77.591 * [progress]: [Phase 1 of 3] Setting up.
0.002 * * * [progress]: [1/2] Preparing points
0.180 * * * [progress]: [2/2] Setting up program.
0.189 * [progress]: [Phase 2 of 3] Improving.
0.189 * [simplify]: Simplifying:
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.189 * * [simplify]: iteration 0: 13 enodes
0.196 * * [simplify]: iteration 1: 29 enodes
0.210 * * [simplify]: iteration 2: 58 enodes
0.238 * * [simplify]: iteration 3: 114 enodes
0.334 * * [simplify]: iteration 4: 285 enodes
0.566 * * [simplify]: iteration 5: 809 enodes
2.125 * * [simplify]: iteration 6: 2615 enodes
4.093 * * [simplify]: iteration complete: 5001 enodes
4.094 * * [simplify]: Extracting #0: cost 1 inf + 0
4.094 * * [simplify]: Extracting #1: cost 103 inf + 0
4.097 * * [simplify]: Extracting #2: cost 431 inf + 1
4.103 * * [simplify]: Extracting #3: cost 997 inf + 8
4.114 * * [simplify]: Extracting #4: cost 1397 inf + 6788
4.152 * * [simplify]: Extracting #5: cost 861 inf + 62543
4.230 * * [simplify]: Extracting #6: cost 379 inf + 206165
4.403 * * [simplify]: Extracting #7: cost 48 inf + 517189
4.605 * * [simplify]: Extracting #8: cost 0 inf + 561700
4.820 * * [simplify]: Extracting #9: cost 0 inf + 554777
5.046 * * [simplify]: Extracting #10: cost 0 inf + 553693
5.282 * * [simplify]: Extracting #11: cost 0 inf + 553344
5.509 * [simplify]: Simplified to:
  (/ (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))
5.510 * * [progress]: iteration 1 / 4
5.510 * * * [progress]: picking best candidate
5.519 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))>
5.519 * * * [progress]: localizing error
5.568 * * * [progress]: generating rewritten candidates
5.568 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2)
5.614 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1)
5.658 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1)
5.671 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
5.786 * * * [progress]: generating series expansions
5.786 * * * * [progress]: [ 1 / 4 ] generating series at (2 2)
5.791 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
5.791 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
5.791 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
5.791 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
5.791 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
5.791 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
5.791 * [taylor]: Taking taylor expansion of 0.5 in k
5.791 * [backup-simplify]: Simplify 0.5 into 0.5
5.792 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
5.792 * [taylor]: Taking taylor expansion of 1.0 in k
5.792 * [backup-simplify]: Simplify 1.0 into 1.0
5.792 * [taylor]: Taking taylor expansion of k in k
5.792 * [backup-simplify]: Simplify 0 into 0
5.792 * [backup-simplify]: Simplify 1 into 1
5.792 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
5.792 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
5.792 * [taylor]: Taking taylor expansion of 2.0 in k
5.792 * [backup-simplify]: Simplify 2.0 into 2.0
5.792 * [taylor]: Taking taylor expansion of (* n PI) in k
5.792 * [taylor]: Taking taylor expansion of n in k
5.792 * [backup-simplify]: Simplify n into n
5.792 * [taylor]: Taking taylor expansion of PI in k
5.792 * [backup-simplify]: Simplify PI into PI
5.792 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.792 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
5.792 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
5.793 * [backup-simplify]: Simplify (- 0) into 0
5.793 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
5.794 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
5.794 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
5.794 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
5.794 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
5.794 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
5.794 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
5.794 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
5.794 * [taylor]: Taking taylor expansion of 0.5 in n
5.794 * [backup-simplify]: Simplify 0.5 into 0.5
5.794 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
5.794 * [taylor]: Taking taylor expansion of 1.0 in n
5.794 * [backup-simplify]: Simplify 1.0 into 1.0
5.794 * [taylor]: Taking taylor expansion of k in n
5.794 * [backup-simplify]: Simplify k into k
5.794 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
5.794 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
5.794 * [taylor]: Taking taylor expansion of 2.0 in n
5.794 * [backup-simplify]: Simplify 2.0 into 2.0
5.795 * [taylor]: Taking taylor expansion of (* n PI) in n
5.795 * [taylor]: Taking taylor expansion of n in n
5.795 * [backup-simplify]: Simplify 0 into 0
5.795 * [backup-simplify]: Simplify 1 into 1
5.795 * [taylor]: Taking taylor expansion of PI in n
5.795 * [backup-simplify]: Simplify PI into PI
5.795 * [backup-simplify]: Simplify (* 0 PI) into 0
5.796 * [backup-simplify]: Simplify (* 2.0 0) into 0
5.798 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.800 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
5.801 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.801 * [backup-simplify]: Simplify (- k) into (- k)
5.801 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
5.801 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
5.803 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
5.804 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
5.805 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
5.805 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
5.806 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
5.806 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
5.806 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
5.806 * [taylor]: Taking taylor expansion of 0.5 in n
5.806 * [backup-simplify]: Simplify 0.5 into 0.5
5.806 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
5.806 * [taylor]: Taking taylor expansion of 1.0 in n
5.806 * [backup-simplify]: Simplify 1.0 into 1.0
5.806 * [taylor]: Taking taylor expansion of k in n
5.806 * [backup-simplify]: Simplify k into k
5.806 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
5.806 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
5.806 * [taylor]: Taking taylor expansion of 2.0 in n
5.806 * [backup-simplify]: Simplify 2.0 into 2.0
5.806 * [taylor]: Taking taylor expansion of (* n PI) in n
5.806 * [taylor]: Taking taylor expansion of n in n
5.806 * [backup-simplify]: Simplify 0 into 0
5.806 * [backup-simplify]: Simplify 1 into 1
5.806 * [taylor]: Taking taylor expansion of PI in n
5.806 * [backup-simplify]: Simplify PI into PI
5.807 * [backup-simplify]: Simplify (* 0 PI) into 0
5.807 * [backup-simplify]: Simplify (* 2.0 0) into 0
5.809 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.810 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
5.811 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.812 * [backup-simplify]: Simplify (- k) into (- k)
5.812 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
5.812 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
5.813 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
5.814 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
5.816 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
5.816 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
5.816 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
5.816 * [taylor]: Taking taylor expansion of 0.5 in k
5.816 * [backup-simplify]: Simplify 0.5 into 0.5
5.816 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
5.816 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
5.816 * [taylor]: Taking taylor expansion of 1.0 in k
5.816 * [backup-simplify]: Simplify 1.0 into 1.0
5.816 * [taylor]: Taking taylor expansion of k in k
5.816 * [backup-simplify]: Simplify 0 into 0
5.816 * [backup-simplify]: Simplify 1 into 1
5.816 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
5.816 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
5.816 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
5.816 * [taylor]: Taking taylor expansion of 2.0 in k
5.816 * [backup-simplify]: Simplify 2.0 into 2.0
5.816 * [taylor]: Taking taylor expansion of PI in k
5.816 * [backup-simplify]: Simplify PI into PI
5.817 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.818 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.818 * [taylor]: Taking taylor expansion of (log n) in k
5.818 * [taylor]: Taking taylor expansion of n in k
5.818 * [backup-simplify]: Simplify n into n
5.818 * [backup-simplify]: Simplify (log n) into (log n)
5.818 * [backup-simplify]: Simplify (- 0) into 0
5.819 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
5.820 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
5.821 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
5.822 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
5.824 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
5.825 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
5.826 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.827 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
5.829 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
5.830 * [backup-simplify]: Simplify (- 0) into 0
5.830 * [backup-simplify]: Simplify (+ 0 0) into 0
5.831 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
5.832 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
5.833 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
5.836 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.836 * [taylor]: Taking taylor expansion of 0 in k
5.836 * [backup-simplify]: Simplify 0 into 0
5.836 * [backup-simplify]: Simplify 0 into 0
5.837 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
5.839 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
5.840 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
5.840 * [backup-simplify]: Simplify (+ 0 0) into 0
5.840 * [backup-simplify]: Simplify (- 1) into -1
5.841 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.842 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
5.845 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
5.849 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
5.853 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
5.854 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.856 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.860 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
5.860 * [backup-simplify]: Simplify (- 0) into 0
5.861 * [backup-simplify]: Simplify (+ 0 0) into 0
5.861 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
5.863 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
5.865 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
5.867 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.868 * [taylor]: Taking taylor expansion of 0 in k
5.868 * [backup-simplify]: Simplify 0 into 0
5.868 * [backup-simplify]: Simplify 0 into 0
5.868 * [backup-simplify]: Simplify 0 into 0
5.869 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
5.872 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
5.875 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
5.875 * [backup-simplify]: Simplify (+ 0 0) into 0
5.876 * [backup-simplify]: Simplify (- 0) into 0
5.876 * [backup-simplify]: Simplify (+ 0 0) into 0
5.878 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
5.881 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
5.885 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
5.891 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
5.903 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
5.904 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))
5.904 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
