.894 * [backup-simplify]: Simplify 1/2 into 1/2
10.894 * [taylor]: Taking taylor expansion of k in k
10.894 * [backup-simplify]: Simplify 0 into 0
10.894 * [backup-simplify]: Simplify 1 into 1
10.894 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
10.894 * [taylor]: Taking taylor expansion of (log n) in k
10.894 * [taylor]: Taking taylor expansion of n in k
10.894 * [backup-simplify]: Simplify n into n
10.894 * [backup-simplify]: Simplify (log n) into (log n)
10.894 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
10.894 * [taylor]: Taking taylor expansion of (* 2 PI) in k
10.894 * [taylor]: Taking taylor expansion of 2 in k
10.894 * [backup-simplify]: Simplify 2 into 2
10.894 * [taylor]: Taking taylor expansion of PI in k
10.894 * [backup-simplify]: Simplify PI into PI
10.895 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
10.895 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.896 * [backup-simplify]: Simplify (* 1/2 0) into 0
10.896 * [backup-simplify]: Simplify (- 0) into 0
10.896 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
10.897 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
10.897 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
10.898 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI))))
10.899 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
10.900 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
10.900 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
10.901 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
10.902 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
10.903 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
10.903 * [backup-simplify]: Simplify (- 0) into 0
10.903 * [backup-simplify]: Simplify (+ 0 0) into 0
10.903 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0
10.904 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
10.905 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
10.906 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
10.906 * [taylor]: Taking taylor expansion of 0 in k
10.906 * [backup-simplify]: Simplify 0 into 0
10.906 * [backup-simplify]: Simplify 0 into 0
10.907 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
10.907 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
10.908 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
10.909 * [backup-simplify]: Simplify (+ 0 0) into 0
10.909 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
10.909 * [backup-simplify]: Simplify (- 1/2) into -1/2
10.910 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
10.911 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
10.912 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI)))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))))
10.914 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
10.919 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
10.921 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
10.922 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
10.926 * [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
10.927 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
10.927 * [backup-simplify]: Simplify (- 0) into 0
10.927 * [backup-simplify]: Simplify (+ 0 0) into 0
10.928 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0
10.930 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
10.931 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
10.934 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
10.934 * [taylor]: Taking taylor expansion of 0 in k
10.934 * [backup-simplify]: Simplify 0 into 0
10.934 * [backup-simplify]: Simplify 0 into 0
10.934 * [backup-simplify]: Simplify 0 into 0
10.935 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
10.936 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
10.939 * [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
10.939 * [backup-simplify]: Simplify (+ 0 0) into 0
10.940 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
10.940 * [backup-simplify]: Simplify (- 0) into 0
10.940 * [backup-simplify]: Simplify (+ 0 0) into 0
10.942 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
10.944 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI))))))) into 0
10.946 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
10.949 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
10.955 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
10.955 * [backup-simplify]: Simplify (pow (* (* (/ 1 n) 2) PI) (/ (- 1/2 (/ (/ 1 k) 2)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))))
10.955 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
10.955 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k
10.955 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k
10.955 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k
10.955 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k
10.955 * [taylor]: Taking taylor expansion of 1/2 in k
10.955 * [backup-simplify]: Simplify 1/2 into 1/2
10.955 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
10.955 * [taylor]: Taking taylor expansion of 1/2 in k
10.955 * [backup-simplify]: Simplify 1/2 into 1/2
10.955 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
10.955 * [taylor]: Taking taylor expansion of 1/2 in k
10.955 * [backup-simplify]: Simplify 1/2 into 1/2
10.955 * [taylor]: Taking taylor expansion of (/ 1 k) in k
10.955 * [taylor]: Taking taylor expansion of k in k
10.955 * [backup-simplify]: Simplify 0 into 0
10.955 * [backup-simplify]: Simplify 1 into 1
10.956 * [backup-simplify]: Simplify (/ 1 1) into 1
10.956 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
10.956 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
10.956 * [taylor]: Taking taylor expansion of 2 in k
10.956 * [backup-simplify]: Simplify 2 into 2
10.956 * [taylor]: Taking taylor expansion of (/ PI n) in k
10.956 * [taylor]: Taking taylor expansion of PI in k
10.956 * [backup-simplify]: Simplify PI into PI
10.956 * [taylor]: Taking taylor expansion of n in k
10.956 * [backup-simplify]: Simplify n into n
10.956 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
10.956 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
10.956 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
10.956 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
10.956 * [backup-simplify]: Simplify (- 1/2) into -1/2
10.957 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
10.957 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4
10.957 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
10.957 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))))
10.957 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
10.957 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
10.957 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
10.957 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
10.957 * [taylor]: Taking taylor expansion of 1/2 in n
10.957 * [backup-simplify]: Simplify 1/2 into 1/2
10.957 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
10.957 * [taylor]: Taking taylor expansion of 1/2 in n
10.957 * [backup-simplify]: Simplify 1/2 into 1/2
10.957 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
10.957 * [taylor]: Taking taylor expansion of 1/2 in n
10.957 * [backup-simplify]: Simplify 1/2 into 1/2
10.957 * [taylor]: Taking taylor expansion of (/ 1 k) in n
10.957 * [taylor]: Taking taylor expansion of k in n
10.957 * [backup-simplify]: Simplify k into k
10.957 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
10.957 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
10.957 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
10.957 * [taylor]: Taking taylor expansion of 2 in n
10.957 * [backup-simplify]: Simplify 2 into 2
10.957 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.957 * [taylor]: Taking taylor expansion of PI in n
10.957 * [backup-simplify]: Simplify PI into PI
10.958 * [taylor]: Taking taylor expansion of n in n
10.958 * [backup-simplify]: Simplify 0 into 0
10.958 * [backup-simplify]: Simplify 1 into 1
10.958 * [backup-simplify]: Simplify (/ PI 1) into PI
10.958 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
10.959 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.959 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
10.959 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
10.959 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
10.959 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
10.960 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
10.961 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
10.961 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
10.962 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
10.962 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
10.962 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
10.962 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
10.962 * [taylor]: Taking taylor expansion of 1/2 in n
10.962 * [backup-simplify]: Simplify 1/2 into 1/2
10.962 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
10.962 * [taylor]: Taking taylor expansion of 1/2 in n
10.962 * [backup-simplify]: Simplify 1/2 into 1/2
10.962 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
10.962 * [taylor]: Taking taylor expansion of 1/2 in n
10.962 * [backup-simplify]: Simplify 1/2 into 1/2
10.962 * [taylor]: Taking taylor expansion of (/ 1 k) in n
10.962 * [taylor]: Taking taylor expansion of k in n
10.962 * [backup-simplify]: Simplify k into k
10.962 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
10.962 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
10.962 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
10.962 * [taylor]: Taking taylor expansion of 2 in n
10.962 * [backup-simplify]: Simplify 2 into 2
10.962 * [taylor]: Taking taylor expansion of (/ PI n) in n
10.962 * [taylor]: Taking taylor expansion of PI in n
10.962 * [backup-simplify]: Simplify PI into PI
10.962 * [taylor]: Taking taylor expansion of n in n
10.962 * [backup-simplify]: Simplify 0 into 0
10.962 * [backup-simplify]: Simplify 1 into 1
10.962 * [backup-simplify]: Simplify (/ PI 1) into PI
10.963 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
10.963 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.963 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
10.963 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
10.963 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
10.964 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
10.965 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
10.965 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
10.966 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
10.966 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k
10.966 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
10.966 * [taylor]: Taking taylor expansion of 1/2 in k
10.966 * [backup-simplify]: Simplify 1/2 into 1/2
10.966 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
10.966 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
10.966 * [taylor]: Taking taylor expansion of 1/2 in k
10.966 * [backup-simplify]: Simplify 1/2 into 1/2
10.966 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
10.966 * [taylor]: Taking taylor expansion of 1/2 in k
10.966 * [backup-simplify]: Simplify 1/2 into 1/2
10.966 * [taylor]: Taking taylor expansion of (/ 1 k) in k
10.966 * [taylor]: Taking taylor expansion of k in k
10.966 * [backup-simplify]: Simplify 0 into 0
10.966 * [backup-simplify]: Simplify 1 into 1
10.967 * [backup-simplify]: Simplify (/ 1 1) into 1
10.967 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
10.967 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
10.967 * [taylor]: Taking taylor expansion of (* 2 PI) in k
10.967 * [taylor]: Taking taylor expansion of 2 in k
10.967 * [backup-simplify]: Simplify 2 into 2
10.967 * [taylor]: Taking taylor expansion of PI in k
10.967 * [backup-simplify]: Simplify PI into PI
10.967 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
10.968 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
10.968 * [taylor]: Taking taylor expansion of (log n) in k
10.968 * [taylor]: Taking taylor expansion of n in k
10.968 * [backup-simplify]: Simplify n into n
10.968 * [backup-simplify]: Simplify (log n) into (log n)
10.968 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
10.968 * [backup-simplify]: Simplify (- 1/2) into -1/2
10.969 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
10.969 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
10.969 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
10.970 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
10.971 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
10.972 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
10.973 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
10.975 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
10.975 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
10.977 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
10.977 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
10.978 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
10.978 * [backup-simplify]: Simplify (- 0) into 0
10.978 * [backup-simplify]: Simplify (+ 0 0) into 0
10.979 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
10.980 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
10.982 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
10.984 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
10.984 * [taylor]: Taking taylor expansion of 0 in k
10.984 * [backup-simplify]: Simplify 0 into 0
10.984 * [backup-simplify]: Simplify 0 into 0
10.984 * [backup-simplify]: Simplify 0 into 0
10.985 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
10.986 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
10.989 * [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
10.990 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
10.990 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
10.991 * [backup-simplify]: Simplify (- 0) into 0
10.991 * [backup-simplify]: Simplify (+ 0 0) into 0
10.992 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
10.993 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
10.995 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
10.997 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
10.998 * [taylor]: Taking taylor expansion of 0 in k
10.998 * [backup-simplify]: Simplify 0 into 0
10.998 * [backup-simplify]: Simplify 0 into 0
10.998 * [backup-simplify]: Simplify 0 into 0
10.998 * [backup-simplify]: Simplify 0 into 0
10.999 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.000 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.006 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
11.007 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.008 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
11.008 * [backup-simplify]: Simplify (- 0) into 0
11.009 * [backup-simplify]: Simplify (+ 0 0) into 0
11.010 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0
11.012 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.014 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
11.017 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 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
11.017 * [taylor]: Taking taylor expansion of 0 in k
11.017 * [backup-simplify]: Simplify 0 into 0
11.017 * [backup-simplify]: Simplify 0 into 0
11.018 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))
11.018 * [backup-simplify]: Simplify (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)))
11.018 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0
11.019 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
11.019 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k
11.019 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k
11.019 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
11.019 * [taylor]: Taking taylor expansion of 1/2 in k
11.019 * [backup-simplify]: Simplify 1/2 into 1/2
11.019 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
11.019 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.019 * [taylor]: Taking taylor expansion of 1/2 in k
11.019 * [backup-simplify]: Simplify 1/2 into 1/2
11.019 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.019 * [taylor]: Taking taylor expansion of k in k
11.019 * [backup-simplify]: Simplify 0 into 0
11.019 * [backup-simplify]: Simplify 1 into 1
11.019 * [backup-simplify]: Simplify (/ 1 1) into 1
11.019 * [taylor]: Taking taylor expansion of 1/2 in k
11.019 * [backup-simplify]: Simplify 1/2 into 1/2
11.019 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
11.019 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
11.020 * [taylor]: Taking taylor expansion of -2 in k
11.020 * [backup-simplify]: Simplify -2 into -2
11.020 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.020 * [taylor]: Taking taylor expansion of PI in k
11.020 * [backup-simplify]: Simplify PI into PI
11.020 * [taylor]: Taking taylor expansion of n in k
11.020 * [backup-simplify]: Simplify n into n
11.020 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.020 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
11.020 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
11.020 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.021 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.021 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
11.021 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
11.021 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
11.021 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
11.022 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
11.022 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
11.022 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.022 * [taylor]: Taking taylor expansion of 1/2 in n
11.022 * [backup-simplify]: Simplify 1/2 into 1/2
11.022 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.022 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.022 * [taylor]: Taking taylor expansion of 1/2 in n
11.022 * [backup-simplify]: Simplify 1/2 into 1/2
11.022 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.022 * [taylor]: Taking taylor expansion of k in n
11.022 * [backup-simplify]: Simplify k into k
11.022 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.022 * [taylor]: Taking taylor expansion of 1/2 in n
11.022 * [backup-simplify]: Simplify 1/2 into 1/2
11.022 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
11.022 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
11.022 * [taylor]: Taking taylor expansion of -2 in n
11.022 * [backup-simplify]: Simplify -2 into -2
11.022 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.022 * [taylor]: Taking taylor expansion of PI in n
11.022 * [backup-simplify]: Simplify PI into PI
11.022 * [taylor]: Taking taylor expansion of n in n
11.022 * [backup-simplify]: Simplify 0 into 0
11.022 * [backup-simplify]: Simplify 1 into 1
11.023 * [backup-simplify]: Simplify (/ PI 1) into PI
11.023 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
11.024 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
11.024 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.025 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.025 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
11.026 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.027 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
11.029 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
11.029 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
11.029 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
11.029 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
11.029 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.029 * [taylor]: Taking taylor expansion of 1/2 in n
11.029 * [backup-simplify]: Simplify 1/2 into 1/2
11.029 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.029 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.029 * [taylor]: Taking taylor expansion of 1/2 in n
11.029 * [backup-simplify]: Simplify 1/2 into 1/2
11.029 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.029 * [taylor]: Taking taylor expansion of k in n