5.905 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
5.905 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
5.905 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
5.905 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
5.905 * [taylor]: Taking taylor expansion of 0.5 in k
5.905 * [backup-simplify]: Simplify 0.5 into 0.5
5.905 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
5.905 * [taylor]: Taking taylor expansion of 1.0 in k
5.905 * [backup-simplify]: Simplify 1.0 into 1.0
5.905 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.905 * [taylor]: Taking taylor expansion of k in k
5.905 * [backup-simplify]: Simplify 0 into 0
5.905 * [backup-simplify]: Simplify 1 into 1
5.905 * [backup-simplify]: Simplify (/ 1 1) into 1
5.905 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
5.905 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
5.906 * [taylor]: Taking taylor expansion of 2.0 in k
5.906 * [backup-simplify]: Simplify 2.0 into 2.0
5.906 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.906 * [taylor]: Taking taylor expansion of PI in k
5.906 * [backup-simplify]: Simplify PI into PI
5.906 * [taylor]: Taking taylor expansion of n in k
5.906 * [backup-simplify]: Simplify n into n
5.906 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.906 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
5.906 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
5.906 * [backup-simplify]: Simplify (- 1) into -1
5.907 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.908 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
5.908 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
5.908 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
5.908 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
5.908 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
5.908 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
5.908 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
5.908 * [taylor]: Taking taylor expansion of 0.5 in n
5.909 * [backup-simplify]: Simplify 0.5 into 0.5
5.909 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
5.909 * [taylor]: Taking taylor expansion of 1.0 in n
5.909 * [backup-simplify]: Simplify 1.0 into 1.0
5.909 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.909 * [taylor]: Taking taylor expansion of k in n
5.909 * [backup-simplify]: Simplify k into k
5.909 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.909 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
5.909 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
5.909 * [taylor]: Taking taylor expansion of 2.0 in n
5.909 * [backup-simplify]: Simplify 2.0 into 2.0
5.909 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.909 * [taylor]: Taking taylor expansion of PI in n
5.909 * [backup-simplify]: Simplify PI into PI
5.909 * [taylor]: Taking taylor expansion of n in n
5.909 * [backup-simplify]: Simplify 0 into 0
5.909 * [backup-simplify]: Simplify 1 into 1
5.910 * [backup-simplify]: Simplify (/ PI 1) into PI
5.910 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.912 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.912 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.912 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
5.912 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
5.914 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.915 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
5.917 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
5.917 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
5.917 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
5.917 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
5.917 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
5.917 * [taylor]: Taking taylor expansion of 0.5 in n
5.917 * [backup-simplify]: Simplify 0.5 into 0.5
5.917 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
5.917 * [taylor]: Taking taylor expansion of 1.0 in n
5.917 * [backup-simplify]: Simplify 1.0 into 1.0
5.917 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.917 * [taylor]: Taking taylor expansion of k in n
5.917 * [backup-simplify]: Simplify k into k
5.917 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.917 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
5.917 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
5.917 * [taylor]: Taking taylor expansion of 2.0 in n
5.917 * [backup-simplify]: Simplify 2.0 into 2.0
5.917 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.917 * [taylor]: Taking taylor expansion of PI in n
5.917 * [backup-simplify]: Simplify PI into PI
5.917 * [taylor]: Taking taylor expansion of n in n
5.917 * [backup-simplify]: Simplify 0 into 0
5.917 * [backup-simplify]: Simplify 1 into 1
5.918 * [backup-simplify]: Simplify (/ PI 1) into PI
5.919 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.920 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.920 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.920 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
5.920 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
5.922 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.923 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
5.925 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
5.925 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
5.925 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
5.925 * [taylor]: Taking taylor expansion of 0.5 in k
5.925 * [backup-simplify]: Simplify 0.5 into 0.5
5.925 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
5.925 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
5.925 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
5.925 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
5.925 * [taylor]: Taking taylor expansion of 2.0 in k
5.925 * [backup-simplify]: Simplify 2.0 into 2.0
5.925 * [taylor]: Taking taylor expansion of PI in k
5.925 * [backup-simplify]: Simplify PI into PI
5.926 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
5.928 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
5.928 * [taylor]: Taking taylor expansion of (log n) in k
5.928 * [taylor]: Taking taylor expansion of n in k
5.928 * [backup-simplify]: Simplify n into n
5.928 * [backup-simplify]: Simplify (log n) into (log n)
5.928 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
5.928 * [taylor]: Taking taylor expansion of 1.0 in k
5.928 * [backup-simplify]: Simplify 1.0 into 1.0
5.928 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.928 * [taylor]: Taking taylor expansion of k in k
5.928 * [backup-simplify]: Simplify 0 into 0
5.928 * [backup-simplify]: Simplify 1 into 1
5.929 * [backup-simplify]: Simplify (/ 1 1) into 1
5.929 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.930 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
5.931 * [backup-simplify]: Simplify (- 1) into -1
5.931 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.933 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
5.934 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
5.935 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
5.937 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
5.938 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.939 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
5.941 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
5.941 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.942 * [backup-simplify]: Simplify (- 0) into 0
5.942 * [backup-simplify]: Simplify (+ 0 0) into 0
5.943 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
5.944 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.946 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
5.948 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.948 * [taylor]: Taking taylor expansion of 0 in k
5.948 * [backup-simplify]: Simplify 0 into 0
5.948 * [backup-simplify]: Simplify 0 into 0
5.948 * [backup-simplify]: Simplify 0 into 0
5.949 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.955 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
5.959 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
5.959 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.960 * [backup-simplify]: Simplify (- 0) into 0
5.960 * [backup-simplify]: Simplify (+ 0 0) into 0
5.961 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
5.962 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.964 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
5.967 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.967 * [taylor]: Taking taylor expansion of 0 in k
5.967 * [backup-simplify]: Simplify 0 into 0
5.967 * [backup-simplify]: Simplify 0 into 0
5.967 * [backup-simplify]: Simplify 0 into 0
5.967 * [backup-simplify]: Simplify 0 into 0
5.968 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.970 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.977 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
5.977 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.978 * [backup-simplify]: Simplify (- 0) into 0
5.978 * [backup-simplify]: Simplify (+ 0 0) into 0
5.979 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
5.981 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
5.983 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
5.986 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
5.986 * [taylor]: Taking taylor expansion of 0 in k
5.986 * [backup-simplify]: Simplify 0 into 0
5.986 * [backup-simplify]: Simplify 0 into 0
5.987 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
5.988 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))
5.988 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
5.988 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
5.988 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
5.988 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
5.988 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
5.989 * [taylor]: Taking taylor expansion of 0.5 in k
5.989 * [backup-simplify]: Simplify 0.5 into 0.5
5.989 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
5.989 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.989 * [taylor]: Taking taylor expansion of k in k
5.989 * [backup-simplify]: Simplify 0 into 0
5.989 * [backup-simplify]: Simplify 1 into 1
5.989 * [backup-simplify]: Simplify (/ 1 1) into 1
5.989 * [taylor]: Taking taylor expansion of 1.0 in k
5.989 * [backup-simplify]: Simplify 1.0 into 1.0
5.989 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
5.989 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
5.989 * [taylor]: Taking taylor expansion of -2.0 in k
5.989 * [backup-simplify]: Simplify -2.0 into -2.0
5.989 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.989 * [taylor]: Taking taylor expansion of PI in k
5.989 * [backup-simplify]: Simplify PI into PI
5.989 * [taylor]: Taking taylor expansion of n in k
5.989 * [backup-simplify]: Simplify n into n
5.990 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.990 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
5.990 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
5.990 * [backup-simplify]: Simplify (+ 1 0) into 1
5.991 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
5.991 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
5.991 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
5.991 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
5.991 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
5.991 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
5.992 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
5.992 * [taylor]: Taking taylor expansion of 0.5 in n
5.992 * [backup-simplify]: Simplify 0.5 into 0.5
5.992 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
5.992 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.992 * [taylor]: Taking taylor expansion of k in n