11.029 * [backup-simplify]: Simplify k into k
11.029 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.029 * [taylor]: Taking taylor expansion of 1/2 in n
11.029 * [backup-simplify]: Simplify 1/2 into 1/2
11.029 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
11.029 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
11.029 * [taylor]: Taking taylor expansion of -2 in n
11.029 * [backup-simplify]: Simplify -2 into -2
11.029 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.029 * [taylor]: Taking taylor expansion of PI in n
11.029 * [backup-simplify]: Simplify PI into PI
11.029 * [taylor]: Taking taylor expansion of n in n
11.029 * [backup-simplify]: Simplify 0 into 0
11.029 * [backup-simplify]: Simplify 1 into 1
11.030 * [backup-simplify]: Simplify (/ PI 1) into PI
11.030 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
11.031 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
11.031 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.031 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.031 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
11.032 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.033 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
11.034 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
11.034 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k
11.034 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
11.034 * [taylor]: Taking taylor expansion of 1/2 in k
11.034 * [backup-simplify]: Simplify 1/2 into 1/2
11.034 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
11.034 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
11.034 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.034 * [taylor]: Taking taylor expansion of 1/2 in k
11.034 * [backup-simplify]: Simplify 1/2 into 1/2
11.034 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.034 * [taylor]: Taking taylor expansion of k in k
11.034 * [backup-simplify]: Simplify 0 into 0
11.034 * [backup-simplify]: Simplify 1 into 1
11.034 * [backup-simplify]: Simplify (/ 1 1) into 1
11.034 * [taylor]: Taking taylor expansion of 1/2 in k
11.034 * [backup-simplify]: Simplify 1/2 into 1/2
11.034 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
11.034 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
11.034 * [taylor]: Taking taylor expansion of (* -2 PI) in k
11.034 * [taylor]: Taking taylor expansion of -2 in k
11.034 * [backup-simplify]: Simplify -2 into -2
11.034 * [taylor]: Taking taylor expansion of PI in k
11.034 * [backup-simplify]: Simplify PI into PI
11.035 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
11.035 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
11.035 * [taylor]: Taking taylor expansion of (log n) in k
11.035 * [taylor]: Taking taylor expansion of n in k
11.035 * [backup-simplify]: Simplify n into n
11.035 * [backup-simplify]: Simplify (log n) into (log n)
11.036 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.036 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.036 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
11.039 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
11.040 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
11.041 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n)))
11.042 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
11.042 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
11.043 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.044 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
11.045 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
11.045 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.045 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
11.045 * [backup-simplify]: Simplify (+ 0 0) into 0
11.046 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
11.047 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.047 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
11.049 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.049 * [taylor]: Taking taylor expansion of 0 in k
11.049 * [backup-simplify]: Simplify 0 into 0
11.049 * [backup-simplify]: Simplify 0 into 0
11.049 * [backup-simplify]: Simplify 0 into 0
11.050 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.050 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
11.053 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
11.053 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.054 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
11.054 * [backup-simplify]: Simplify (+ 0 0) into 0
11.055 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
11.056 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.057 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
11.058 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.058 * [taylor]: Taking taylor expansion of 0 in k
11.058 * [backup-simplify]: Simplify 0 into 0
11.058 * [backup-simplify]: Simplify 0 into 0
11.058 * [backup-simplify]: Simplify 0 into 0
11.058 * [backup-simplify]: Simplify 0 into 0
11.059 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.060 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.064 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
11.064 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.065 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
11.065 * [backup-simplify]: Simplify (+ 0 0) into 0
11.066 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
11.067 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.068 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
11.070 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 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
11.070 * [taylor]: Taking taylor expansion of 0 in k
11.070 * [backup-simplify]: Simplify 0 into 0
11.070 * [backup-simplify]: Simplify 0 into 0
11.071 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))
11.071 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1)
11.071 * [backup-simplify]: Simplify (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) into (pow (* 2 n) (* 1/2 (- 1/2 (* 1/2 k))))
11.071 * [approximate]: Taking taylor expansion of (pow (* 2 n) (* 1/2 (- 1/2 (* 1/2 k)))) in (n k) around 0
11.072 * [taylor]: Taking taylor expansion of (pow (* 2 n) (* 1/2 (- 1/2 (* 1/2 k)))) in k
11.072 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 n)))) in k
11.072 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 n))) in k
11.072 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k
11.072 * [taylor]: Taking taylor expansion of 1/2 in k
11.072 * [backup-simplify]: Simplify 1/2 into 1/2
11.072 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
11.072 * [taylor]: Taking taylor expansion of 1/2 in k
11.072 * [backup-simplify]: Simplify 1/2 into 1/2
11.072 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
11.072 * [taylor]: Taking taylor expansion of 1/2 in k
11.072 * [backup-simplify]: Simplify 1/2 into 1/2
11.072 * [taylor]: Taking taylor expansion of k in k
11.072 * [backup-simplify]: Simplify 0 into 0
11.072 * [backup-simplify]: Simplify 1 into 1
11.072 * [taylor]: Taking taylor expansion of (log (* 2 n)) in k
11.072 * [taylor]: Taking taylor expansion of (* 2 n) in k
11.072 * [taylor]: Taking taylor expansion of 2 in k
11.072 * [backup-simplify]: Simplify 2 into 2
11.072 * [taylor]: Taking taylor expansion of n in k
11.072 * [backup-simplify]: Simplify n into n
11.072 * [backup-simplify]: Simplify (* 2 n) into (* 2 n)
11.072 * [backup-simplify]: Simplify (log (* 2 n)) into (log (* 2 n))
11.072 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.072 * [backup-simplify]: Simplify (- 0) into 0
11.073 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.073 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
11.073 * [backup-simplify]: Simplify (* 1/4 (log (* 2 n))) into (* 1/4 (log (* 2 n)))
11.073 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 n)))) into (pow (* 2 n) 1/4)
11.073 * [taylor]: Taking taylor expansion of (pow (* 2 n) (* 1/2 (- 1/2 (* 1/2 k)))) in n
11.073 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 n)))) in n
11.073 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 n))) in n
11.073 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
11.073 * [taylor]: Taking taylor expansion of 1/2 in n
11.073 * [backup-simplify]: Simplify 1/2 into 1/2
11.073 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
11.073 * [taylor]: Taking taylor expansion of 1/2 in n
11.073 * [backup-simplify]: Simplify 1/2 into 1/2
11.073 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
11.073 * [taylor]: Taking taylor expansion of 1/2 in n
11.073 * [backup-simplify]: Simplify 1/2 into 1/2
11.073 * [taylor]: Taking taylor expansion of k in n
11.073 * [backup-simplify]: Simplify k into k
11.073 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n
11.073 * [taylor]: Taking taylor expansion of (* 2 n) in n
11.073 * [taylor]: Taking taylor expansion of 2 in n
11.073 * [backup-simplify]: Simplify 2 into 2
11.073 * [taylor]: Taking taylor expansion of n in n
11.073 * [backup-simplify]: Simplify 0 into 0
11.073 * [backup-simplify]: Simplify 1 into 1
11.074 * [backup-simplify]: Simplify (* 2 0) into 0
11.074 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2
11.074 * [backup-simplify]: Simplify (log 2) into (log 2)
11.074 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
11.075 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
11.075 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
11.075 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
11.075 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n))
11.076 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log 2) (log n))) into (* 1/2 (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))))
11.076 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))))) into (exp (* 1/2 (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))))
11.076 * [taylor]: Taking taylor expansion of (pow (* 2 n) (* 1/2 (- 1/2 (* 1/2 k)))) in n
11.076 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 n)))) in n
11.076 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 n))) in n
11.076 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
11.076 * [taylor]: Taking taylor expansion of 1/2 in n
11.076 * [backup-simplify]: Simplify 1/2 into 1/2
11.076 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
11.076 * [taylor]: Taking taylor expansion of 1/2 in n
11.076 * [backup-simplify]: Simplify 1/2 into 1/2
11.076 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
11.076 * [taylor]: Taking taylor expansion of 1/2 in n
11.076 * [backup-simplify]: Simplify 1/2 into 1/2
11.076 * [taylor]: Taking taylor expansion of k in n
11.076 * [backup-simplify]: Simplify k into k
11.076 * [taylor]: Taking taylor expansion of (log (* 2 n)) in n
11.076 * [taylor]: Taking taylor expansion of (* 2 n) in n
11.076 * [taylor]: Taking taylor expansion of 2 in n
11.076 * [backup-simplify]: Simplify 2 into 2
11.076 * [taylor]: Taking taylor expansion of n in n
11.076 * [backup-simplify]: Simplify 0 into 0
11.076 * [backup-simplify]: Simplify 1 into 1
11.077 * [backup-simplify]: Simplify (* 2 0) into 0
11.077 * [backup-simplify]: Simplify (+ (* 2 1) (* 0 0)) into 2
11.077 * [backup-simplify]: Simplify (log 2) into (log 2)
11.077 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
11.077 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
11.077 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
11.077 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
11.078 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n))
11.078 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log 2) (log n))) into (* 1/2 (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))))
11.079 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))))) into (exp (* 1/2 (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))))
11.079 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))))) in k
11.079 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k)))) in k
11.079 * [taylor]: Taking taylor expansion of 1/2 in k
11.079 * [backup-simplify]: Simplify 1/2 into 1/2
11.079 * [taylor]: Taking taylor expansion of (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))) in k
11.079 * [taylor]: Taking taylor expansion of (+ (log 2) (log n)) in k
11.079 * [taylor]: Taking taylor expansion of (log 2) in k
11.079 * [taylor]: Taking taylor expansion of 2 in k
11.079 * [backup-simplify]: Simplify 2 into 2
11.080 * [backup-simplify]: Simplify (log 2) into (log 2)
11.080 * [taylor]: Taking taylor expansion of (log n) in k
11.080 * [taylor]: Taking taylor expansion of n in k
11.080 * [backup-simplify]: Simplify n into n
11.080 * [backup-simplify]: Simplify (log n) into (log n)
11.080 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
11.080 * [taylor]: Taking taylor expansion of 1/2 in k
11.080 * [backup-simplify]: Simplify 1/2 into 1/2
11.080 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
11.080 * [taylor]: Taking taylor expansion of 1/2 in k
11.080 * [backup-simplify]: Simplify 1/2 into 1/2
11.080 * [taylor]: Taking taylor expansion of k in k
11.080 * [backup-simplify]: Simplify 0 into 0
11.080 * [backup-simplify]: Simplify 1 into 1
11.080 * [backup-simplify]: Simplify (+ (log 2) (log n)) into (+ (log 2) (log n))
11.081 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.081 * [backup-simplify]: Simplify (- 0) into 0
11.082 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.082 * [backup-simplify]: Simplify (* (+ (log 2) (log n)) 1/2) into (* 1/2 (+ (log 2) (log n)))
11.083 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log 2) (log n)))) into (* 1/4 (+ (log 2) (log n)))
11.083 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log 2) (log n)))) into (exp (* 1/4 (+ (log 2) (log n))))
11.083 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log 2) (log n)))) into (exp (* 1/4 (+ (log 2) (log n))))
11.085 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 1) (* 0 0))) into 0
11.086 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
11.087 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
11.087 * [backup-simplify]: Simplify (- 0) into 0
11.087 * [backup-simplify]: Simplify (+ 0 0) into 0
11.088 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0
11.089 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n))
11.089 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log 2) (log n)))) into 0
11.090 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.091 * [taylor]: Taking taylor expansion of 0 in k
11.091 * [backup-simplify]: Simplify 0 into 0
11.091 * [backup-simplify]: Simplify 0 into 0
11.091 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
11.092 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.092 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.094 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
11.094 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
11.095 * [backup-simplify]: Simplify (+ 0 0) into 0
11.095 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) -1/2) (* 0 1/2)) into (- (+ (* 1/2 (log 2)) (* 1/2 (log n))))
11.096 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log 2) (log n))))) into (- (+ (* 1/4 (log 2)) (* 1/4 (log n))))
11.097 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/4 (log 2)) (* 1/4 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log 2)) (* 1/4 (log n))) (exp (* 1/4 (+ (log 2) (log n))))))
11.098 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/4 (log 2)) (* 1/4 (log n))) (exp (* 1/4 (+ (log 2) (log n)))))) into (* -1 (* (+ (* 1/4 (log 2)) (* 1/4 (log n))) (exp (* 1/4 (+ (log 2) (log n))))))
11.099 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
11.100 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
11.101 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
11.101 * [backup-simplify]: Simplify (- 0) into 0
11.101 * [backup-simplify]: Simplify (+ 0 0) into 0
11.102 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0
11.102 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log 2)) into (+ (log 2) (log n))
11.103 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log 2) (log n))))) into 0
11.104 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (log 2) (log n)) (- 1/2 (* 1/2 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.104 * [taylor]: Taking taylor expansion of 0 in k
11.104 * [backup-simplify]: Simplify 0 into 0
11.104 * [backup-simplify]: Simplify 0 into 0
11.104 * [backup-simplify]: Simplify 0 into 0
11.105 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
11.105 * [backup-simplify]: Simplify (- 0) into 0
11.105 * [backup-simplify]: Simplify (+ 0 0) into 0
11.107 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
11.108 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
11.108 * [backup-simplify]: Simplify (+ 0 0) into 0
11.109 * [backup-simplify]: Simplify (+ (* (+ (log 2) (log n)) 0) (+ (* 0 -1/2) (* 0 1/2))) into 0
11.110 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (* 1/2 (log 2)) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log 2) (log n)))))) into 0
11.111 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log 2) (log n)))) (+ (* (/ (pow (- (+ (* 1/4 (log 2)) (* 1/4 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log 2) (log n))) (* 1/32 (pow (log 2) 2)))) (exp (* 1/4 (+ (log 2) (log n)))))
11.113 * [backup-simplify]: Simplify (* (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log 2) (log n))) (* 1/32 (pow (log 2) 2)))) (exp (* 1/4 (+ (log 2) (log n))))) into (* (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log 2) (log n))) (* 1/32 (pow (log 2) 2)))) (exp (* 1/4 (+ (log 2) (log n)))))
11.116 * [backup-simplify]: Simplify (+ (* (* (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log 2) (log n))) (* 1/32 (pow (log 2) 2)))) (exp (* 1/4 (+ (log 2) (log n))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/4 (log 2)) (* 1/4 (log n))) (exp (* 1/4 (+ (log 2) (log n)))))) (* k 1)) (exp (* 1/4 (+ (log 2) (log n)))))) into (- (+ (* 1/32 (* (pow (log 2) 2) (* (exp (* 1/4 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/32 (* (exp (* 1/4 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/16 (* (log 2) (* (exp (* 1/4 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (exp (* 1/4 (+ (log 2) (log n))))))) (+ (* 1/4 (* (log 2) (* (exp (* 1/4 (+ (log 2) (log n)))) k))) (* 1/4 (* (exp (* 1/4 (+ (log 2) (log n)))) (* (log n) k)))))
11.116 * [backup-simplify]: Simplify (pow (* (/ 1 n) 2) (/ (- 1/2 (/ (/ 1 k) 2)) 2)) into (pow (/ 2 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))))
11.116 * [approximate]: Taking taylor expansion of (pow (/ 2 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
11.116 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k
11.116 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 2 n)))) in k
11.116 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 2 n))) in k
11.116 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k
11.116 * [taylor]: Taking taylor expansion of 1/2 in k
11.116 * [backup-simplify]: Simplify 1/2 into 1/2
11.116 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
11.116 * [taylor]: Taking taylor expansion of 1/2 in k
11.116 * [backup-simplify]: Simplify 1/2 into 1/2
11.116 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.116 * [taylor]: Taking taylor expansion of 1/2 in k
11.116 * [backup-simplify]: Simplify 1/2 into 1/2
11.116 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.116 * [taylor]: Taking taylor expansion of k in k
11.116 * [backup-simplify]: Simplify 0 into 0
11.116 * [backup-simplify]: Simplify 1 into 1
11.117 * [backup-simplify]: Simplify (/ 1 1) into 1
11.117 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in k
11.117 * [taylor]: Taking taylor expansion of (/ 2 n) in k
11.117 * [taylor]: Taking taylor expansion of 2 in k
11.117 * [backup-simplify]: Simplify 2 into 2
11.117 * [taylor]: Taking taylor expansion of n in k
11.117 * [backup-simplify]: Simplify n into n
11.117 * [backup-simplify]: Simplify (/ 2 n) into (/ 2 n)
11.117 * [backup-simplify]: Simplify (log (/ 2 n)) into (log (/ 2 n))
11.117 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.117 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.118 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.118 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4
11.118 * [backup-simplify]: Simplify (* -1/4 (log (/ 2 n))) into (* -1/4 (log (/ 2 n)))
11.118 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 2 n)))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 2 n)))))
11.118 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
11.118 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 2 n)))) in n
11.118 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 2 n))) in n
11.118 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
11.118 * [taylor]: Taking taylor expansion of 1/2 in n
11.118 * [backup-simplify]: Simplify 1/2 into 1/2
11.118 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.118 * [taylor]: Taking taylor expansion of 1/2 in n
11.118 * [backup-simplify]: Simplify 1/2 into 1/2
11.118 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.118 * [taylor]: Taking taylor expansion of 1/2 in n
11.118 * [backup-simplify]: Simplify 1/2 into 1/2
11.118 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.118 * [taylor]: Taking taylor expansion of k in n
11.118 * [backup-simplify]: Simplify k into k
11.118 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.118 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n
11.118 * [taylor]: Taking taylor expansion of (/ 2 n) in n
11.118 * [taylor]: Taking taylor expansion of 2 in n
11.118 * [backup-simplify]: Simplify 2 into 2
11.118 * [taylor]: Taking taylor expansion of n in n
11.118 * [backup-simplify]: Simplify 0 into 0
11.118 * [backup-simplify]: Simplify 1 into 1
11.119 * [backup-simplify]: Simplify (/ 2 1) into 2
11.119 * [backup-simplify]: Simplify (log 2) into (log 2)
11.119 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.119 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.119 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.119 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
11.120 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n))
11.120 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log 2) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))
11.120 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))
11.120 * [taylor]: Taking taylor expansion of (pow (/ 2 n) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
11.120 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 2 n)))) in n
11.120 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (/ 2 n))) in n
11.120 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
11.120 * [taylor]: Taking taylor expansion of 1/2 in n
11.120 * [backup-simplify]: Simplify 1/2 into 1/2
11.120 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.120 * [taylor]: Taking taylor expansion of 1/2 in n
11.120 * [backup-simplify]: Simplify 1/2 into 1/2
11.120 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.121 * [taylor]: Taking taylor expansion of 1/2 in n
11.121 * [backup-simplify]: Simplify 1/2 into 1/2
11.121 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.121 * [taylor]: Taking taylor expansion of k in n
11.121 * [backup-simplify]: Simplify k into k
11.121 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.121 * [taylor]: Taking taylor expansion of (log (/ 2 n)) in n
11.121 * [taylor]: Taking taylor expansion of (/ 2 n) in n
11.121 * [taylor]: Taking taylor expansion of 2 in n
11.121 * [backup-simplify]: Simplify 2 into 2
11.121 * [taylor]: Taking taylor expansion of n in n
11.121 * [backup-simplify]: Simplify 0 into 0
11.121 * [backup-simplify]: Simplify 1 into 1
11.121 * [backup-simplify]: Simplify (/ 2 1) into 2
11.121 * [backup-simplify]: Simplify (log 2) into (log 2)
11.121 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.121 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.121 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.121 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
11.122 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n))
11.122 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log 2) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))
11.123 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))
11.123 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) in k
11.123 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))) in k
11.123 * [taylor]: Taking taylor expansion of 1/2 in k
11.123 * [backup-simplify]: Simplify 1/2 into 1/2
11.123 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))) in k
11.123 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
11.123 * [taylor]: Taking taylor expansion of 1/2 in k
11.123 * [backup-simplify]: Simplify 1/2 into 1/2
11.123 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.123 * [taylor]: Taking taylor expansion of 1/2 in k
11.123 * [backup-simplify]: Simplify 1/2 into 1/2
11.123 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.123 * [taylor]: Taking taylor expansion of k in k
11.123 * [backup-simplify]: Simplify 0 into 0
11.123 * [backup-simplify]: Simplify 1 into 1
11.123 * [backup-simplify]: Simplify (/ 1 1) into 1
11.123 * [taylor]: Taking taylor expansion of (- (log 2) (log n)) in k
11.123 * [taylor]: Taking taylor expansion of (log 2) in k
11.123 * [taylor]: Taking taylor expansion of 2 in k
11.123 * [backup-simplify]: Simplify 2 into 2
11.124 * [backup-simplify]: Simplify (log 2) into (log 2)
11.124 * [taylor]: Taking taylor expansion of (log n) in k
11.124 * [taylor]: Taking taylor expansion of n in k
11.124 * [backup-simplify]: Simplify n into n
11.124 * [backup-simplify]: Simplify (log n) into (log n)
11.124 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.124 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.124 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.124 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
11.125 * [backup-simplify]: Simplify (+ (log 2) (- (log n))) into (- (log 2) (log n))
11.125 * [backup-simplify]: Simplify (* -1/2 (- (log 2) (log n))) into (* -1/2 (- (log 2) (log n)))
11.125 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log 2) (log n)))) into (* -1/4 (- (log 2) (log n)))
11.126 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))
11.126 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n)))))
11.127 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)))) into 0
11.129 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2 1)))) 1) into 0
11.129 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.129 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
11.130 * [backup-simplify]: Simplify (- 0) into 0
11.130 * [backup-simplify]: Simplify (+ 0 0) into 0
11.131 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
11.131 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n))
11.131 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log 2) (log n)))) into 0
11.132 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.132 * [taylor]: Taking taylor expansion of 0 in k
11.132 * [backup-simplify]: Simplify 0 into 0
11.132 * [backup-simplify]: Simplify 0 into 0
11.132 * [backup-simplify]: Simplify 0 into 0
11.133 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.135 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 2 1)))) 2) into 0
11.135 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.138 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
11.139 * [backup-simplify]: Simplify (- 0) into 0
11.139 * [backup-simplify]: Simplify (+ 0 0) into 0
11.140 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
11.140 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n))
11.141 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log 2) (log n))))) into 0
11.142 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.142 * [taylor]: Taking taylor expansion of 0 in k
11.142 * [backup-simplify]: Simplify 0 into 0
11.142 * [backup-simplify]: Simplify 0 into 0
11.142 * [backup-simplify]: Simplify 0 into 0
11.142 * [backup-simplify]: Simplify 0 into 0
11.142 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* 2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.145 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 2 1)))) 6) into 0
11.145 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.146 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
11.146 * [backup-simplify]: Simplify (- 0) into 0
11.147 * [backup-simplify]: Simplify (+ 0 0) into 0
11.147 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0
11.148 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log 2)) into (- (log 2) (log n))
11.149 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log 2) (log n)))))) into 0
11.150 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log 2) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
11.150 * [taylor]: Taking taylor expansion of 0 in k
11.150 * [backup-simplify]: Simplify 0 into 0
11.150 * [backup-simplify]: Simplify 0 into 0
11.150 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log 2) (log (/ 1 n)))))) into (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))))
11.150 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) 2) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2)) into (pow (/ -2 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)))
11.150 * [approximate]: Taking taylor expansion of (pow (/ -2 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in (n k) around 0
11.150 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
11.150 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -2 n)))) in k
11.150 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -2 n))) in k
11.150 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
11.150 * [taylor]: Taking taylor expansion of 1/2 in k
11.151 * [backup-simplify]: Simplify 1/2 into 1/2
11.151 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
11.151 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.151 * [taylor]: Taking taylor expansion of 1/2 in k
11.151 * [backup-simplify]: Simplify 1/2 into 1/2
11.151 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.151 * [taylor]: Taking taylor expansion of k in k
11.151 * [backup-simplify]: Simplify 0 into 0
11.151 * [backup-simplify]: Simplify 1 into 1
11.151 * [backup-simplify]: Simplify (/ 1 1) into 1
11.151 * [taylor]: Taking taylor expansion of 1/2 in k
11.151 * [backup-simplify]: Simplify 1/2 into 1/2
11.151 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in k
11.151 * [taylor]: Taking taylor expansion of (/ -2 n) in k
11.151 * [taylor]: Taking taylor expansion of -2 in k
11.151 * [backup-simplify]: Simplify -2 into -2
11.151 * [taylor]: Taking taylor expansion of n in k
11.151 * [backup-simplify]: Simplify n into n
11.151 * [backup-simplify]: Simplify (/ -2 n) into (/ -2 n)
11.151 * [backup-simplify]: Simplify (log (/ -2 n)) into (log (/ -2 n))
11.151 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.152 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.152 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
11.152 * [backup-simplify]: Simplify (* 1/4 (log (/ -2 n))) into (* 1/4 (log (/ -2 n)))
11.152 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -2 n)))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -2 n)))))
11.152 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
11.152 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -2 n)))) in n
11.152 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -2 n))) in n
11.152 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.152 * [taylor]: Taking taylor expansion of 1/2 in n
11.152 * [backup-simplify]: Simplify 1/2 into 1/2
11.152 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.152 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.152 * [taylor]: Taking taylor expansion of 1/2 in n
11.152 * [backup-simplify]: Simplify 1/2 into 1/2
11.152 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.152 * [taylor]: Taking taylor expansion of k in n
11.152 * [backup-simplify]: Simplify k into k
11.152 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.152 * [taylor]: Taking taylor expansion of 1/2 in n
11.152 * [backup-simplify]: Simplify 1/2 into 1/2
11.152 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n
11.152 * [taylor]: Taking taylor expansion of (/ -2 n) in n
11.152 * [taylor]: Taking taylor expansion of -2 in n
11.152 * [backup-simplify]: Simplify -2 into -2
11.152 * [taylor]: Taking taylor expansion of n in n
11.152 * [backup-simplify]: Simplify 0 into 0
11.152 * [backup-simplify]: Simplify 1 into 1
11.153 * [backup-simplify]: Simplify (/ -2 1) into -2
11.153 * [backup-simplify]: Simplify (log -2) into (log -2)
11.153 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.153 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.153 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
11.154 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n))
11.154 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log -2) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))
11.154 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))
11.154 * [taylor]: Taking taylor expansion of (pow (/ -2 n) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
11.154 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -2 n)))) in n
11.154 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (/ -2 n))) in n
11.154 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.154 * [taylor]: Taking taylor expansion of 1/2 in n
11.154 * [backup-simplify]: Simplify 1/2 into 1/2
11.154 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.154 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.154 * [taylor]: Taking taylor expansion of 1/2 in n
11.154 * [backup-simplify]: Simplify 1/2 into 1/2
11.154 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.155 * [taylor]: Taking taylor expansion of k in n
11.155 * [backup-simplify]: Simplify k into k
11.155 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.155 * [taylor]: Taking taylor expansion of 1/2 in n
11.155 * [backup-simplify]: Simplify 1/2 into 1/2
11.155 * [taylor]: Taking taylor expansion of (log (/ -2 n)) in n
11.155 * [taylor]: Taking taylor expansion of (/ -2 n) in n
11.155 * [taylor]: Taking taylor expansion of -2 in n
11.155 * [backup-simplify]: Simplify -2 into -2
11.155 * [taylor]: Taking taylor expansion of n in n
11.155 * [backup-simplify]: Simplify 0 into 0
11.155 * [backup-simplify]: Simplify 1 into 1
11.155 * [backup-simplify]: Simplify (/ -2 1) into -2
11.155 * [backup-simplify]: Simplify (log -2) into (log -2)
11.155 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.155 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.155 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
11.156 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n))
11.156 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log -2) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))
11.157 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))
11.157 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) in k
11.157 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))) in k
11.157 * [taylor]: Taking taylor expansion of 1/2 in k
11.157 * [backup-simplify]: Simplify 1/2 into 1/2
11.157 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))) in k
11.157 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
11.157 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.157 * [taylor]: Taking taylor expansion of 1/2 in k
11.157 * [backup-simplify]: Simplify 1/2 into 1/2
11.157 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.157 * [taylor]: Taking taylor expansion of k in k
11.157 * [backup-simplify]: Simplify 0 into 0
11.157 * [backup-simplify]: Simplify 1 into 1
11.157 * [backup-simplify]: Simplify (/ 1 1) into 1
11.157 * [taylor]: Taking taylor expansion of 1/2 in k
11.157 * [backup-simplify]: Simplify 1/2 into 1/2
11.157 * [taylor]: Taking taylor expansion of (- (log -2) (log n)) in k
11.157 * [taylor]: Taking taylor expansion of (log -2) in k
11.157 * [taylor]: Taking taylor expansion of -2 in k
11.157 * [backup-simplify]: Simplify -2 into -2
11.157 * [backup-simplify]: Simplify (log -2) into (log -2)
11.157 * [taylor]: Taking taylor expansion of (log n) in k
11.157 * [taylor]: Taking taylor expansion of n in k
11.158 * [backup-simplify]: Simplify n into n
11.158 * [backup-simplify]: Simplify (log n) into (log n)
11.158 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.158 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.158 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
11.158 * [backup-simplify]: Simplify (+ (log -2) (- (log n))) into (- (log -2) (log n))
11.159 * [backup-simplify]: Simplify (* 1/2 (- (log -2) (log n))) into (* 1/2 (- (log -2) (log n)))
11.159 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log -2) (log n)))) into (* 1/4 (- (log -2) (log n)))
11.159 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))
11.160 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n)))))
11.160 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)))) into 0
11.161 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -2 1)))) 1) into 0
11.161 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.161 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
11.162 * [backup-simplify]: Simplify (+ 0 0) into 0
11.162 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
11.162 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n))
11.163 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log -2) (log n)))) into 0
11.164 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.164 * [taylor]: Taking taylor expansion of 0 in k
11.164 * [backup-simplify]: Simplify 0 into 0
11.164 * [backup-simplify]: Simplify 0 into 0
11.164 * [backup-simplify]: Simplify 0 into 0
11.164 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.166 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -2 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -2 1)))) 2) into 0
11.166 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.166 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
11.167 * [backup-simplify]: Simplify (+ 0 0) into 0
11.167 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
11.168 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n))
11.168 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log -2) (log n))))) into 0
11.169 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.169 * [taylor]: Taking taylor expansion of 0 in k
11.169 * [backup-simplify]: Simplify 0 into 0
11.169 * [backup-simplify]: Simplify 0 into 0
11.169 * [backup-simplify]: Simplify 0 into 0
11.169 * [backup-simplify]: Simplify 0 into 0
11.170 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -2 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.173 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow -2 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow -2 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow -2 1)))) 6) into 0
11.173 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.174 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
11.174 * [backup-simplify]: Simplify (+ 0 0) into 0
11.175 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))))) into 0
11.175 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -2)) into (- (log -2) (log n))
11.176 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -2) (log n)))))) into 0
11.177 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -2) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
11.178 * [taylor]: Taking taylor expansion of 0 in k
11.178 * [backup-simplify]: Simplify 0 into 0
11.178 * [backup-simplify]: Simplify 0 into 0
11.178 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -2) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))))
11.178 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1 1)
11.178 * [backup-simplify]: Simplify (* (* n 2) PI) into (* 2 (* n PI))
11.178 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
11.178 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