5.992 * [backup-simplify]: Simplify k into k
5.992 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.992 * [taylor]: Taking taylor expansion of 1.0 in n
5.992 * [backup-simplify]: Simplify 1.0 into 1.0
5.992 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
5.992 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
5.992 * [taylor]: Taking taylor expansion of -2.0 in n
5.992 * [backup-simplify]: Simplify -2.0 into -2.0
5.992 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.992 * [taylor]: Taking taylor expansion of PI in n
5.992 * [backup-simplify]: Simplify PI into PI
5.992 * [taylor]: Taking taylor expansion of n in n
5.992 * [backup-simplify]: Simplify 0 into 0
5.992 * [backup-simplify]: Simplify 1 into 1
5.993 * [backup-simplify]: Simplify (/ PI 1) into PI
5.993 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
5.995 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
5.995 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
5.995 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
5.997 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
5.999 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
6.000 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
6.001 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
6.001 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
6.001 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
6.001 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
6.001 * [taylor]: Taking taylor expansion of 0.5 in n
6.001 * [backup-simplify]: Simplify 0.5 into 0.5
6.001 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
6.001 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.001 * [taylor]: Taking taylor expansion of k in n
6.001 * [backup-simplify]: Simplify k into k
6.001 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.001 * [taylor]: Taking taylor expansion of 1.0 in n
6.001 * [backup-simplify]: Simplify 1.0 into 1.0
6.001 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
6.001 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
6.001 * [taylor]: Taking taylor expansion of -2.0 in n
6.001 * [backup-simplify]: Simplify -2.0 into -2.0
6.001 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.001 * [taylor]: Taking taylor expansion of PI in n
6.001 * [backup-simplify]: Simplify PI into PI
6.001 * [taylor]: Taking taylor expansion of n in n
6.001 * [backup-simplify]: Simplify 0 into 0
6.001 * [backup-simplify]: Simplify 1 into 1
6.002 * [backup-simplify]: Simplify (/ PI 1) into PI
6.003 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
6.004 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
6.004 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
6.004 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
6.006 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.007 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
6.008 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
6.008 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
6.008 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
6.008 * [taylor]: Taking taylor expansion of 0.5 in k
6.008 * [backup-simplify]: Simplify 0.5 into 0.5
6.008 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
6.009 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
6.009 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.009 * [taylor]: Taking taylor expansion of k in k
6.009 * [backup-simplify]: Simplify 0 into 0
6.009 * [backup-simplify]: Simplify 1 into 1
6.009 * [backup-simplify]: Simplify (/ 1 1) into 1
6.009 * [taylor]: Taking taylor expansion of 1.0 in k
6.009 * [backup-simplify]: Simplify 1.0 into 1.0
6.009 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
6.009 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
6.009 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
6.009 * [taylor]: Taking taylor expansion of -2.0 in k
6.009 * [backup-simplify]: Simplify -2.0 into -2.0
6.009 * [taylor]: Taking taylor expansion of PI in k
6.009 * [backup-simplify]: Simplify PI into PI
6.010 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
6.011 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
6.011 * [taylor]: Taking taylor expansion of (log n) in k
6.011 * [taylor]: Taking taylor expansion of n in k
6.011 * [backup-simplify]: Simplify n into n
6.011 * [backup-simplify]: Simplify (log n) into (log n)
6.011 * [backup-simplify]: Simplify (+ 1 0) into 1
6.011 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
6.013 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
6.014 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
6.015 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
6.016 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
6.018 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
6.019 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.020 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
6.021 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
6.022 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.022 * [backup-simplify]: Simplify (+ 0 0) into 0
6.023 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
6.024 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.025 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
6.028 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
6.028 * [taylor]: Taking taylor expansion of 0 in k
6.028 * [backup-simplify]: Simplify 0 into 0
6.028 * [backup-simplify]: Simplify 0 into 0
6.028 * [backup-simplify]: Simplify 0 into 0
6.029 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.030 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
6.033 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
6.034 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
6.034 * [backup-simplify]: Simplify (+ 0 0) into 0
6.035 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
6.037 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.038 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
6.041 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
6.041 * [taylor]: Taking taylor expansion of 0 in k
6.041 * [backup-simplify]: Simplify 0 into 0
6.041 * [backup-simplify]: Simplify 0 into 0
6.041 * [backup-simplify]: Simplify 0 into 0
6.041 * [backup-simplify]: Simplify 0 into 0
6.043 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.044 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
6.050 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0
6.050 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
6.051 * [backup-simplify]: Simplify (+ 0 0) into 0
6.052 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
6.053 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.055 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
6.058 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
6.058 * [taylor]: Taking taylor expansion of 0 in k
6.058 * [backup-simplify]: Simplify 0 into 0
6.058 * [backup-simplify]: Simplify 0 into 0
6.060 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
6.060 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1)
6.061 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
6.061 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
6.061 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
6.061 * [taylor]: Taking taylor expansion of 2.0 in n
6.061 * [backup-simplify]: Simplify 2.0 into 2.0
6.061 * [taylor]: Taking taylor expansion of (* n PI) in n
6.061 * [taylor]: Taking taylor expansion of n in n
6.061 * [backup-simplify]: Simplify 0 into 0
6.061 * [backup-simplify]: Simplify 1 into 1
6.061 * [taylor]: Taking taylor expansion of PI in n
6.061 * [backup-simplify]: Simplify PI into PI
6.061 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
6.061 * [taylor]: Taking taylor expansion of 2.0 in n
6.061 * [backup-simplify]: Simplify 2.0 into 2.0
6.061 * [taylor]: Taking taylor expansion of (* n PI) in n
6.061 * [taylor]: Taking taylor expansion of n in n
6.061 * [backup-simplify]: Simplify 0 into 0
6.061 * [backup-simplify]: Simplify 1 into 1
6.061 * [taylor]: Taking taylor expansion of PI in n
6.061 * [backup-simplify]: Simplify PI into PI
6.062 * [backup-simplify]: Simplify (* 0 PI) into 0
6.062 * [backup-simplify]: Simplify (* 2.0 0) into 0
6.062 * [backup-simplify]: Simplify 0 into 0
6.064 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.065 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
6.066 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
6.067 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
6.068 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
6.068 * [backup-simplify]: Simplify 0 into 0
6.069 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
6.070 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
6.071 * [backup-simplify]: Simplify 0 into 0
6.072 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
6.073 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
6.073 * [backup-simplify]: Simplify 0 into 0
6.075 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
6.077 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
6.077 * [backup-simplify]: Simplify 0 into 0
6.078 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
6.080 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
6.080 * [backup-simplify]: Simplify 0 into 0
6.082 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
6.084 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
6.084 * [backup-simplify]: Simplify 0 into 0
6.085 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
6.086 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
6.086 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
6.086 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
6.086 * [taylor]: Taking taylor expansion of 2.0 in n
6.086 * [backup-simplify]: Simplify 2.0 into 2.0
6.086 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.086 * [taylor]: Taking taylor expansion of PI in n
6.086 * [backup-simplify]: Simplify PI into PI
6.086 * [taylor]: Taking taylor expansion of n in n
6.086 * [backup-simplify]: Simplify 0 into 0
6.086 * [backup-simplify]: Simplify 1 into 1
6.086 * [backup-simplify]: Simplify (/ PI 1) into PI
6.086 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
6.086 * [taylor]: Taking taylor expansion of 2.0 in n
6.086 * [backup-simplify]: Simplify 2.0 into 2.0
6.087 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.087 * [taylor]: Taking taylor expansion of PI in n
6.087 * [backup-simplify]: Simplify PI into PI
6.087 * [taylor]: Taking taylor expansion of n in n
6.087 * [backup-simplify]: Simplify 0 into 0
6.087 * [backup-simplify]: Simplify 1 into 1
6.087 * [backup-simplify]: Simplify (/ PI 1) into PI
6.088 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
6.088 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
6.090 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.090 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
6.090 * [backup-simplify]: Simplify 0 into 0
6.091 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.093 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
6.093 * [backup-simplify]: Simplify 0 into 0
6.094 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.096 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
6.096 * [backup-simplify]: Simplify 0 into 0
6.097 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.098 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
6.098 * [backup-simplify]: Simplify 0 into 0
6.100 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.101 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
6.102 * [backup-simplify]: Simplify 0 into 0
6.103 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.105 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