11.178 * [taylor]: Taking taylor expansion of 2 in n
11.178 * [backup-simplify]: Simplify 2 into 2
11.178 * [taylor]: Taking taylor expansion of (* n PI) in n
11.178 * [taylor]: Taking taylor expansion of n in n
11.178 * [backup-simplify]: Simplify 0 into 0
11.178 * [backup-simplify]: Simplify 1 into 1
11.178 * [taylor]: Taking taylor expansion of PI in n
11.178 * [backup-simplify]: Simplify PI into PI
11.178 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
11.178 * [taylor]: Taking taylor expansion of 2 in n
11.178 * [backup-simplify]: Simplify 2 into 2
11.178 * [taylor]: Taking taylor expansion of (* n PI) in n
11.178 * [taylor]: Taking taylor expansion of n in n
11.178 * [backup-simplify]: Simplify 0 into 0
11.178 * [backup-simplify]: Simplify 1 into 1
11.178 * [taylor]: Taking taylor expansion of PI in n
11.178 * [backup-simplify]: Simplify PI into PI
11.179 * [backup-simplify]: Simplify (* 0 PI) into 0
11.180 * [backup-simplify]: Simplify (* 2 0) into 0
11.180 * [backup-simplify]: Simplify 0 into 0
11.181 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.183 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
11.184 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.185 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.186 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
11.186 * [backup-simplify]: Simplify 0 into 0
11.187 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
11.188 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
11.188 * [backup-simplify]: Simplify 0 into 0
11.190 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.191 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
11.191 * [backup-simplify]: Simplify 0 into 0
11.193 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.195 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
11.195 * [backup-simplify]: Simplify 0 into 0
11.197 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.199 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
11.199 * [backup-simplify]: Simplify 0 into 0
11.201 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
11.203 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
11.203 * [backup-simplify]: Simplify 0 into 0
11.204 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
11.204 * [backup-simplify]: Simplify (* (* (/ 1 n) 2) PI) into (* 2 (/ PI n))
11.204 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
11.204 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
11.204 * [taylor]: Taking taylor expansion of 2 in n
11.204 * [backup-simplify]: Simplify 2 into 2
11.204 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.204 * [taylor]: Taking taylor expansion of PI in n
11.204 * [backup-simplify]: Simplify PI into PI
11.204 * [taylor]: Taking taylor expansion of n in n
11.204 * [backup-simplify]: Simplify 0 into 0
11.204 * [backup-simplify]: Simplify 1 into 1
11.205 * [backup-simplify]: Simplify (/ PI 1) into PI
11.205 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
11.205 * [taylor]: Taking taylor expansion of 2 in n
11.205 * [backup-simplify]: Simplify 2 into 2
11.205 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.205 * [taylor]: Taking taylor expansion of PI in n
11.205 * [backup-simplify]: Simplify PI into PI
11.205 * [taylor]: Taking taylor expansion of n in n
11.205 * [backup-simplify]: Simplify 0 into 0
11.205 * [backup-simplify]: Simplify 1 into 1
11.205 * [backup-simplify]: Simplify (/ PI 1) into PI
11.206 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.206 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.207 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.208 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
11.208 * [backup-simplify]: Simplify 0 into 0
11.210 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.211 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
11.211 * [backup-simplify]: Simplify 0 into 0
11.212 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.213 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.213 * [backup-simplify]: Simplify 0 into 0
11.214 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.216 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.216 * [backup-simplify]: Simplify 0 into 0
11.217 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.218 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.219 * [backup-simplify]: Simplify 0 into 0
11.220 * [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
11.221 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.221 * [backup-simplify]: Simplify 0 into 0
11.222 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
11.222 * [backup-simplify]: Simplify (* (* (/ 1 (- n)) 2) PI) into (* -2 (/ PI n))
11.222 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
11.222 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
11.222 * [taylor]: Taking taylor expansion of -2 in n
11.222 * [backup-simplify]: Simplify -2 into -2
11.222 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.222 * [taylor]: Taking taylor expansion of PI in n
11.222 * [backup-simplify]: Simplify PI into PI
11.222 * [taylor]: Taking taylor expansion of n in n
11.222 * [backup-simplify]: Simplify 0 into 0
11.222 * [backup-simplify]: Simplify 1 into 1
11.223 * [backup-simplify]: Simplify (/ PI 1) into PI
11.223 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
11.223 * [taylor]: Taking taylor expansion of -2 in n
11.223 * [backup-simplify]: Simplify -2 into -2
11.223 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.223 * [taylor]: Taking taylor expansion of PI in n
11.223 * [backup-simplify]: Simplify PI into PI
11.223 * [taylor]: Taking taylor expansion of n in n
11.223 * [backup-simplify]: Simplify 0 into 0
11.223 * [backup-simplify]: Simplify 1 into 1
11.224 * [backup-simplify]: Simplify (/ PI 1) into PI
11.224 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
11.225 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
11.226 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.227 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
11.227 * [backup-simplify]: Simplify 0 into 0
11.228 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.229 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
11.229 * [backup-simplify]: Simplify 0 into 0
11.230 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.231 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.231 * [backup-simplify]: Simplify 0 into 0
11.232 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.234 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.234 * [backup-simplify]: Simplify 0 into 0
11.235 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.236 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.236 * [backup-simplify]: Simplify 0 into 0
11.237 * [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
11.239 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.239 * [backup-simplify]: Simplify 0 into 0
11.240 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
11.240 * * * * [progress]: [ 4 / 4 ] generating series at (2 2)
11.240 * [backup-simplify]: Simplify (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k)))
11.240 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in (n k) around 0
11.240 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in k
11.241 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in k
11.241 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in k
11.241 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in k
11.241 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in k
11.241 * [taylor]: Taking taylor expansion of 1/2 in k
11.241 * [backup-simplify]: Simplify 1/2 into 1/2
11.241 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
11.241 * [taylor]: Taking taylor expansion of 1/2 in k
11.241 * [backup-simplify]: Simplify 1/2 into 1/2
11.241 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
11.241 * [taylor]: Taking taylor expansion of 1/2 in k
11.241 * [backup-simplify]: Simplify 1/2 into 1/2
11.241 * [taylor]: Taking taylor expansion of k in k
11.241 * [backup-simplify]: Simplify 0 into 0
11.241 * [backup-simplify]: Simplify 1 into 1
11.241 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
11.241 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
11.241 * [taylor]: Taking taylor expansion of 2 in k
11.241 * [backup-simplify]: Simplify 2 into 2
11.241 * [taylor]: Taking taylor expansion of (* n PI) in k
11.241 * [taylor]: Taking taylor expansion of n in k
11.241 * [backup-simplify]: Simplify n into n
11.241 * [taylor]: Taking taylor expansion of PI in k
11.241 * [backup-simplify]: Simplify PI into PI
11.241 * [backup-simplify]: Simplify (* n PI) into (* n PI)
11.241 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
11.241 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
11.242 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.242 * [backup-simplify]: Simplify (- 0) into 0
11.243 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.243 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
11.243 * [backup-simplify]: Simplify (* 1/4 (log (* 2 (* n PI)))) into (* 1/4 (log (* 2 (* n PI))))
11.243 * [backup-simplify]: Simplify (exp (* 1/4 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/4)
11.243 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
11.243 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.243 * [taylor]: Taking taylor expansion of k in k
11.243 * [backup-simplify]: Simplify 0 into 0
11.244 * [backup-simplify]: Simplify 1 into 1
11.244 * [backup-simplify]: Simplify (/ 1 1) into 1
11.244 * [backup-simplify]: Simplify (sqrt 0) into 0
11.246 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
11.246 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n
11.246 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
11.246 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
11.246 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
11.246 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
11.246 * [taylor]: Taking taylor expansion of 1/2 in n
11.246 * [backup-simplify]: Simplify 1/2 into 1/2
11.246 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
11.246 * [taylor]: Taking taylor expansion of 1/2 in n
11.246 * [backup-simplify]: Simplify 1/2 into 1/2
11.246 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
11.246 * [taylor]: Taking taylor expansion of 1/2 in n
11.246 * [backup-simplify]: Simplify 1/2 into 1/2
11.246 * [taylor]: Taking taylor expansion of k in n
11.246 * [backup-simplify]: Simplify k into k
11.246 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
11.246 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
11.246 * [taylor]: Taking taylor expansion of 2 in n
11.246 * [backup-simplify]: Simplify 2 into 2
11.246 * [taylor]: Taking taylor expansion of (* n PI) in n
11.246 * [taylor]: Taking taylor expansion of n in n
11.246 * [backup-simplify]: Simplify 0 into 0
11.246 * [backup-simplify]: Simplify 1 into 1
11.246 * [taylor]: Taking taylor expansion of PI in n
11.246 * [backup-simplify]: Simplify PI into PI
11.247 * [backup-simplify]: Simplify (* 0 PI) into 0
11.247 * [backup-simplify]: Simplify (* 2 0) into 0
11.248 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.249 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
11.250 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.250 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
11.250 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
11.250 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
11.250 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
11.251 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.251 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
11.252 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
11.252 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
11.252 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.252 * [taylor]: Taking taylor expansion of k in n
11.252 * [backup-simplify]: Simplify k into k
11.252 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.252 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
11.252 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.253 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
11.253 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) (sqrt (/ 1 k))) in n
11.253 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1/2 (* 1/2 k)))) in n
11.253 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI))))) in n
11.253 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 k))) (log (* 2 (* n PI)))) in n
11.253 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 k))) in n
11.253 * [taylor]: Taking taylor expansion of 1/2 in n
11.253 * [backup-simplify]: Simplify 1/2 into 1/2
11.253 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
11.253 * [taylor]: Taking taylor expansion of 1/2 in n
11.253 * [backup-simplify]: Simplify 1/2 into 1/2
11.253 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
11.253 * [taylor]: Taking taylor expansion of 1/2 in n
11.253 * [backup-simplify]: Simplify 1/2 into 1/2
11.253 * [taylor]: Taking taylor expansion of k in n
11.253 * [backup-simplify]: Simplify k into k
11.253 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
11.253 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
11.253 * [taylor]: Taking taylor expansion of 2 in n
11.253 * [backup-simplify]: Simplify 2 into 2
11.253 * [taylor]: Taking taylor expansion of (* n PI) in n
11.253 * [taylor]: Taking taylor expansion of n in n
11.253 * [backup-simplify]: Simplify 0 into 0
11.253 * [backup-simplify]: Simplify 1 into 1
11.253 * [taylor]: Taking taylor expansion of PI in n
11.253 * [backup-simplify]: Simplify PI into PI
11.253 * [backup-simplify]: Simplify (* 0 PI) into 0
11.253 * [backup-simplify]: Simplify (* 2 0) into 0
11.257 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.258 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
11.258 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.258 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
11.258 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
11.259 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
11.259 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 k))) into (* 1/2 (- 1/2 (* 1/2 k)))
11.259 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.260 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 k))) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
11.261 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))
11.261 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
11.261 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.261 * [taylor]: Taking taylor expansion of k in n
11.261 * [backup-simplify]: Simplify k into k
11.261 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.261 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
11.261 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.261 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
11.262 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (sqrt (/ 1 k))) into (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))
11.262 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) in k
11.262 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
11.262 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.262 * [taylor]: Taking taylor expansion of k in k
11.262 * [backup-simplify]: Simplify 0 into 0
11.262 * [backup-simplify]: Simplify 1 into 1
11.263 * [backup-simplify]: Simplify (/ 1 1) into 1
11.263 * [backup-simplify]: Simplify (sqrt 0) into 0
11.264 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
11.264 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) in k
11.264 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
11.264 * [taylor]: Taking taylor expansion of 1/2 in k
11.264 * [backup-simplify]: Simplify 1/2 into 1/2
11.264 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
11.264 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
11.264 * [taylor]: Taking taylor expansion of 1/2 in k
11.264 * [backup-simplify]: Simplify 1/2 into 1/2
11.264 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
11.264 * [taylor]: Taking taylor expansion of 1/2 in k
11.264 * [backup-simplify]: Simplify 1/2 into 1/2
11.264 * [taylor]: Taking taylor expansion of k in k
11.264 * [backup-simplify]: Simplify 0 into 0
11.264 * [backup-simplify]: Simplify 1 into 1
11.264 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
11.264 * [taylor]: Taking taylor expansion of (log n) in k
11.264 * [taylor]: Taking taylor expansion of n in k
11.264 * [backup-simplify]: Simplify n into n
11.265 * [backup-simplify]: Simplify (log n) into (log n)
11.265 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
11.265 * [taylor]: Taking taylor expansion of (* 2 PI) in k
11.265 * [taylor]: Taking taylor expansion of 2 in k
11.265 * [backup-simplify]: Simplify 2 into 2
11.265 * [taylor]: Taking taylor expansion of PI in k
11.265 * [backup-simplify]: Simplify PI into PI
11.265 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.266 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.266 * [backup-simplify]: Simplify (* 1/2 0) into 0
11.266 * [backup-simplify]: Simplify (- 0) into 0
11.267 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.267 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.268 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
11.269 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (+ (log n) (log (* 2 PI))))) into (* 1/4 (+ (log n) (log (* 2 PI))))
11.269 * [backup-simplify]: Simplify (exp (* 1/4 (+ (log n) (log (* 2 PI))))) into (exp (* 1/4 (+ (log n) (log (* 2 PI)))))
11.270 * [backup-simplify]: Simplify (* 0 (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) into 0
11.270 * [backup-simplify]: Simplify 0 into 0
11.271 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.271 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
11.272 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
11.272 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
11.273 * [backup-simplify]: Simplify (- 0) into 0
11.273 * [backup-simplify]: Simplify (+ 0 0) into 0
11.273 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 k)))) into 0
11.274 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.275 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
11.277 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.279 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
11.279 * [taylor]: Taking taylor expansion of 0 in k
11.279 * [backup-simplify]: Simplify 0 into 0
11.279 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
11.280 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
11.282 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
11.283 * [backup-simplify]: Simplify (+ 0 0) into 0
11.284 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
11.284 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.285 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.286 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
11.290 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI)))))) into (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))))
11.293 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
11.297 * [backup-simplify]: Simplify (+ (* 0 (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) (* +nan.0 (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
11.299 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/4 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))
11.299 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.300 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
11.301 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
11.303 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
11.306 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
11.308 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
11.308 * [backup-simplify]: Simplify (- 0) into 0
11.308 * [backup-simplify]: Simplify (+ 0 0) into 0
11.309 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k))))) into 0
11.311 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.313 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