6.105 * [backup-simplify]: Simplify 0 into 0
6.106 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
6.106 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
6.106 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
6.107 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
6.107 * [taylor]: Taking taylor expansion of -2.0 in n
6.107 * [backup-simplify]: Simplify -2.0 into -2.0
6.107 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.107 * [taylor]: Taking taylor expansion of PI in n
6.107 * [backup-simplify]: Simplify PI into PI
6.107 * [taylor]: Taking taylor expansion of n in n
6.107 * [backup-simplify]: Simplify 0 into 0
6.107 * [backup-simplify]: Simplify 1 into 1
6.107 * [backup-simplify]: Simplify (/ PI 1) into PI
6.107 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
6.107 * [taylor]: Taking taylor expansion of -2.0 in n
6.107 * [backup-simplify]: Simplify -2.0 into -2.0
6.107 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.107 * [taylor]: Taking taylor expansion of PI in n
6.108 * [backup-simplify]: Simplify PI into PI
6.108 * [taylor]: Taking taylor expansion of n in n
6.108 * [backup-simplify]: Simplify 0 into 0
6.108 * [backup-simplify]: Simplify 1 into 1
6.108 * [backup-simplify]: Simplify (/ PI 1) into PI
6.109 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
6.109 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
6.110 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.111 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
6.111 * [backup-simplify]: Simplify 0 into 0
6.112 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.113 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
6.113 * [backup-simplify]: Simplify 0 into 0
6.114 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.115 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
6.115 * [backup-simplify]: Simplify 0 into 0
6.116 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.118 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
6.118 * [backup-simplify]: Simplify 0 into 0
6.123 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.125 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
6.125 * [backup-simplify]: Simplify 0 into 0
6.126 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.128 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
6.128 * [backup-simplify]: Simplify 0 into 0
6.129 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
6.129 * * * * [progress]: [ 3 / 4 ] generating series at (2 1)
6.129 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k)))
6.129 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0
6.129 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
6.129 * [taylor]: Taking taylor expansion of 1.0 in k
6.129 * [backup-simplify]: Simplify 1.0 into 1.0
6.129 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
6.129 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.129 * [taylor]: Taking taylor expansion of k in k
6.129 * [backup-simplify]: Simplify 0 into 0
6.129 * [backup-simplify]: Simplify 1 into 1
6.130 * [backup-simplify]: Simplify (/ 1 1) into 1
6.130 * [backup-simplify]: Simplify (sqrt 0) into 0
6.132 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.132 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
6.132 * [taylor]: Taking taylor expansion of 1.0 in k
6.132 * [backup-simplify]: Simplify 1.0 into 1.0
6.132 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
6.132 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.132 * [taylor]: Taking taylor expansion of k in k
6.132 * [backup-simplify]: Simplify 0 into 0
6.132 * [backup-simplify]: Simplify 1 into 1
6.132 * [backup-simplify]: Simplify (/ 1 1) into 1
6.133 * [backup-simplify]: Simplify (sqrt 0) into 0
6.134 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.135 * [backup-simplify]: Simplify (* 1.0 0) into 0
6.135 * [backup-simplify]: Simplify 0 into 0
6.136 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
6.136 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
6.138 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
6.141 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.143 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
6.143 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
6.144 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.148 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.151 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
6.151 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
6.153 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0)))))
6.153 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k))
6.153 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0
6.153 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
6.153 * [taylor]: Taking taylor expansion of 1.0 in k
6.153 * [backup-simplify]: Simplify 1.0 into 1.0
6.153 * [taylor]: Taking taylor expansion of (sqrt k) in k
6.153 * [taylor]: Taking taylor expansion of k in k
6.153 * [backup-simplify]: Simplify 0 into 0
6.153 * [backup-simplify]: Simplify 1 into 1
6.154 * [backup-simplify]: Simplify (sqrt 0) into 0
6.155 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.156 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
6.156 * [taylor]: Taking taylor expansion of 1.0 in k
6.156 * [backup-simplify]: Simplify 1.0 into 1.0
6.156 * [taylor]: Taking taylor expansion of (sqrt k) in k
6.156 * [taylor]: Taking taylor expansion of k in k
6.156 * [backup-simplify]: Simplify 0 into 0
6.156 * [backup-simplify]: Simplify 1 into 1
6.156 * [backup-simplify]: Simplify (sqrt 0) into 0
6.157 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.158 * [backup-simplify]: Simplify (* 1.0 0) into 0
6.158 * [backup-simplify]: Simplify 0 into 0
6.160 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
6.160 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
6.163 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.165 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
6.166 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
6.170 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.172 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
6.172 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
6.174 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 k) 3)) (+ (* (- +nan.0) (pow (/ 1 k) 2)) (* (- +nan.0) (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
6.174 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k)))
6.174 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0
6.174 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
6.174 * [taylor]: Taking taylor expansion of 1.0 in k
6.174 * [backup-simplify]: Simplify 1.0 into 1.0
6.174 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
6.174 * [taylor]: Taking taylor expansion of (/ -1 k) in k
6.174 * [taylor]: Taking taylor expansion of -1 in k
6.174 * [backup-simplify]: Simplify -1 into -1
6.174 * [taylor]: Taking taylor expansion of k in k
6.174 * [backup-simplify]: Simplify 0 into 0
6.174 * [backup-simplify]: Simplify 1 into 1
6.175 * [backup-simplify]: Simplify (/ -1 1) into -1
6.175 * [backup-simplify]: Simplify (sqrt 0) into 0
6.177 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
6.177 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
6.177 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
6.177 * [taylor]: Taking taylor expansion of 1.0 in k
6.177 * [backup-simplify]: Simplify 1.0 into 1.0
6.177 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
6.177 * [taylor]: Taking taylor expansion of (/ -1 k) in k
6.177 * [taylor]: Taking taylor expansion of -1 in k
6.177 * [backup-simplify]: Simplify -1 into -1
6.177 * [taylor]: Taking taylor expansion of k in k
6.177 * [backup-simplify]: Simplify 0 into 0
6.177 * [backup-simplify]: Simplify 1 into 1
6.178 * [backup-simplify]: Simplify (/ -1 1) into -1
6.178 * [backup-simplify]: Simplify (sqrt 0) into 0
6.179 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
6.180 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
6.180 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.181 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
6.184 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.186 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
6.187 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
6.188 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.191 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.196 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
6.196 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
6.197 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow (/ 1 (- k)) 2)) (+ (* (- +nan.0) (/ 1 (- k))) +nan.0)) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
6.197 * * * * [progress]: [ 4 / 4 ] generating series at (2)
6.198 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))))
6.198 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0
6.198 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n
6.198 * [taylor]: Taking taylor expansion of 1.0 in n
6.198 * [backup-simplify]: Simplify 1.0 into 1.0
6.198 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n
6.198 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
6.198 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.198 * [taylor]: Taking taylor expansion of k in n
6.199 * [backup-simplify]: Simplify k into k
6.199 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.199 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
6.199 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.199 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
6.199 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
6.199 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
6.199 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
6.199 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
6.199 * [taylor]: Taking taylor expansion of 0.5 in n
6.199 * [backup-simplify]: Simplify 0.5 into 0.5
6.199 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
6.199 * [taylor]: Taking taylor expansion of 1.0 in n
6.199 * [backup-simplify]: Simplify 1.0 into 1.0
6.199 * [taylor]: Taking taylor expansion of k in n
6.199 * [backup-simplify]: Simplify k into k
6.199 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
6.199 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
6.199 * [taylor]: Taking taylor expansion of 2.0 in n
6.199 * [backup-simplify]: Simplify 2.0 into 2.0
6.199 * [taylor]: Taking taylor expansion of (* n PI) in n
6.199 * [taylor]: Taking taylor expansion of n in n
6.199 * [backup-simplify]: Simplify 0 into 0
6.199 * [backup-simplify]: Simplify 1 into 1
6.200 * [taylor]: Taking taylor expansion of PI in n
6.200 * [backup-simplify]: Simplify PI into PI
6.200 * [backup-simplify]: Simplify (* 0 PI) into 0
6.200 * [backup-simplify]: Simplify (* 2.0 0) into 0
6.202 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.204 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
6.205 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.205 * [backup-simplify]: Simplify (- k) into (- k)
6.205 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
6.205 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
6.206 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
6.208 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
6.209 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
6.209 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
6.209 * [taylor]: Taking taylor expansion of 1.0 in k
6.209 * [backup-simplify]: Simplify 1.0 into 1.0
6.209 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
6.209 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
6.209 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.209 * [taylor]: Taking taylor expansion of k in k