11.316 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.318 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
11.318 * [taylor]: Taking taylor expansion of 0 in k
11.318 * [backup-simplify]: Simplify 0 into 0
11.318 * [backup-simplify]: Simplify 0 into 0
11.320 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
11.321 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
11.325 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
11.325 * [backup-simplify]: Simplify (+ 0 0) into 0
11.326 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
11.326 * [backup-simplify]: Simplify (- 0) into 0
11.327 * [backup-simplify]: Simplify (+ 0 0) into 0
11.329 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
11.333 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI))))))) into 0
11.337 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))
11.338 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
11.341 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
11.351 * [backup-simplify]: Simplify (+ (* 0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))) (+ (* +nan.0 (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) (* +nan.0 (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) into (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n))))))))
11.356 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n))))))))
11.357 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.357 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
11.359 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.360 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
11.367 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
11.368 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
11.369 * [backup-simplify]: Simplify (- 0) into 0
11.369 * [backup-simplify]: Simplify (+ 0 0) into 0
11.370 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 k)))))) into 0
11.372 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
11.374 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
11.376 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 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
11.379 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
11.379 * [taylor]: Taking taylor expansion of 0 in k
11.379 * [backup-simplify]: Simplify 0 into 0
11.379 * [backup-simplify]: Simplify 0 into 0
11.379 * [backup-simplify]: Simplify 0 into 0
11.382 * [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
11.383 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.389 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
11.389 * [backup-simplify]: Simplify (+ 0 0) into 0
11.393 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
11.394 * [backup-simplify]: Simplify (- 0) into 0
11.394 * [backup-simplify]: Simplify (+ 0 0) into 0
11.397 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
11.400 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))) (* 0 (* 1/2 (+ (log n) (log (* 2 PI)))))))) into 0
11.404 * [backup-simplify]: Simplify (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 3) 6)) (* (/ (pow (- (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/384 (pow (log n) 3)) (+ (* 1/128 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/128 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/384 (pow (log (* 2 PI)) 3)))))))
11.404 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.407 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
11.417 * [backup-simplify]: Simplify (+ (* 0 (* -1 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/384 (pow (log n) 3)) (+ (* 1/128 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/128 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/384 (pow (log (* 2 PI)) 3)))))))) (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (pow (log n) 2)) (+ (* 1/16 (* (log n) (log (* 2 PI)))) (* 1/32 (pow (log (* 2 PI)) 2)))))) (+ (* +nan.0 (* -1 (* (+ (* 1/4 (log n)) (* 1/4 (log (* 2 PI)))) (exp (* 1/4 (+ (log n) (log (* 2 PI)))))))) (* +nan.0 (exp (* 1/4 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
11.424 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))))))))))))))
11.436 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n))) (- (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/4 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (- (+ (* +nan.0 (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) k))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (pow k 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))))))))))))))))))))
11.437 * [backup-simplify]: Simplify (/ (pow (* (* (/ 1 n) 2) PI) (/ (- 1/2 (/ (/ 1 k) 2)) 2)) (sqrt (/ 1 k))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k))
11.437 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in (n k) around 0
11.437 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in k
11.437 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in k
11.437 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in k
11.437 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in k
11.437 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in k
11.437 * [taylor]: Taking taylor expansion of 1/2 in k
11.437 * [backup-simplify]: Simplify 1/2 into 1/2
11.437 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
11.437 * [taylor]: Taking taylor expansion of 1/2 in k
11.437 * [backup-simplify]: Simplify 1/2 into 1/2
11.437 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.437 * [taylor]: Taking taylor expansion of 1/2 in k
11.438 * [backup-simplify]: Simplify 1/2 into 1/2
11.438 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.438 * [taylor]: Taking taylor expansion of k in k
11.438 * [backup-simplify]: Simplify 0 into 0
11.438 * [backup-simplify]: Simplify 1 into 1
11.438 * [backup-simplify]: Simplify (/ 1 1) into 1
11.438 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
11.438 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
11.438 * [taylor]: Taking taylor expansion of 2 in k
11.438 * [backup-simplify]: Simplify 2 into 2
11.438 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.438 * [taylor]: Taking taylor expansion of PI in k
11.438 * [backup-simplify]: Simplify PI into PI
11.438 * [taylor]: Taking taylor expansion of n in k
11.438 * [backup-simplify]: Simplify n into n
11.438 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.439 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
11.439 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
11.439 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.439 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.440 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.440 * [backup-simplify]: Simplify (* 1/2 -1/2) into -1/4
11.441 * [backup-simplify]: Simplify (* -1/4 (log (* 2 (/ PI n)))) into (* -1/4 (log (* 2 (/ PI n))))
11.441 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))))
11.441 * [taylor]: Taking taylor expansion of (sqrt k) in k
11.441 * [taylor]: Taking taylor expansion of k in k
11.441 * [backup-simplify]: Simplify 0 into 0
11.441 * [backup-simplify]: Simplify 1 into 1
11.441 * [backup-simplify]: Simplify (sqrt 0) into 0
11.443 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
11.443 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n
11.443 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
11.443 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
11.443 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
11.443 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
11.443 * [taylor]: Taking taylor expansion of 1/2 in n
11.443 * [backup-simplify]: Simplify 1/2 into 1/2
11.443 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.443 * [taylor]: Taking taylor expansion of 1/2 in n
11.443 * [backup-simplify]: Simplify 1/2 into 1/2
11.443 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.443 * [taylor]: Taking taylor expansion of 1/2 in n
11.443 * [backup-simplify]: Simplify 1/2 into 1/2
11.443 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.443 * [taylor]: Taking taylor expansion of k in n
11.443 * [backup-simplify]: Simplify k into k
11.443 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.444 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
11.444 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
11.444 * [taylor]: Taking taylor expansion of 2 in n
11.444 * [backup-simplify]: Simplify 2 into 2
11.444 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.444 * [taylor]: Taking taylor expansion of PI in n
11.444 * [backup-simplify]: Simplify PI into PI
11.444 * [taylor]: Taking taylor expansion of n in n
11.444 * [backup-simplify]: Simplify 0 into 0
11.444 * [backup-simplify]: Simplify 1 into 1
11.445 * [backup-simplify]: Simplify (/ PI 1) into PI
11.445 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.446 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.446 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.446 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.446 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.446 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
11.448 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.449 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
11.451 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
11.451 * [taylor]: Taking taylor expansion of (sqrt k) in n
11.451 * [taylor]: Taking taylor expansion of k in n
11.451 * [backup-simplify]: Simplify k into k
11.451 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
11.451 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
11.451 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) (sqrt k)) in n
11.451 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))) in n
11.451 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n))))) in n
11.451 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (log (* 2 (/ PI n)))) in n
11.451 * [taylor]: Taking taylor expansion of (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) in n
11.451 * [taylor]: Taking taylor expansion of 1/2 in n
11.451 * [backup-simplify]: Simplify 1/2 into 1/2
11.451 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
11.451 * [taylor]: Taking taylor expansion of 1/2 in n
11.451 * [backup-simplify]: Simplify 1/2 into 1/2
11.451 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.451 * [taylor]: Taking taylor expansion of 1/2 in n
11.451 * [backup-simplify]: Simplify 1/2 into 1/2
11.451 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.451 * [taylor]: Taking taylor expansion of k in n
11.451 * [backup-simplify]: Simplify k into k
11.452 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.452 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
11.452 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
11.452 * [taylor]: Taking taylor expansion of 2 in n
11.452 * [backup-simplify]: Simplify 2 into 2
11.452 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.452 * [taylor]: Taking taylor expansion of PI in n
11.452 * [backup-simplify]: Simplify PI into PI
11.452 * [taylor]: Taking taylor expansion of n in n
11.452 * [backup-simplify]: Simplify 0 into 0
11.452 * [backup-simplify]: Simplify 1 into 1
11.452 * [backup-simplify]: Simplify (/ PI 1) into PI
11.453 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.454 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.454 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.454 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
11.454 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
11.454 * [backup-simplify]: Simplify (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) into (* 1/2 (- 1/2 (* 1/2 (/ 1 k))))
11.456 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.457 * [backup-simplify]: Simplify (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
11.459 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
11.459 * [taylor]: Taking taylor expansion of (sqrt k) in n
11.459 * [taylor]: Taking taylor expansion of k in n
11.459 * [backup-simplify]: Simplify k into k
11.459 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
11.459 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
11.461 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (sqrt k)) into (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (sqrt k))
11.461 * [taylor]: Taking taylor expansion of (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (sqrt k)) in k
11.461 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) in k
11.461 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
11.461 * [taylor]: Taking taylor expansion of 1/2 in k
11.461 * [backup-simplify]: Simplify 1/2 into 1/2
11.461 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
11.461 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
11.461 * [taylor]: Taking taylor expansion of 1/2 in k
11.461 * [backup-simplify]: Simplify 1/2 into 1/2
11.461 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.461 * [taylor]: Taking taylor expansion of 1/2 in k
11.461 * [backup-simplify]: Simplify 1/2 into 1/2
11.461 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.461 * [taylor]: Taking taylor expansion of k in k
11.461 * [backup-simplify]: Simplify 0 into 0
11.461 * [backup-simplify]: Simplify 1 into 1
11.461 * [backup-simplify]: Simplify (/ 1 1) into 1
11.461 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
11.461 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
11.461 * [taylor]: Taking taylor expansion of (* 2 PI) in k
11.461 * [taylor]: Taking taylor expansion of 2 in k
11.462 * [backup-simplify]: Simplify 2 into 2
11.462 * [taylor]: Taking taylor expansion of PI in k
11.462 * [backup-simplify]: Simplify PI into PI
11.462 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
11.463 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
11.463 * [taylor]: Taking taylor expansion of (log n) in k
11.463 * [taylor]: Taking taylor expansion of n in k
11.463 * [backup-simplify]: Simplify n into n
11.463 * [backup-simplify]: Simplify (log n) into (log n)
11.464 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.464 * [backup-simplify]: Simplify (- 1/2) into -1/2
11.464 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
11.465 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
11.466 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
11.467 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
11.468 * [backup-simplify]: Simplify (* 1/2 (* -1/2 (- (log (* 2 PI)) (log n)))) into (* -1/4 (- (log (* 2 PI)) (log n)))
11.469 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))
11.469 * [taylor]: Taking taylor expansion of (sqrt k) in k
11.469 * [taylor]: Taking taylor expansion of k in k
11.469 * [backup-simplify]: Simplify 0 into 0
11.469 * [backup-simplify]: Simplify 1 into 1
11.470 * [backup-simplify]: Simplify (sqrt 0) into 0
11.471 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
11.472 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 0) into 0
11.472 * [backup-simplify]: Simplify 0 into 0
11.473 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.474 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
11.476 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
11.476 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.476 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
11.477 * [backup-simplify]: Simplify (- 0) into 0
11.477 * [backup-simplify]: Simplify (+ 0 0) into 0
11.478 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))) into 0
11.479 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.481 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
11.482 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.484 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
11.484 * [taylor]: Taking taylor expansion of 0 in k
11.484 * [backup-simplify]: Simplify 0 into 0
11.484 * [backup-simplify]: Simplify 0 into 0
11.485 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))
11.487 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))
11.487 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
11.489 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.490 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
11.493 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
11.493 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.494 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
11.494 * [backup-simplify]: Simplify (- 0) into 0
11.495 * [backup-simplify]: Simplify (+ 0 0) into 0
11.496 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k)))))) into 0
11.497 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.499 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
11.501 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.503 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
11.503 * [taylor]: Taking taylor expansion of 0 in k
11.503 * [backup-simplify]: Simplify 0 into 0
11.503 * [backup-simplify]: Simplify 0 into 0
11.503 * [backup-simplify]: Simplify 0 into 0
11.510 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
11.512 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 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 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))
11.513 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))
11.514 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
11.515 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.515 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.519 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
11.519 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.520 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
11.520 * [backup-simplify]: Simplify (- 0) into 0
11.520 * [backup-simplify]: Simplify (+ 0 0) into 0
11.521 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1/2 (* 1/2 (/ 1 k))))))) into 0
11.522 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
11.523 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1/2 (* 1/2 (/ 1 k)))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
11.524 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 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
11.526 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
11.526 * [taylor]: Taking taylor expansion of 0 in k
11.526 * [backup-simplify]: Simplify 0 into 0
11.526 * [backup-simplify]: Simplify 0 into 0
11.526 * [backup-simplify]: Simplify 0 into 0
11.526 * [backup-simplify]: Simplify 0 into 0
11.528 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
11.529 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 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 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))
11.530 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))
11.533 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 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 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))))))))
11.533 * [backup-simplify]: Simplify (/ (pow (* (* (/ 1 (- n)) 2) PI) (/ (- 1/2 (/ (/ 1 (- k)) 2)) 2)) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k)))
11.533 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in (n k) around 0
11.533 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in k
11.533 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in k
11.533 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in k
11.533 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in k
11.533 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in k
11.533 * [taylor]: Taking taylor expansion of 1/2 in k
11.533 * [backup-simplify]: Simplify 1/2 into 1/2
11.533 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
11.533 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.533 * [taylor]: Taking taylor expansion of 1/2 in k
11.533 * [backup-simplify]: Simplify 1/2 into 1/2
11.533 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.533 * [taylor]: Taking taylor expansion of k in k
11.533 * [backup-simplify]: Simplify 0 into 0
11.533 * [backup-simplify]: Simplify 1 into 1
11.533 * [backup-simplify]: Simplify (/ 1 1) into 1
11.534 * [taylor]: Taking taylor expansion of 1/2 in k
11.534 * [backup-simplify]: Simplify 1/2 into 1/2
11.534 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
11.534 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
11.534 * [taylor]: Taking taylor expansion of -2 in k
11.534 * [backup-simplify]: Simplify -2 into -2
11.534 * [taylor]: Taking taylor expansion of (/ PI n) in k
11.534 * [taylor]: Taking taylor expansion of PI in k
11.534 * [backup-simplify]: Simplify PI into PI
11.534 * [taylor]: Taking taylor expansion of n in k
11.534 * [backup-simplify]: Simplify n into n
11.534 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
11.534 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
11.534 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
11.534 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.534 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.535 * [backup-simplify]: Simplify (* 1/2 1/2) into 1/4
11.535 * [backup-simplify]: Simplify (* 1/4 (log (* -2 (/ PI n)))) into (* 1/4 (log (* -2 (/ PI n))))
11.535 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
11.535 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
11.535 * [taylor]: Taking taylor expansion of (/ -1 k) in k
11.535 * [taylor]: Taking taylor expansion of -1 in k
11.535 * [backup-simplify]: Simplify -1 into -1
11.535 * [taylor]: Taking taylor expansion of k in k
11.535 * [backup-simplify]: Simplify 0 into 0
11.535 * [backup-simplify]: Simplify 1 into 1
11.535 * [backup-simplify]: Simplify (/ -1 1) into -1
11.535 * [backup-simplify]: Simplify (sqrt 0) into 0
11.536 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
11.536 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))))
11.536 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n
11.536 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
11.536 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
11.537 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
11.537 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.537 * [taylor]: Taking taylor expansion of 1/2 in n
11.537 * [backup-simplify]: Simplify 1/2 into 1/2
11.537 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.537 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.537 * [taylor]: Taking taylor expansion of 1/2 in n
11.537 * [backup-simplify]: Simplify 1/2 into 1/2
11.537 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.537 * [taylor]: Taking taylor expansion of k in n
11.537 * [backup-simplify]: Simplify k into k
11.537 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.537 * [taylor]: Taking taylor expansion of 1/2 in n
11.537 * [backup-simplify]: Simplify 1/2 into 1/2
11.537 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
11.537 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
11.537 * [taylor]: Taking taylor expansion of -2 in n
11.537 * [backup-simplify]: Simplify -2 into -2
11.537 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.537 * [taylor]: Taking taylor expansion of PI in n
11.537 * [backup-simplify]: Simplify PI into PI
11.537 * [taylor]: Taking taylor expansion of n in n
11.537 * [backup-simplify]: Simplify 0 into 0
11.537 * [backup-simplify]: Simplify 1 into 1
11.537 * [backup-simplify]: Simplify (/ PI 1) into PI
11.538 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
11.538 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
11.538 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.539 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.539 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
11.540 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.540 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
11.541 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
11.541 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
11.541 * [taylor]: Taking taylor expansion of (/ -1 k) in n
11.541 * [taylor]: Taking taylor expansion of -1 in n
11.541 * [backup-simplify]: Simplify -1 into -1
11.541 * [taylor]: Taking taylor expansion of k in n
11.541 * [backup-simplify]: Simplify k into k
11.541 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
11.541 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
11.541 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
11.542 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
11.542 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
11.542 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) (sqrt (/ -1 k))) in n
11.542 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))) in n
11.542 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n))))) in n
11.543 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (log (* -2 (/ PI n)))) in n
11.543 * [taylor]: Taking taylor expansion of (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) in n
11.543 * [taylor]: Taking taylor expansion of 1/2 in n
11.543 * [backup-simplify]: Simplify 1/2 into 1/2
11.543 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
11.543 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
11.543 * [taylor]: Taking taylor expansion of 1/2 in n
11.543 * [backup-simplify]: Simplify 1/2 into 1/2
11.543 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.543 * [taylor]: Taking taylor expansion of k in n
11.543 * [backup-simplify]: Simplify k into k
11.543 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.543 * [taylor]: Taking taylor expansion of 1/2 in n
11.543 * [backup-simplify]: Simplify 1/2 into 1/2
11.543 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
11.543 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
11.543 * [taylor]: Taking taylor expansion of -2 in n
11.543 * [backup-simplify]: Simplify -2 into -2
11.543 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.543 * [taylor]: Taking taylor expansion of PI in n
11.543 * [backup-simplify]: Simplify PI into PI
11.543 * [taylor]: Taking taylor expansion of n in n
11.543 * [backup-simplify]: Simplify 0 into 0
11.543 * [backup-simplify]: Simplify 1 into 1
11.544 * [backup-simplify]: Simplify (/ PI 1) into PI
11.544 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
11.546 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
11.546 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
11.546 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
11.546 * [backup-simplify]: Simplify (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) into (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2))
11.547 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.549 * [backup-simplify]: Simplify (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
11.550 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
11.550 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
11.550 * [taylor]: Taking taylor expansion of (/ -1 k) in n
11.550 * [taylor]: Taking taylor expansion of -1 in n
11.550 * [backup-simplify]: Simplify -1 into -1
11.550 * [taylor]: Taking taylor expansion of k in n
11.550 * [backup-simplify]: Simplify k into k
11.550 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
11.550 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
11.550 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
11.550 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
11.552 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
11.552 * [taylor]: Taking taylor expansion of (/ (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) in k
11.552 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) in k
11.552 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
11.552 * [taylor]: Taking taylor expansion of 1/2 in k
11.552 * [backup-simplify]: Simplify 1/2 into 1/2
11.552 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
11.552 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
11.552 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
11.552 * [taylor]: Taking taylor expansion of 1/2 in k
11.552 * [backup-simplify]: Simplify 1/2 into 1/2
11.552 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.552 * [taylor]: Taking taylor expansion of k in k
11.552 * [backup-simplify]: Simplify 0 into 0
11.552 * [backup-simplify]: Simplify 1 into 1
11.553 * [backup-simplify]: Simplify (/ 1 1) into 1
11.553 * [taylor]: Taking taylor expansion of 1/2 in k
11.553 * [backup-simplify]: Simplify 1/2 into 1/2
11.553 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
11.553 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
11.553 * [taylor]: Taking taylor expansion of (* -2 PI) in k
11.553 * [taylor]: Taking taylor expansion of -2 in k
11.553 * [backup-simplify]: Simplify -2 into -2
11.553 * [taylor]: Taking taylor expansion of PI in k
11.553 * [backup-simplify]: Simplify PI into PI
11.554 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
11.555 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
11.555 * [taylor]: Taking taylor expansion of (log n) in k
11.555 * [taylor]: Taking taylor expansion of n in k
11.555 * [backup-simplify]: Simplify n into n
11.555 * [backup-simplify]: Simplify (log n) into (log n)
11.555 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
11.556 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
11.556 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
11.557 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
11.558 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
11.559 * [backup-simplify]: Simplify (* 1/2 (* 1/2 (- (log (* -2 PI)) (log n)))) into (* 1/4 (- (log (* -2 PI)) (log n)))
11.560 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
11.560 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
11.560 * [taylor]: Taking taylor expansion of (/ -1 k) in k
11.560 * [taylor]: Taking taylor expansion of -1 in k
11.560 * [backup-simplify]: Simplify -1 into -1
11.560 * [taylor]: Taking taylor expansion of k in k
11.560 * [backup-simplify]: Simplify 0 into 0
11.560 * [backup-simplify]: Simplify 1 into 1
11.561 * [backup-simplify]: Simplify (/ -1 1) into -1
11.561 * [backup-simplify]: Simplify (sqrt 0) into 0
11.562 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
11.564 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
11.565 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
11.566 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.566 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
11.568 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
11.568 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.569 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
11.569 * [backup-simplify]: Simplify (+ 0 0) into 0
11.570 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2))) into 0
11.571 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.573 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
11.575 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.576 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
11.576 * [taylor]: Taking taylor expansion of 0 in k
11.576 * [backup-simplify]: Simplify 0 into 0
11.576 * [backup-simplify]: Simplify 0 into 0
11.577 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
11.580 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
11.582 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))
11.583 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))
11.583 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.584 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
11.586 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
11.586 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.587 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
11.587 * [backup-simplify]: Simplify (+ 0 0) into 0
11.588 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (* 1/2 (/ 1 k)) 1/2)))) into 0
11.589 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
11.589 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (* 1/2 (/ 1 k)) 1/2)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
11.591 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.591 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.591 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
11.592 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 1/2 (* (+ (* 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
11.592 * [taylor]: Taking taylor expansion of 0 in k
11.592 * [backup-simplify]: Simplify 0 into 0
11.592 * [backup-simplify]: Simplify 0 into 0
11.592 * [backup-simplify]: Simplify 0 into 0
11.593 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.595 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
11.598 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))
11.599 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))))
11.601 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 1/2 (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) k)))))))
11.601 * * * [progress]: simplifying candidates
11.601 * * * * [progress]: [ 1 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (exp (* (+ (+ (log n) (log 2)) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
11.601 * * * * [progress]: [ 2 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (exp (* (+ (log (* n 2)) (log PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
11.601 * * * * [progress]: [ 3 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (exp (* (log (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
11.601 * * * * [progress]: [ 4 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (exp (* (log (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
11.602 * * * * [progress]: [ 5 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (* 1 (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
11.602 * * * * [progress]: [ 6 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (* 1 (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
11.602 * * * * [progress]: [ 7 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (* 1 (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
11.602 * * * * [progress]: [ 8 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (/ (pow (* (* n 2) PI) (/ 1/2 2)) (pow (* (* n 2) PI) (/ (/ k 2) 2))) (sqrt k))))>
11.602 * * * * [progress]: [ 9 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2)))) (cbrt (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
11.602 * * * * [progress]: [ 10 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (sqrt (/ (- 1/2 (/ k 2)) 2))) (sqrt (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
11.602 * * * * [progress]: [ 11 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2))) (sqrt k))))>
11.602 * * * * [progress]: [ 12 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))) (/ (cbrt (- 1/2 (/ k 2))) (sqrt 2))) (sqrt k))))>
11.602 * * * * [progress]: [ 13 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)) (/ (cbrt (- 1/2 (/ k 2))) 2)) (sqrt k))))>
11.602 * * * * [progress]: [ 14 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1/2 (/ k 2))) (cbrt 2))) (sqrt k))))>
11.602 * * * * [progress]: [ 15 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (sqrt k))))>
11.602 * * * * [progress]: [ 16 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) 1)) (/ (sqrt (- 1/2 (/ k 2))) 2)) (sqrt k))))>
11.602 * * * * [progress]: [ 17 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) (sqrt k))))>
11.602 * * * * [progress]: [ 18 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) (sqrt k))))>
11.602 * * * * [progress]: [ 19 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.602 * * * * [progress]: [ 20 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (cbrt 2))) (sqrt k))))>
11.602 * * * * [progress]: [ 21 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (sqrt k))))>
11.602 * * * * [progress]: [ 22 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1)) (/ (- (sqrt 1/2) (sqrt (/ k 2))) 2)) (sqrt k))))>
11.602 * * * * [progress]: [ 23 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (cbrt 2))) (sqrt k))))>
11.602 * * * * [progress]: [ 24 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (sqrt k))))>
11.603 * * * * [progress]: [ 25 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1)) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 2)) (sqrt k))))>
11.603 * * * * [progress]: [ 26 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) (sqrt k))))>
11.603 * * * * [progress]: [ 27 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) (sqrt k))))>
11.603 * * * * [progress]: [ 28 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.603 * * * * [progress]: [ 29 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) 1) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.603 * * * * [progress]: [ 30 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (/ 1 2)) (sqrt k))))>
11.603 * * * * [progress]: [ 31 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
11.603 * * * * [progress]: [ 32 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (sqrt k))))>
11.603 * * * * [progress]: [ 33 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (exp (log (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
11.603 * * * * [progress]: [ 34 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (log (exp (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
11.603 * * * * [progress]: [ 35 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
11.603 * * * * [progress]: [ 36 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (cbrt (* (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
11.603 * * * * [progress]: [ 37 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* (sqrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
11.603 * * * * [progress]: [ 38 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* 1 (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))))>
11.603 * * * * [progress]: [ 39 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2))) (sqrt k))))>
11.603 * * * * [progress]: [ 40 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (posit16->real (real->posit16 (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt k))))>