6.209 * [backup-simplify]: Simplify 0 into 0
6.209 * [backup-simplify]: Simplify 1 into 1
6.210 * [backup-simplify]: Simplify (/ 1 1) into 1
6.210 * [backup-simplify]: Simplify (sqrt 0) into 0
6.212 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.212 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
6.212 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
6.212 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
6.212 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
6.212 * [taylor]: Taking taylor expansion of 0.5 in k
6.212 * [backup-simplify]: Simplify 0.5 into 0.5
6.212 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
6.212 * [taylor]: Taking taylor expansion of 1.0 in k
6.212 * [backup-simplify]: Simplify 1.0 into 1.0
6.212 * [taylor]: Taking taylor expansion of k in k
6.212 * [backup-simplify]: Simplify 0 into 0
6.212 * [backup-simplify]: Simplify 1 into 1
6.212 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
6.212 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
6.212 * [taylor]: Taking taylor expansion of 2.0 in k
6.212 * [backup-simplify]: Simplify 2.0 into 2.0
6.212 * [taylor]: Taking taylor expansion of (* n PI) in k
6.212 * [taylor]: Taking taylor expansion of n in k
6.212 * [backup-simplify]: Simplify n into n
6.212 * [taylor]: Taking taylor expansion of PI in k
6.212 * [backup-simplify]: Simplify PI into PI
6.212 * [backup-simplify]: Simplify (* n PI) into (* n PI)
6.212 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
6.213 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
6.213 * [backup-simplify]: Simplify (- 0) into 0
6.213 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
6.214 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
6.214 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
6.214 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
6.214 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
6.214 * [taylor]: Taking taylor expansion of 1.0 in k
6.214 * [backup-simplify]: Simplify 1.0 into 1.0
6.214 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
6.214 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
6.214 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.214 * [taylor]: Taking taylor expansion of k in k
6.214 * [backup-simplify]: Simplify 0 into 0
6.214 * [backup-simplify]: Simplify 1 into 1
6.215 * [backup-simplify]: Simplify (/ 1 1) into 1
6.215 * [backup-simplify]: Simplify (sqrt 0) into 0
6.216 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.217 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
6.217 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
6.217 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
6.217 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
6.217 * [taylor]: Taking taylor expansion of 0.5 in k
6.217 * [backup-simplify]: Simplify 0.5 into 0.5
6.217 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
6.217 * [taylor]: Taking taylor expansion of 1.0 in k
6.217 * [backup-simplify]: Simplify 1.0 into 1.0
6.217 * [taylor]: Taking taylor expansion of k in k
6.217 * [backup-simplify]: Simplify 0 into 0
6.217 * [backup-simplify]: Simplify 1 into 1
6.217 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
6.217 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
6.217 * [taylor]: Taking taylor expansion of 2.0 in k
6.217 * [backup-simplify]: Simplify 2.0 into 2.0
6.217 * [taylor]: Taking taylor expansion of (* n PI) in k
6.217 * [taylor]: Taking taylor expansion of n in k
6.217 * [backup-simplify]: Simplify n into n
6.217 * [taylor]: Taking taylor expansion of PI in k
6.217 * [backup-simplify]: Simplify PI into PI
6.217 * [backup-simplify]: Simplify (* n PI) into (* n PI)
6.217 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
6.217 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
6.218 * [backup-simplify]: Simplify (- 0) into 0
6.218 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
6.219 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
6.219 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
6.219 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
6.219 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0
6.220 * [backup-simplify]: Simplify (* 1.0 0) into 0
6.220 * [taylor]: Taking taylor expansion of 0 in n
6.220 * [backup-simplify]: Simplify 0 into 0
6.220 * [backup-simplify]: Simplify 0 into 0
6.221 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
6.221 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0
6.222 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0
6.223 * [backup-simplify]: Simplify (- 1) into -1
6.223 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.225 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5)
6.226 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI)))))
6.226 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
6.228 * [backup-simplify]: Simplify (+ (* 0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))
6.230 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
6.230 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n
6.230 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n
6.230 * [taylor]: Taking taylor expansion of +nan.0 in n
6.230 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.230 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
6.231 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
6.231 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
6.231 * [taylor]: Taking taylor expansion of 0.5 in n
6.231 * [backup-simplify]: Simplify 0.5 into 0.5
6.231 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
6.231 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
6.231 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
6.231 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
6.231 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
6.231 * [taylor]: Taking taylor expansion of 1.0 in n
6.231 * [backup-simplify]: Simplify 1.0 into 1.0
6.231 * [taylor]: Taking taylor expansion of (log PI) in n
6.231 * [taylor]: Taking taylor expansion of PI in n
6.231 * [backup-simplify]: Simplify PI into PI
6.231 * [backup-simplify]: Simplify (log PI) into (log PI)
6.232 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
6.234 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
6.234 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
6.234 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
6.234 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
6.234 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
6.234 * [taylor]: Taking taylor expansion of 1.0 in n
6.234 * [backup-simplify]: Simplify 1.0 into 1.0
6.234 * [taylor]: Taking taylor expansion of (log n) in n
6.234 * [taylor]: Taking taylor expansion of n in n
6.234 * [backup-simplify]: Simplify 0 into 0
6.234 * [backup-simplify]: Simplify 1 into 1
6.235 * [backup-simplify]: Simplify (log 1) into 0
6.235 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
6.235 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
6.236 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
6.236 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
6.236 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
6.236 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
6.236 * [taylor]: Taking taylor expansion of 1.0 in n
6.236 * [backup-simplify]: Simplify 1.0 into 1.0
6.236 * [taylor]: Taking taylor expansion of (log 2.0) in n
6.236 * [taylor]: Taking taylor expansion of 2.0 in n
6.236 * [backup-simplify]: Simplify 2.0 into 2.0
6.236 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
6.237 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
6.239 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
6.239 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
6.241 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
6.242 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))
6.244 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))
6.246 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
6.248 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))
6.249 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))
6.251 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
6.251 * [backup-simplify]: Simplify 0 into 0
6.252 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
6.253 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
6.254 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0
6.255 * [backup-simplify]: Simplify (- 0) into 0
6.255 * [backup-simplify]: Simplify (+ 0 0) into 0
6.256 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0
6.258 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0
6.259 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
6.260 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
6.263 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.267 * [backup-simplify]: Simplify (+ (* 0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5)))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))
6.272 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))
6.273 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) in n
6.273 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))) in n
6.273 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n
6.273 * [taylor]: Taking taylor expansion of +nan.0 in n
6.273 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.273 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
6.273 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
6.273 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
6.273 * [taylor]: Taking taylor expansion of 0.5 in n
6.273 * [backup-simplify]: Simplify 0.5 into 0.5
6.273 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
6.273 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
6.273 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
6.273 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
6.273 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
6.273 * [taylor]: Taking taylor expansion of 1.0 in n
6.273 * [backup-simplify]: Simplify 1.0 into 1.0
6.273 * [taylor]: Taking taylor expansion of (log PI) in n
6.273 * [taylor]: Taking taylor expansion of PI in n
6.273 * [backup-simplify]: Simplify PI into PI
6.274 * [backup-simplify]: Simplify (log PI) into (log PI)
6.275 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
6.276 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
6.276 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
6.276 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
6.276 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
6.276 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
6.276 * [taylor]: Taking taylor expansion of 1.0 in n
6.277 * [backup-simplify]: Simplify 1.0 into 1.0
6.277 * [taylor]: Taking taylor expansion of (log n) in n
6.277 * [taylor]: Taking taylor expansion of n in n
6.277 * [backup-simplify]: Simplify 0 into 0
6.277 * [backup-simplify]: Simplify 1 into 1
6.277 * [backup-simplify]: Simplify (log 1) into 0
6.277 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
6.277 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
6.278 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
6.278 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
6.278 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
6.278 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
6.278 * [taylor]: Taking taylor expansion of 1.0 in n
6.278 * [backup-simplify]: Simplify 1.0 into 1.0
6.278 * [taylor]: Taking taylor expansion of (log 2.0) in n
6.278 * [taylor]: Taking taylor expansion of 2.0 in n
6.278 * [backup-simplify]: Simplify 2.0 into 2.0
6.278 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
6.287 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