11.603 * * * * [progress]: [ 41 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (exp (* (+ (log n) (log 2)) (/ (- 1/2 (/ k 2)) 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.603 * * * * [progress]: [ 42 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (exp (* (log (* n 2)) (/ (- 1/2 (/ k 2)) 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.603 * * * * [progress]: [ 43 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (exp (* (log (* n 2)) (/ (- 1/2 (/ k 2)) 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.603 * * * * [progress]: [ 44 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (* 1 (/ (- 1/2 (/ k 2)) 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.603 * * * * [progress]: [ 45 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (* 1 (/ (- 1/2 (/ k 2)) 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 46 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (/ (pow (* n 2) (/ 1/2 2)) (pow (* n 2) (/ (/ k 2) 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 47 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2)))) (cbrt (/ (- 1/2 (/ k 2)) 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 48 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (sqrt (/ (- 1/2 (/ k 2)) 2))) (sqrt (/ (- 1/2 (/ k 2)) 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 49 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 50 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2))) (/ (cbrt (- 1/2 (/ k 2))) (sqrt 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 51 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1)) (/ (cbrt (- 1/2 (/ k 2))) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 52 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1/2 (/ k 2))) (cbrt 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 53 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 54 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ (sqrt (- 1/2 (/ k 2))) 1)) (/ (sqrt (- 1/2 (/ k 2))) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 55 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 56 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 57 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 58 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (cbrt 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 59 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (/ (- (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 60 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1)) (/ (- (sqrt 1/2) (sqrt (/ k 2))) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 61 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (cbrt 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 62 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 63 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1)) (/ (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 64 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1/2 (/ k 2)) (cbrt 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.604 * * * * [progress]: [ 65 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ 1 (sqrt 2))) (/ (- 1/2 (/ k 2)) (sqrt 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.605 * * * * [progress]: [ 66 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ 1 1)) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.605 * * * * [progress]: [ 67 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) 1) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.605 * * * * [progress]: [ 68 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (- 1/2 (/ k 2))) (/ 1 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.605 * * * * [progress]: [ 69 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow 2 (/ (- 1/2 (/ k 2)) 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.606 * * * * [progress]: [ 70 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) 1) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.606 * * * * [progress]: [ 71 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (exp (log (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.606 * * * * [progress]: [ 72 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (log (exp (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.606 * * * * [progress]: [ 73 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (* (* (cbrt (pow (* n 2) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)))) (cbrt (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.606 * * * * [progress]: [ 74 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (* (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow (* n 2) (/ (- 1/2 (/ k 2)) 2))) (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.606 * * * * [progress]: [ 75 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (* (sqrt (pow (* n 2) (/ (- 1/2 (/ k 2)) 2))) (sqrt (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.606 * * * * [progress]: [ 76 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (* 1 (pow (* n 2) (/ (- 1/2 (/ k 2)) 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.606 * * * * [progress]: [ 77 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (* (pow (* n 2) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (pow (* n 2) (/ (/ (- 1/2 (/ k 2)) 2) 2))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.606 * * * * [progress]: [ 78 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (posit16->real (real->posit16 (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.606 * * * * [progress]: [ 79 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) 1) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.606 * * * * [progress]: [ 80 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) 1) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.606 * * * * [progress]: [ 81 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (pow (* (* n 2) PI) 1) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.606 * * * * [progress]: [ 82 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (exp (+ (+ (log n) (log 2)) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.606 * * * * [progress]: [ 83 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (exp (+ (log (* n 2)) (log PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.606 * * * * [progress]: [ 84 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (exp (log (* (* n 2) PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.606 * * * * [progress]: [ 85 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (log (exp (* (* n 2) PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.606 * * * * [progress]: [ 86 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (cbrt (* (* (* (* n n) n) (* (* 2 2) 2)) (* (* PI PI) PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.607 * * * * [progress]: [ 87 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (cbrt (* (* (* (* n 2) (* n 2)) (* n 2)) (* (* PI PI) PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.607 * * * * [progress]: [ 88 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.607 * * * * [progress]: [ 89 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (cbrt (* (* (* (* n 2) PI) (* (* n 2) PI)) (* (* n 2) PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.607 * * * * [progress]: [ 90 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (sqrt (* (* n 2) PI)) (sqrt (* (* n 2) PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.607 * * * * [progress]: [ 91 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* 1 (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.607 * * * * [progress]: [ 92 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* (* n 2) (* (cbrt PI) (cbrt PI))) (cbrt PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.607 * * * * [progress]: [ 93 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* (* n 2) (sqrt PI)) (sqrt PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.607 * * * * [progress]: [ 94 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* (* n 2) 1) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.607 * * * * [progress]: [ 95 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.607 * * * * [progress]: [ 96 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (posit16->real (real->posit16 (* (* n 2) PI))) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.607 * * * * [progress]: [ 97 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* PI (* n 2)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.607 * * * * [progress]: [ 98 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (pow (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)) 1)))>
11.607 * * * * [progress]: [ 99 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (exp (- (* (+ (+ (log n) (log 2)) (log PI)) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
11.607 * * * * [progress]: [ 100 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (exp (- (* (+ (log (* n 2)) (log PI)) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
11.607 * * * * [progress]: [ 101 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (exp (- (* (log (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
11.607 * * * * [progress]: [ 102 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (exp (- (* (log (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k))))))>
11.607 * * * * [progress]: [ 103 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (exp (- (log (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k))))))>
11.607 * * * * [progress]: [ 104 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (exp (log (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
11.607 * * * * [progress]: [ 105 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (log (exp (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
11.607 * * * * [progress]: [ 106 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (cbrt (/ (* (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k))))))>
11.608 * * * * [progress]: [ 107 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (* (cbrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))) (cbrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
11.608 * * * * [progress]: [ 108 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (cbrt (* (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
11.608 * * * * [progress]: [ 109 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow 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))))))>
11.608 * * * * [progress]: [ 110 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (- (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (- (sqrt k)))))>
11.608 * * * * [progress]: [ 111 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow PI (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k))))))>
11.608 * * * * [progress]: [ 112 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow PI (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k))))))>
11.608 * * * * [progress]: [ 113 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
11.608 * * * * [progress]: [ 114 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (pow PI (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
11.608 * * * * [progress]: [ 115 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow PI (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
11.608 * * * * [progress]: [ 116 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow PI (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
11.608 * * * * [progress]: [ 117 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (sqrt k))))))>
11.608 * * * * [progress]: [ 118 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt (cbrt k))))))>
11.608 * * * * [progress]: [ 119 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt (sqrt k))))))>
11.608 * * * * [progress]: [ 120 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt 1)) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))))>
11.608 * * * * [progress]: [ 121 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt (sqrt k))))))>
11.608 * * * * [progress]: [ 122 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) 1) (/ (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))))>
11.608 * * * * [progress]: [ 123 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (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))))))>
11.608 * * * * [progress]: [ 124 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (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))))))>
11.609 * * * * [progress]: [ 125 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (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))))))>
11.609 * * * * [progress]: [ 126 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 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)))))>
11.609 * * * * [progress]: [ 127 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (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))))))>
11.609 * * * * [progress]: [ 128 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow 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)))))>
11.609 * * * * [progress]: [ 129 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k))))))>
11.609 * * * * [progress]: [ 130 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k))))))>
11.609 * * * * [progress]: [ 131 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
11.609 * * * * [progress]: [ 132 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ 1 (sqrt 1)) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
11.609 * * * * [progress]: [ 133 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))))))>
11.609 * * * * [progress]: [ 134 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ 1 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
11.609 * * * * [progress]: [ 135 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (cbrt (sqrt k))))))>
11.609 * * * * [progress]: [ 136 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (cbrt k))))))>
11.609 * * * * [progress]: [ 137 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (sqrt k))))))>
11.609 * * * * [progress]: [ 138 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt 1)) (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt k)))))>
11.609 * * * * [progress]: [ 139 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (sqrt k))) (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (sqrt k))))))>
11.609 * * * * [progress]: [ 140 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) 1) (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt k)))))>
11.609 * * * * [progress]: [ 141 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* 1 (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))))>
11.609 * * * * [progress]: [ 142 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (/ 1 (sqrt k)))))>
11.609 * * * * [progress]: [ 143 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))))))>
11.610 * * * * [progress]: [ 144 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k)))))>
11.610 * * * * [progress]: [ 145 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k)))))>
11.610 * * * * [progress]: [ 146 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (sqrt (sqrt k)))))>
11.610 * * * * [progress]: [ 147 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (sqrt k))))>
11.610 * * * * [progress]: [ 148 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (sqrt (sqrt k)))))>
11.610 * * * * [progress]: [ 149 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1) (sqrt k))))>
11.610 * * * * [progress]: [ 150 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow PI (/ (- 1/2 (/ k 2)) 2))))))>
11.610 * * * * [progress]: [ 151 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt k) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))))))>
11.610 * * * * [progress]: [ 152 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow 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)))))))>
11.610 * * * * [progress]: [ 153 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ 1 (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))))))>
11.610 * * * * [progress]: [ 154 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (/ (sqrt k) (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2))))))>
11.610 * * * * [progress]: [ 155 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ 1/2 2)) (* (sqrt k) (pow (* (* n 2) PI) (/ (/ k 2) 2))))))>
11.610 * * * * [progress]: [ 156 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (posit16->real (real->posit16 (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))))>
11.610 * * * * [progress]: [ 157 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))) (sqrt k))))>
11.610 * * * * [progress]: [ 158 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (sqrt k))))>
11.610 * * * * [progress]: [ 159 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (sqrt k))))>
11.610 * * * * [progress]: [ 160 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (- (+ (* 1/32 (* (pow (log 2) 2) (* (exp (* 1/4 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/32 (* (exp (* 1/4 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/16 (* (log 2) (* (exp (* 1/4 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (exp (* 1/4 (+ (log 2) (log n))))))) (+ (* 1/4 (* (log 2) (* (exp (* 1/4 (+ (log 2) (log n)))) k))) (* 1/4 (* (exp (* 1/4 (+ (log 2) (log n)))) (* (log n) k))))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.610 * * * * [progress]: [ 161 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k))))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.610 * * * * [progress]: [ 162 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n)))))) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.610 * * * * [progress]: [ 163 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.610 * * * * [progress]: [ 164 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.611 * * * * [progress]: [ 165 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* 2 (* n PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
11.611 * * * * [progress]: [ 166 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (- (+ (* +nan.0 (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) k))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (pow k 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))))))))))))))))))))))>
11.611 * * * * [progress]: [ 167 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))))))))))>
11.611 * * * * [progress]: [ 168 / 168 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (- (+ (* +nan.0 (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) k)))))))))>
11.613 * [simplify]: Simplifying:
  (* (+ (+ (log n) (log 2)) (log PI)) (/ (- 1/2 (/ k 2)) 2))
  (* (+ (log (* n 2)) (log PI)) (/ (- 1/2 (/ k 2)) 2))
  (* (log (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2))
  (* (log (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2))
  (* 1 (/ (- 1/2 (/ k 2)) 2))
  (* 1 (/ (- 1/2 (/ k 2)) 2))
  (* 1 (/ (- 1/2 (/ k 2)) 2))
  (pow (* (* n 2) PI) (/ 1/2 2))
  (pow (* (* n 2) PI) (/ (/ k 2) 2))
  (pow (* (* n 2) PI) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2))))
  (pow (* (* n 2) PI) (sqrt (/ (- 1/2 (/ k 2)) 2)))
  (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2)))
  (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1))
  (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2)))
  (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) 1))
  (pow (* (* n 2) PI) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ 1 (sqrt 2)))
  (pow (* (* n 2) PI) (/ 1 1))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2)))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2)))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1))
  (pow (* (* n 2) PI) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ 1 (sqrt 2)))
  (pow (* (* n 2) PI) (/ 1 1))
  (pow (* (* n 2) PI) 1)
  (pow (* (* n 2) PI) (- 1/2 (/ k 2)))
  (pow (* n 2) (/ (- 1/2 (/ k 2)) 2))
  (pow PI (/ (- 1/2 (/ k 2)) 2))
  (log (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (exp (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))))
  (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (sqrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (sqrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2))
  (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2))
  (real->posit16 (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (* (+ (log n) (log 2)) (/ (- 1/2 (/ k 2)) 2))
  (* (log (* n 2)) (/ (- 1/2 (/ k 2)) 2))
  (* (log (* n 2)) (/ (- 1/2 (/ k 2)) 2))
  (* 1 (/ (- 1/2 (/ k 2)) 2))
  (* 1 (/ (- 1/2 (/ k 2)) 2))
  (pow (* n 2) (/ 1/2 2))
  (pow (* n 2) (/ (/ k 2) 2))
  (pow (* n 2) (* (cbrt (/ (- 1/2 (/ k 2)) 2)) (cbrt (/ (- 1/2 (/ k 2)) 2))))
  (pow (* n 2) (sqrt (/ (- 1/2 (/ k 2)) 2)))
  (pow (* n 2) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (* (cbrt 2) (cbrt 2))))
  (pow (* n 2) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2)))
  (pow (* n 2) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) 1))
  (pow (* n 2) (/ (sqrt (- 1/2 (/ k 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n 2) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2)))
  (pow (* n 2) (/ (sqrt (- 1/2 (/ k 2))) 1))
  (pow (* n 2) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n 2) (/ 1 (sqrt 2)))
  (pow (* n 2) (/ 1 1))
  (pow (* n 2) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n 2) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2)))
  (pow (* n 2) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) 1))
  (pow (* n 2) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n 2) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2)))
  (pow (* n 2) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) 1))
  (pow (* n 2) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* n 2) (/ 1 (sqrt 2)))
  (pow (* n 2) (/ 1 1))
  (pow (* n 2) 1)
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow n (/ (- 1/2 (/ k 2)) 2))
  (pow 2 (/ (- 1/2 (/ k 2)) 2))
  (log (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)))
  (exp (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)))
  (* (cbrt (pow (* n 2) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* n 2) (/ (- 1/2 (/ k 2)) 2))))
  (cbrt (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)))
  (* (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow (* n 2) (/ (- 1/2 (/ k 2)) 2))) (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)))
  (sqrt (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)))
  (sqrt (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)))
  (pow (* n 2) (/ (/ (- 1/2 (/ k 2)) 2) 2))
  (pow (* n 2) (/ (/ (- 1/2 (/ k 2)) 2) 2))
  (real->posit16 (pow (* n 2) (/ (- 1/2 (/ k 2)) 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)) 2)) (log (sqrt k)))
  (- (* (+ (log (* n 2)) (log PI)) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k)))
  (- (* (log (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k)))
  (- (* (log (* (* n 2) PI)) (/ (- 1/2 (/ k 2)) 2)) (log (sqrt k)))
  (- (log (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (log (sqrt k)))
  (log (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))
  (exp (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))
  (/ (* (* (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))
  (cbrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))
  (* (* (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))
  (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))
  (sqrt (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))
  (- (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (- (sqrt k))
  (/ (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow PI (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))
  (/ (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow PI (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))
  (/ (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow PI (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1))
  (/ (pow PI (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow PI (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) 1)
  (/ (pow PI (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt 1))
  (/ (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))
  (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))) 1)
  (/ (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 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)))
  (/ (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 (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 1))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 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)))
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) 1)
  (/ (sqrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ 1 1)
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (cbrt k)))
  (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt 1))
  (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt k))
  (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) 1)
  (/ (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (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 (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) 1)
  (/ (sqrt k) (pow PI (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt k) (cbrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))))
  (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2))))
  (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)))
  (/ (sqrt k) (pow (* (* n 2) PI) (/ (/ (- 1/2 (/ k 2)) 2) 2)))
  (* (sqrt k) (pow (* (* n 2) PI) (/ (/ k 2) 2)))
  (real->posit16 (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))
  (- (+ (* 1/16 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (+ (* 1/32 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (* 1/32 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/4 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/4 (* k (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))))))
  (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))
  (- (+ (* 1/32 (* (pow (log 2) 2) (* (exp (* 1/4 (+ (log 2) (log n)))) (pow k 2)))) (+ (* 1/32 (* (exp (* 1/4 (+ (log 2) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (* 1/16 (* (log 2) (* (exp (* 1/4 (+ (log 2) (log n)))) (* (log n) (pow k 2))))) (exp (* 1/4 (+ (log 2) (log n))))))) (+ (* 1/4 (* (log 2) (* (exp (* 1/4 (+ (log 2) (log n)))) k))) (* 1/4 (* (exp (* 1/4 (+ (log 2) (log n)))) (* (log n) k)))))
  (exp (* 1/2 (* (- (log 2) (log (/ 1 n))) (- 1/2 (* 1/2 k)))))
  (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log -2) (log (/ -1 n))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (- (+ (* +nan.0 (exp (* 1/4 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) k))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2)))) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (pow k 2) (* (exp (* 1/4 (+ (log n) (log (* 2 PI))))) (log (* 2 PI))))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))))))))
  (- (+ (* +nan.0 (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) k)))))))
11.617 * * [simplify]: iteration 0: 370 enodes
11.744 * * [simplify]: iteration 1: 986 enodes
12.007 * * [simplify]: iteration 2: 2000 enodes
12.416 * * [simplify]: iteration complete: 2000 enodes
12.416 * * [simplify]: Extracting #0: cost 136 inf + 0
12.418 * * [simplify]: Extracting #1: cost 381 inf + 1
12.420 * * [simplify]: Extracting #2: cost 658 inf + 1195
12.431 * * [simplify]: Extracting #3: cost 656 inf + 35689
12.458 * * [simplify]: Extracting #4: cost 448 inf + 119539
12.492 * * [simplify]: Extracting #5: cost 249 inf + 211775
12.527 * * [simplify]: Extracting #6: cost 139 inf + 259531
12.595 * * [simplify]: Extracting #7: cost 76 inf + 296789
12.652 * * [simplify]: Extracting #8: cost 35 inf + 324188
12.703 * * [simplify]: Extracting #9: cost 20 inf + 335298
12.763 * * [simplify]: Extracting #10: cost 4 inf + 351848
12.843 * * [simplify]: Extracting #11: cost 0 inf + 358392
12.917 * * [simplify]: Extracting #12: cost 0 inf + 357832
12.994 * * [simplify]: Extracting #13: cost 0 inf + 357592
13.052 * [simplify]: Simplified to:
  (* (- 1/4 (/ k 4)) (log (* (* n 2) PI)))
  (* (- 1/4 (/ k 4)) (log (* (* n 2) PI)))
  (* (- 1/4 (/ k 4)) (log (* (* n 2) PI)))
  (* (- 1/4 (/ k 4)) (log (* (* n 2) PI)))
  (- 1/4 (/ k 4))
  (- 1/4 (/ k 4))
  (- 1/4 (/ k 4))
  (pow (* (* n 2) PI) 1/4)
  (pow (* (* n 2) PI) (/ k 4))
  (pow (* (* n 2) PI) (* (cbrt (- 1/4 (/ k 4))) (cbrt (- 1/4 (/ k 4)))))
  (pow (* (* n 2) PI) (sqrt (- 1/4 (/ k 4))))
  (pow (* (* n 2) PI) (* (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2))))
  (pow (* (* n 2) PI) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2)))
  (pow (* (* n 2) PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* n 2) PI) (/ (/ (sqrt (- 1/2 (/ k 2))) (cbrt 2)) (cbrt 2)))
  (pow (* (* n 2) PI) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2)))
  (pow (* (* n 2) PI) (sqrt (- 1/2 (/ k 2))))
  (pow (* (* n 2) PI) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* (* n 2) PI) (/ 1 (sqrt 2)))
  (* (* n 2) PI)
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2)))
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* n 2) PI) (/ (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (cbrt 2)) (cbrt 2)))
  (pow (* (* n 2) PI) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2)))
  (pow (* (* n 2) PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (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) (- 1/2 (/ k 2)))
  (pow (* n 2) (- 1/4 (/ k 4)))
  (pow PI (- 1/4 (/ k 4)))
  (* (- 1/4 (/ k 4)) (log (* (* n 2) PI)))
  (exp (pow (* (* n 2) PI) (- 1/4 (/ k 4))))
  (* (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))))
  (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4))))
  (pow (pow (* (* n 2) PI) (- 1/4 (/ k 4))) 3)
  (sqrt (pow (* (* n 2) PI) (- 1/4 (/ k 4))))
  (sqrt (pow (* (* n 2) PI) (- 1/4 (/ k 4))))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 4))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 4))
  (real->posit16 (pow (* (* n 2) PI) (- 1/4 (/ k 4))))
  (* (log (* n 2)) (- 1/4 (/ k 4)))
  (* (log (* n 2)) (- 1/4 (/ k 4)))
  (* (log (* n 2)) (- 1/4 (/ k 4)))
  (- 1/4 (/ k 4))
  (- 1/4 (/ k 4))
  (pow (* n 2) 1/4)
  (pow (* n 2) (/ k 4))
  (pow (* n 2) (* (cbrt (- 1/4 (/ k 4))) (cbrt (- 1/4 (/ k 4)))))
  (pow (* n 2) (sqrt (- 1/4 (/ k 4))))
  (pow (* n 2) (* (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2)) (/ (cbrt (- 1/2 (/ k 2))) (cbrt 2))))
  (pow (* n 2) (/ (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))) (sqrt 2)))
  (pow (* n 2) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n 2) (/ (/ (sqrt (- 1/2 (/ k 2))) (cbrt 2)) (cbrt 2)))
  (pow (* n 2) (/ (sqrt (- 1/2 (/ k 2))) (sqrt 2)))
  (pow (* n 2) (sqrt (- 1/2 (/ k 2))))
  (pow (* n 2) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* n 2) (/ 1 (sqrt 2)))
  (* n 2)
  (pow (* n 2) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (* (cbrt 2) (cbrt 2))))
  (pow (* n 2) (/ (+ (sqrt 1/2) (sqrt (/ k 2))) (sqrt 2)))
  (pow (* n 2) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* n 2) (/ (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (cbrt 2)) (cbrt 2)))
  (pow (* n 2) (/ (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))) (sqrt 2)))
  (pow (* n 2) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* n 2) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* n 2) (/ 1 (sqrt 2)))
  (* n 2)
  (* n 2)
  (pow (* n 2) (- 1/2 (/ k 2)))
  (pow n (- 1/4 (/ k 4)))
  (pow 2 (- 1/4 (/ k 4)))
  (* (log (* n 2)) (- 1/4 (/ k 4)))
  (exp (pow (* n 2) (- 1/4 (/ k 4))))
  (* (cbrt (pow (* n 2) (- 1/4 (/ k 4)))) (cbrt (pow (* n 2) (- 1/4 (/ k 4)))))
  (cbrt (pow (* n 2) (- 1/4 (/ k 4))))
  (pow (pow (* n 2) (- 1/4 (/ k 4))) 3)
  (sqrt (pow (* n 2) (- 1/4 (/ k 4))))
  (sqrt (pow (* n 2) (- 1/4 (/ k 4))))
  (pow (* n 2) (/ (- 1/2 (/ k 2)) 4))
  (pow (* n 2) (/ (- 1/2 (/ k 2)) 4))
  (real->posit16 (pow (* n 2) (- 1/4 (/ k 4))))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (log (* (* n 2) PI))
  (log (* (* n 2) PI))
  (log (* (* n 2) PI))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* (* n (* n n)) (* 4 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)))
  (* (sqrt PI) (* n 2))
  (* n 2)
  (* 2 PI)
  (real->posit16 (* (* n 2) PI))
  (- (* (- 1/4 (/ k 4)) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (- 1/4 (/ k 4)) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (- 1/4 (/ k 4)) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (- 1/4 (/ k 4)) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (- 1/4 (/ k 4)) (log (* (* n 2) PI))) (log (sqrt k)))
  (- (* (- 1/4 (/ k 4)) (log (* (* n 2) PI))) (log (sqrt k)))
  (exp (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt k)))
  (/ (pow (pow (* (* n 2) PI) (- 1/4 (/ k 4))) 3) (* k (sqrt k)))
  (* (cbrt (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt k))) (cbrt (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt k))))
  (cbrt (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt k)))
  (* (* (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt k)) (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt k))) (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt k)))
  (sqrt (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt k)))
  (sqrt (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt k)))
  (- (pow (* (* n 2) PI) (- 1/4 (/ k 4))))
  (- (sqrt k))
  (/ (pow (* n 2) (- 1/4 (/ k 4))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow PI (- 1/4 (/ k 4))) (cbrt (sqrt k)))
  (/ (pow (* n 2) (- 1/4 (/ k 4))) (fabs (cbrt k)))
  (/ (pow PI (- 1/4 (/ k 4))) (sqrt (cbrt k)))
  (/ (pow (* n 2) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* n 2) (- 1/4 (/ k 4)))
  (/ (pow PI (- 1/4 (/ k 4))) (sqrt k))
  (/ (pow (* n 2) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow PI (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* n 2) (- 1/4 (/ k 4)))
  (/ (pow PI (- 1/4 (/ k 4))) (sqrt k))
  (* (/ (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (cbrt (sqrt k))))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (cbrt (sqrt k)))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (/ (fabs (cbrt k)) (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4))))))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (sqrt (cbrt k)))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4))))))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (sqrt k))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (/ (sqrt (sqrt k)) (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4))))))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))))
  (/ (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (sqrt k))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (fabs (cbrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (sqrt (sqrt k)))
  (sqrt (pow (* (* n 2) PI) (- 1/4 (/ k 4))))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (sqrt k))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (sqrt (sqrt k)))
  (sqrt (pow (* (* n 2) PI) (- 1/4 (/ k 4))))
  (/ (sqrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  1
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  1
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt k))
  (/ (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 4)) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 4)) (cbrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 4)) (fabs (cbrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 4)) (sqrt (cbrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 4)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 4)) (sqrt (sqrt k)))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 4))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 4)) (sqrt k))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 4)) (sqrt (sqrt k)))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 4)) (sqrt (sqrt k)))
  (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 4))
  (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 4)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* (* n 2) PI) (- 1/4 (/ k 4))))
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (fabs (cbrt k)))
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* (* n 2) PI) (- 1/4 (/ k 4)))
  (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* (* n 2) PI) (- 1/4 (/ k 4)))
  (/ (sqrt k) (pow PI (- 1/4 (/ k 4))))
  (/ (sqrt k) (cbrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))))
  (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (- 1/4 (/ k 4)))))
  (/ (sqrt k) (pow (* (* n 2) PI) (- 1/4 (/ k 4))))
  (/ (sqrt k) (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 4)))
  (* (pow (* (* n 2) PI) (/ k 4)) (sqrt k))
  (real->posit16 (/ (pow (* (* n 2) PI) (- 1/4 (/ k 4))) (sqrt k)))
  (- (+ (+ (* (* 1/16 (log (* 2 PI))) (* (exp (* (log (* (* n 2) PI)) 1/4)) (* (* k k) (log n)))) (exp (* (log (* (* n 2) PI)) 1/4))) (* 1/32 (* (* k k) (+ (* (exp (* (log (* (* n 2) PI)) 1/4)) (* (log n) (log n))) (* (* (log (* 2 PI)) (log (* 2 PI))) (exp (* (log (* (* n 2) PI)) 1/4))))))) (* 1/4 (* k (+ (* (exp (* (log (* (* n 2) PI)) 1/4)) (log n)) (* (exp (* (log (* (* n 2) PI)) 1/4)) (log (* 2 PI)))))))
  (exp (* 1/2 (* (log (* (* n 2) PI)) (- 1/2 (* k 1/2)))))
  (exp (* (* 1/2 (- 1/2 (* k 1/2))) (- (log (* -2 PI)) (log (/ -1 n)))))
  (- (+ (* 1/32 (+ (* (* (log 2) (log 2)) (* (exp (* (log (* n 2)) 1/4)) (* k k))) (* (* (* (log n) (log n)) (* k k)) (exp (* (log (* n 2)) 1/4))))) (+ (* (* (* (* (exp (* (log (* n 2)) 1/4)) (log n)) (* k k)) (log 2)) 1/16) (exp (* (log (* n 2)) 1/4)))) (* 1/4 (* k (+ (* (log 2) (exp (* (log (* n 2)) 1/4))) (* (exp (* (log (* n 2)) 1/4)) (log n))))))
  (exp (* 1/2 (* (log (* n 2)) (- 1/2 (* k 1/2)))))
  (exp (* (* (- 1/2 (* k 1/2)) (- (log -2) (log (/ -1 n)))) 1/2))
  (* (* n 2) PI)
  (* (* n 2) PI)
  (* (* n 2) PI)
  (+ (* (* (exp (* (log (* (* n 2) PI)) 1/4)) +nan.0) (- (* k (log n)))) (- (* (exp (* (log (* (* n 2) PI)) 1/4)) +nan.0) (- (* (* (exp (* (log (* (* n 2) PI)) 1/4)) +nan.0) (* (* k k) (log n))) (- (* (* (exp (* (log (* (* n 2) PI)) 1/4)) +nan.0) (* k k)) (- (* +nan.0 (* (* k (exp (* (log (* (* n 2) PI)) 1/4))) (log (* 2 PI)))) (- (* (* +nan.0 (* k k)) (* (* (log (* 2 PI)) (log (* 2 PI))) (exp (* (log (* (* n 2) PI)) 1/4)))) (- (* (* (exp (* (log (* (* n 2) PI)) 1/4)) k) +nan.0) (- (* (* (exp (* (log (* (* n 2) PI)) 1/4)) +nan.0) (* (* (log n) (log n)) (* k k))) (* (* +nan.0 (* k k)) (- (* (* (exp (* (log (* (* n 2) PI)) 1/4)) (log n)) (log (* 2 PI))) (* (exp (* (log (* (* n 2) PI)) 1/4)) (log (* 2 PI)))))))))))))
  (+ (* (/ (exp (* 1/2 (* (log (* (* n 2) PI)) (- 1/2 (* k 1/2))))) (* k (* k k))) (- +nan.0)) (* +nan.0 (- (/ (exp (* 1/2 (* (log (* (* n 2) PI)) (- 1/2 (* k 1/2))))) k) (/ (exp (* 1/2 (* (log (* (* n 2) PI)) (- 1/2 (* k 1/2))))) (* k k)))))
  (+ (* (exp (* (* 1/2 (- 1/2 (* k 1/2))) (- (log (* -2 PI)) (log (/ -1 n))))) (- +nan.0)) (* +nan.0 (- (/ (exp (* (* 1/2 (- 1/2 (* k 1/2))) (- (log (* -2 PI)) (log (/ -1 n))))) (* k k)) (/ (exp (* (* 1/2 (- 1/2 (* k 1/2))) (- (log (* -2 PI)) (log (/ -1 n))))) k))))
13.072 * * * [progress]: adding candidates to table
14.220 * [progress]: [Phase 3 of 3] Extracting.
14.220 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<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))))> #<alt (λ (k n) (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))> #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (pow (* n 2) (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>)
14.221 * * * [regime-changes]: Trying 4 branch expressions: ((* (* 2 PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) n k)
14.221 * * * * [regimes]: Trying to branch on (* (* 2 PI) n) from (#<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<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))))> #<alt (λ (k n) (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))> #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (pow (* n 2) (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>)
14.297 * * * * [regimes]: Trying to branch on (* (* 2 PI) n) from (#<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>)
14.352 * * * * [regimes]: Trying to branch on (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) from (#<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<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))))> #<alt (λ (k n) (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))> #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (pow (* n 2) (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>)
14.402 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<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))))> #<alt (λ (k n) (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))> #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (pow (* n 2) (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>)
14.469 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (* (/ (* (pow (* n 2) (/ (- 1/2 (/ k 2)) 2)) (pow PI (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* (* n 2) PI) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<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))))> #<alt (λ (k n) (/ (pow (* (* (cbrt (* (* n 2) PI)) (cbrt (* (* n 2) PI))) (cbrt (* (* n 2) PI))) (- 1/2 (/ k 2))) (sqrt k)))> #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))> #<alt (λ (k n) (* (pow (* n 2) (- 1/2 (/ k 2))) (/ (pow PI (- 1/2 (/ k 2))) (sqrt k))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>)
14.561 * * * [regime]: Found split indices: #<option (#s(si 4 255))>
14.562 * [simplify]: Simplifying:
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
14.562 * * [simplify]: iteration 0: 12 enodes
14.563 * * [simplify]: iteration 1: 14 enodes
14.564 * * [simplify]: iteration complete: 14 enodes
14.564 * * [simplify]: Extracting #0: cost 1 inf + 0
14.564 * * [simplify]: Extracting #1: cost 3 inf + 0
14.564 * * [simplify]: Extracting #2: cost 6 inf + 0
14.564 * * [simplify]: Extracting #3: cost 9 inf + 1
14.564 * * [simplify]: Extracting #4: cost 8 inf + 44
14.564 * * [simplify]: Extracting #5: cost 4 inf + 171
14.564 * * [simplify]: Extracting #6: cost 0 inf + 1126
14.564 * [simplify]: Simplified to:
  (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k))
23.328 * [regime-testing]: Baseline error score: 0.33980599277657453
23.332 * [regime-testing]: Oracle error score: 0.16997772000347078
23.341 * [regime-testing]: End program error score: 0.33980599277657453