6.288 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
6.289 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
6.290 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
6.292 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))
6.293 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))
6.295 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
6.295 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))) in n
6.295 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n
6.295 * [taylor]: Taking taylor expansion of +nan.0 in n
6.295 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.295 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n
6.295 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
6.295 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
6.295 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
6.295 * [taylor]: Taking taylor expansion of 0.5 in n
6.295 * [backup-simplify]: Simplify 0.5 into 0.5
6.295 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
6.295 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
6.295 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
6.295 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
6.295 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
6.295 * [taylor]: Taking taylor expansion of 1.0 in n
6.295 * [backup-simplify]: Simplify 1.0 into 1.0
6.295 * [taylor]: Taking taylor expansion of (log 2.0) in n
6.296 * [taylor]: Taking taylor expansion of 2.0 in n
6.296 * [backup-simplify]: Simplify 2.0 into 2.0
6.296 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
6.297 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
6.299 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
6.299 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
6.299 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
6.299 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
6.299 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
6.299 * [taylor]: Taking taylor expansion of 1.0 in n
6.299 * [backup-simplify]: Simplify 1.0 into 1.0
6.299 * [taylor]: Taking taylor expansion of (log PI) in n
6.299 * [taylor]: Taking taylor expansion of PI in n
6.299 * [backup-simplify]: Simplify PI into PI
6.300 * [backup-simplify]: Simplify (log PI) into (log PI)
6.301 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
6.302 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
6.302 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
6.302 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
6.302 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
6.302 * [taylor]: Taking taylor expansion of 1.0 in n
6.302 * [backup-simplify]: Simplify 1.0 into 1.0
6.302 * [taylor]: Taking taylor expansion of (log n) in n
6.303 * [taylor]: Taking taylor expansion of n in n
6.303 * [backup-simplify]: Simplify 0 into 0
6.303 * [backup-simplify]: Simplify 1 into 1
6.303 * [backup-simplify]: Simplify (log 1) into 0
6.303 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
6.304 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
6.304 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
6.304 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
6.306 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)
6.307 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))
6.308 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))
6.310 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
6.310 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
6.310 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
6.310 * [taylor]: Taking taylor expansion of 2.0 in n
6.310 * [backup-simplify]: Simplify 2.0 into 2.0
6.310 * [taylor]: Taking taylor expansion of (* n PI) in n
6.310 * [taylor]: Taking taylor expansion of n in n
6.310 * [backup-simplify]: Simplify 0 into 0
6.310 * [backup-simplify]: Simplify 1 into 1
6.310 * [taylor]: Taking taylor expansion of PI in n
6.310 * [backup-simplify]: Simplify PI into PI
6.311 * [backup-simplify]: Simplify (* 0 PI) into 0
6.311 * [backup-simplify]: Simplify (* 2.0 0) into 0
6.313 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.314 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
6.315 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.317 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))
6.318 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
6.321 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))
6.324 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
6.327 * [backup-simplify]: Simplify (- (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))
6.332 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))
6.338 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))
6.345 * [backup-simplify]: Simplify (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))
6.346 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0
6.347 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0
6.349 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0
6.350 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
6.351 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
6.351 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0
6.352 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0
6.353 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0
6.354 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
6.355 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0
6.357 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
6.359 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0
6.361 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1)))) 1) into 0
6.363 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)))) into 0
6.365 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
6.367 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0
6.367 * [backup-simplify]: Simplify (- 0) into 0
6.367 * [backup-simplify]: Simplify 0 into 0
6.367 * [backup-simplify]: Simplify 0 into 0
6.368 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
6.369 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
6.372 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0
6.373 * [backup-simplify]: Simplify (- 0) into 0
6.373 * [backup-simplify]: Simplify (+ 0 0) into 0
6.375 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0
6.376 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0
6.378 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
6.380 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.384 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.389 * [backup-simplify]: Simplify (+ (* 0 (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))
6.401 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))) (+ (* 0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))
6.401 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n
6.401 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n
6.401 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n
6.401 * [taylor]: Taking taylor expansion of +nan.0 in n
6.401 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.401 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n
6.401 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n
6.401 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n
6.401 * [taylor]: Taking taylor expansion of 0.5 in n
6.401 * [backup-simplify]: Simplify 0.5 into 0.5
6.401 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n
6.401 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n
6.401 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
6.401 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
6.401 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
6.401 * [taylor]: Taking taylor expansion of 1.0 in n
6.401 * [backup-simplify]: Simplify 1.0 into 1.0
6.401 * [taylor]: Taking taylor expansion of (log 2.0) in n
6.401 * [taylor]: Taking taylor expansion of 2.0 in n
6.401 * [backup-simplify]: Simplify 2.0 into 2.0
6.402 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
6.403 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
6.404 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
6.404 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n
6.404 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
6.404 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
6.404 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
6.404 * [taylor]: Taking taylor expansion of 1.0 in n
6.404 * [backup-simplify]: Simplify 1.0 into 1.0
6.405 * [taylor]: Taking taylor expansion of (log n) in n
6.405 * [taylor]: Taking taylor expansion of n in n
6.405 * [backup-simplify]: Simplify 0 into 0
6.405 * [backup-simplify]: Simplify 1 into 1
6.405 * [backup-simplify]: Simplify (log 1) into 0
6.405 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
6.406 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
6.406 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
6.406 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
6.406 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
6.406 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
6.406 * [taylor]: Taking taylor expansion of 1.0 in n
6.406 * [backup-simplify]: Simplify 1.0 into 1.0
6.406 * [taylor]: Taking taylor expansion of (log PI) in n
6.406 * [taylor]: Taking taylor expansion of PI in n
6.406 * [backup-simplify]: Simplify PI into PI
6.406 * [backup-simplify]: Simplify (log PI) into (log PI)
6.407 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
6.409 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
6.409 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
6.410 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)
6.412 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))
6.413 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))
6.415 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
6.415 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n
6.415 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n
6.415 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n
6.415 * [taylor]: Taking taylor expansion of +nan.0 in n
6.415 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.415 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n
6.415 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
6.415 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
6.415 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
6.415 * [taylor]: Taking taylor expansion of 0.5 in n
6.415 * [backup-simplify]: Simplify 0.5 into 0.5
6.415 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
6.415 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
6.415 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
6.415 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
6.415 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
6.415 * [taylor]: Taking taylor expansion of 1.0 in n
6.415 * [backup-simplify]: Simplify 1.0 into 1.0
6.415 * [taylor]: Taking taylor expansion of (log 2.0) in n
6.415 * [taylor]: Taking taylor expansion of 2.0 in n
6.415 * [backup-simplify]: Simplify 2.0 into 2.0
6.416 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
6.417 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
6.418 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
6.418 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
6.418 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
6.418 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
6.418 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
6.418 * [taylor]: Taking taylor expansion of 1.0 in n
6.418 * [backup-simplify]: Simplify 1.0 into 1.0
6.418 * [taylor]: Taking taylor expansion of (log PI) in n
6.418 * [taylor]: Taking taylor expansion of PI in n
6.418 * [backup-simplify]: Simplify PI into PI
6.419 * [backup-simplify]: Simplify (log PI) into (log PI)
6.420 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
6.421 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
6.421 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
6.422 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
6.422 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
6.422 * [taylor]: Taking taylor expansion of 1.0 in n
6.422 * [backup-simplify]: Simplify 1.0 into 1.0
6.422 * [taylor]: Taking taylor expansion of (log n) in n
6.422 * [taylor]: Taking taylor expansion of n in n
6.422 * [backup-simplify]: Simplify 0 into 0
6.422 * [backup-simplify]: Simplify 1 into 1
6.422 * [backup-simplify]: Simplify (log 1) into 0
6.423 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
6.423 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
6.423 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
6.424 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
6.425 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)
6.426 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))
6.427 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))
6.429 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
6.429 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
6.429 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
6.429 * [taylor]: Taking taylor expansion of 2.0 in n
6.429 * [backup-simplify]: Simplify 2.0 into 2.0
6.429 * [taylor]: Taking taylor expansion of (* n PI) in n
6.429 * [taylor]: Taking taylor expansion of n in n
6.429 * [backup-simplify]: Simplify 0 into 0
6.429 * [backup-simplify]: Simplify 1 into 1
6.429 * [taylor]: Taking taylor expansion of PI in n
6.429 * [backup-simplify]: Simplify PI into PI
6.430 * [backup-simplify]: Simplify (* 0 PI) into 0
6.430 * [backup-simplify]: Simplify (* 2.0 0) into 0
6.432 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.434 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
6.435 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.435 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n
6.435 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n
6.435 * [taylor]: Taking taylor expansion of +nan.0 in n
6.435 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.435 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n
6.435 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
6.435 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
6.435 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
6.435 * [taylor]: Taking taylor expansion of 0.5 in n
6.435 * [backup-simplify]: Simplify 0.5 into 0.5
6.435 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
6.435 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
6.435 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
6.435 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
6.435 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
6.435 * [taylor]: Taking taylor expansion of 1.0 in n
6.435 * [backup-simplify]: Simplify 1.0 into 1.0
6.435 * [taylor]: Taking taylor expansion of (log 2.0) in n
6.435 * [taylor]: Taking taylor expansion of 2.0 in n
6.435 * [backup-simplify]: Simplify 2.0 into 2.0
6.436 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
6.437 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
6.438 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
6.438 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
6.438 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
6.438 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
6.438 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
6.438 * [taylor]: Taking taylor expansion of 1.0 in n
6.438 * [backup-simplify]: Simplify 1.0 into 1.0
6.438 * [taylor]: Taking taylor expansion of (log PI) in n
6.438 * [taylor]: Taking taylor expansion of PI in n
6.438 * [backup-simplify]: Simplify PI into PI
6.445 * [backup-simplify]: Simplify (log PI) into (log PI)
6.446 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
6.448 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
6.448 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
6.448 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
6.448 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
6.448 * [taylor]: Taking taylor expansion of 1.0 in n
6.448 * [backup-simplify]: Simplify 1.0 into 1.0
6.448 * [taylor]: Taking taylor expansion of (log n) in n
6.448 * [taylor]: Taking taylor expansion of n in n
6.448 * [backup-simplify]: Simplify 0 into 0
6.448 * [backup-simplify]: Simplify 1 into 1
6.448 * [backup-simplify]: Simplify (log 1) into 0
6.449 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
6.449 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
6.449 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
6.450 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
6.451 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)
6.452 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))
6.453 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))
6.455 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
6.455 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n
6.455 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
6.456 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
6.456 * [taylor]: Taking taylor expansion of 2.0 in n
6.456 * [backup-simplify]: Simplify 2.0 into 2.0
6.456 * [taylor]: Taking taylor expansion of (* n PI) in n
6.457 * [taylor]: Taking taylor expansion of n in n
6.457 * [backup-simplify]: Simplify 0 into 0
6.457 * [backup-simplify]: Simplify 1 into 1
6.457 * [taylor]: Taking taylor expansion of PI in n
6.457 * [backup-simplify]: Simplify PI into PI
6.457 * [backup-simplify]: Simplify (* 0 PI) into 0
6.458 * [backup-simplify]: Simplify (* 2.0 0) into 0
6.459 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.461 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
6.462 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.464 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
6.465 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))
6.467 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
6.470 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))
6.473 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
6.475 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
6.476 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
6.478 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2)
6.481 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))
6.484 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
6.487 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))
6.498 * [backup-simplify]: Simplify (+ (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))))))))))))
6.515 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))
6.532 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))
6.552 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))
6.569 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))
6.597 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))))))))))))
6.598 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))))
6.598 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0
6.598 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n
6.598 * [taylor]: Taking taylor expansion of 1.0 in n
6.598 * [backup-simplify]: Simplify 1.0 into 1.0
6.598 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
6.598 * [taylor]: Taking taylor expansion of (sqrt k) in n
6.598 * [taylor]: Taking taylor expansion of k in n
6.598 * [backup-simplify]: Simplify k into k
6.598 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
6.598 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
6.598 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
6.598 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
6.598 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
6.598 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
6.599 * [taylor]: Taking taylor expansion of 0.5 in n
6.599 * [backup-simplify]: Simplify 0.5 into 0.5
6.599 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
6.599 * [taylor]: Taking taylor expansion of 1.0 in n
6.599 * [backup-simplify]: Simplify 1.0 into 1.0
6.599 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.599 * [taylor]: Taking taylor expansion of k in n
6.599 * [backup-simplify]: Simplify k into k
6.599 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.599 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
6.599 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
6.599 * [taylor]: Taking taylor expansion of 2.0 in n
6.599 * [backup-simplify]: Simplify 2.0 into 2.0
6.599 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.599 * [taylor]: Taking taylor expansion of PI in n
6.599 * [backup-simplify]: Simplify PI into PI
6.599 * [taylor]: Taking taylor expansion of n in n
6.599 * [backup-simplify]: Simplify 0 into 0
6.599 * [backup-simplify]: Simplify 1 into 1
6.600 * [backup-simplify]: Simplify (/ PI 1) into PI
6.600 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
6.606 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.606 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.607 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
6.607 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
6.608 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
6.610 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
6.611 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
6.611 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
6.611 * [taylor]: Taking taylor expansion of 1.0 in k
6.611 * [backup-simplify]: Simplify 1.0 into 1.0
6.611 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
6.611 * [taylor]: Taking taylor expansion of (sqrt k) in k
6.611 * [taylor]: Taking taylor expansion of k in k
6.611 * [backup-simplify]: Simplify 0 into 0
6.611 * [backup-simplify]: Simplify 1 into 1
6.612 * [backup-simplify]: Simplify (sqrt 0) into 0
6.613 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.613 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
6.613 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
6.613 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
6.613 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
6.614 * [taylor]: Taking taylor expansion of 0.5 in k
6.614 * [backup-simplify]: Simplify 0.5 into 0.5
6.614 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
6.614 * [taylor]: Taking taylor expansion of 1.0 in k
6.614 * [backup-simplify]: Simplify 1.0 into 1.0
6.614 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.614 * [taylor]: Taking taylor expansion of k in k
6.614 * [backup-simplify]: Simplify 0 into 0
6.614 * [backup-simplify]: Simplify 1 into 1
6.614 * [backup-simplify]: Simplify (/ 1 1) into 1
6.614 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
6.614 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
6.614 * [taylor]: Taking taylor expansion of 2.0 in k
6.614 * [backup-simplify]: Simplify 2.0 into 2.0
6.614 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.614 * [taylor]: Taking taylor expansion of PI in k
6.614 * [backup-simplify]: Simplify PI into PI
6.615 * [taylor]: Taking taylor expansion of n in k
6.615 * [backup-simplify]: Simplify n into n
6.615 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.615 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
6.615 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
6.615 * [backup-simplify]: Simplify (- 1) into -1
6.616 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.616 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
6.616 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
6.616 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
6.617 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
6.617 * [taylor]: Taking taylor expansion of 1.0 in k
6.617 * [backup-simplify]: Simplify 1.0 into 1.0
6.617 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
6.617 * [taylor]: Taking taylor expansion of (sqrt k) in k
6.617 * [taylor]: Taking taylor expansion of k in k
6.617 * [backup-simplify]: Simplify 0 into 0
6.617 * [backup-simplify]: Simplify 1 into 1
6.617 * [backup-simplify]: Simplify (sqrt 0) into 0
6.619 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.619 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
6.619 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
6.619 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
6.619 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
6.619 * [taylor]: Taking taylor expansion of 0.5 in k
6.619 * [backup-simplify]: Simplify 0.5 into 0.5
6.619 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
6.619 * [taylor]: Taking taylor expansion of 1.0 in k
6.619 * [backup-simplify]: Simplify 1.0 into 1.0
6.619 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.619 * [taylor]: Taking taylor expansion of k in k
6.619 * [backup-simplify]: Simplify 0 into 0
6.619 * [backup-simplify]: Simplify 1 into 1
6.619 * [backup-simplify]: Simplify (/ 1 1) into 1
6.620 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
6.620 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
6.620 * [taylor]: Taking taylor expansion of 2.0 in k
6.620 * [backup-simplify]: Simplify 2.0 into 2.0
6.620 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.620 * [taylor]: Taking taylor expansion of PI in k
6.620 * [backup-simplify]: Simplify PI into PI
6.620 * [taylor]: Taking taylor expansion of n in k
6.620 * [backup-simplify]: Simplify n into n
6.620 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.620 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
6.620 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
6.620 * [backup-simplify]: Simplify (- 1) into -1
6.621 * [backup-simplify]: Simplify (+ 0 -1) into -1
6.621 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
6.622 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
6.622 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
6.622 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0
6.623 * [backup-simplify]: Simplify (* 1.0 0) into 0
6.623 * [taylor]: Taking taylor expansion of 0 in n
6.623 * [backup-simplify]: Simplify 0 into 0
6.623 * [backup-simplify]: Simplify 0 into 0
6.624 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))
6.625 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))
6.625 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
6.625 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
6.625 * [taylor]: Taking taylor expansion of +nan.0 in n
6.625 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.625 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
6.625 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
6.625 * [taylor]: Taking taylor expansion of 0.5 in n
6.625 * [backup-simplify]: Simplify 0.5 into 0.5
6.625 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
6.625 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
6.625 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
6.625 * [taylor]: Taking taylor expansion of 2.0 in n
6.625 * [backup-simplify]: Simplify 2.0 into 2.0
6.625 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.625 * [taylor]: Taking taylor expansion of PI in n
6.625 * [backup-simplify]: Simplify PI into PI
6.625 * [taylor]: Taking taylor expansion of n in n
6.625 * [backup-simplify]: Simplify 0 into 0
6.625 * [backup-simplify]: Simplify 1 into 1
6.626 * [backup-simplify]: Simplify (/ PI 1) into PI
6.626 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
6.628 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.628 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
6.628 * [taylor]: Taking taylor expansion of 1.0 in n
6.628 * [backup-simplify]: Simplify 1.0 into 1.0
6.628 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.628 * [taylor]: Taking taylor expansion of k in n
6.628 * [backup-simplify]: Simplify k into k
6.628 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.629 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
6.629 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.630 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
6.631 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
6.632 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
6.633 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
6.634 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
6.636 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
6.637 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
6.638 * [backup-simplify]: Simplify 0 into 0
6.641 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.642 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))
6.643 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))
6.643 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
6.643 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
6.643 * [taylor]: Taking taylor expansion of +nan.0 in n
6.643 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.643 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
6.643 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
6.643 * [taylor]: Taking taylor expansion of 0.5 in n
6.643 * [backup-simplify]: Simplify 0.5 into 0.5
6.643 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
6.643 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
6.644 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
6.644 * [taylor]: Taking taylor expansion of 2.0 in n
6.644 * [backup-simplify]: Simplify 2.0 into 2.0
6.644 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.644 * [taylor]: Taking taylor expansion of PI in n
6.644 * [backup-simplify]: Simplify PI into PI
6.644 * [taylor]: Taking taylor expansion of n in n
6.644 * [backup-simplify]: Simplify 0 into 0
6.644 * [backup-simplify]: Simplify 1 into 1
6.644 * [backup-simplify]: Simplify (/ PI 1) into PI
6.645 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
6.646 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.646 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
6.646 * [taylor]: Taking taylor expansion of 1.0 in n
6.646 * [backup-simplify]: Simplify 1.0 into 1.0
6.646 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.646 * [taylor]: Taking taylor expansion of k in n
6.646 * [backup-simplify]: Simplify k into k
6.646 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.648 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
6.648 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.648 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
6.649 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
6.651 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
6.652 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
6.653 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
6.655 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
6.656 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
6.658 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
6.658 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.659 * [backup-simplify]: Simplify (- 0) into 0
6.659 * [backup-simplify]: Simplify (+ 0 0) into 0
6.660 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.661 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
6.663 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
6.665 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0
6.666 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0
6.669 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
6.670 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0
6.671 * [backup-simplify]: Simplify (- 0) into 0
6.671 * [backup-simplify]: Simplify 0 into 0
6.671 * [backup-simplify]: Simplify 0 into 0
6.675 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.676 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))
6.677 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))
6.678 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
6.678 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
6.678 * [taylor]: Taking taylor expansion of +nan.0 in n
6.678 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.678 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
6.678 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
6.678 * [taylor]: Taking taylor expansion of 0.5 in n
6.678 * [backup-simplify]: Simplify 0.5 into 0.5
6.678 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
6.678 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
6.678 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
6.678 * [taylor]: Taking taylor expansion of 2.0 in n
6.678 * [backup-simplify]: Simplify 2.0 into 2.0
6.678 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.678 * [taylor]: Taking taylor expansion of PI in n
6.678 * [backup-simplify]: Simplify PI into PI
6.678 * [taylor]: Taking taylor expansion of n in n
6.678 * [backup-simplify]: Simplify 0 into 0
6.678 * [backup-simplify]: Simplify 1 into 1
6.678 * [backup-simplify]: Simplify (/ PI 1) into PI
6.679 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
6.680 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.680 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
6.680 * [taylor]: Taking taylor expansion of 1.0 in n
6.680 * [backup-simplify]: Simplify 1.0 into 1.0
6.680 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.680 * [taylor]: Taking taylor expansion of k in n
6.680 * [backup-simplify]: Simplify k into k
6.680 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.682 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
6.682 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
6.682 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
6.684 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
6.685 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
6.686 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
6.687 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
6.689 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
6.690 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
6.695 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2))))))))
6.696 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))))
6.696 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0
6.696 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
6.696 * [taylor]: Taking taylor expansion of 1.0 in n
6.696 * [backup-simplify]: Simplify 1.0 into 1.0
6.696 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
6.697 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
6.697 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
6.697 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
6.697 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
6.697 * [taylor]: Taking taylor expansion of 0.5 in n
6.697 * [backup-simplify]: Simplify 0.5 into 0.5
6.697 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
6.697 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.697 * [taylor]: Taking taylor expansion of k in n
6.697 * [backup-simplify]: Simplify k into k
6.697 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.697 * [taylor]: Taking taylor expansion of 1.0 in n
6.697 * [backup-simplify]: Simplify 1.0 into 1.0
6.697 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
6.697 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
6.697 * [taylor]: Taking taylor expansion of -2.0 in n
6.697 * [backup-simplify]: Simplify -2.0 into -2.0
6.697 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.697 * [taylor]: Taking taylor expansion of PI in n
6.697 * [backup-simplify]: Simplify PI into PI
6.697 * [taylor]: Taking taylor expansion of n in n
6.697 * [backup-simplify]: Simplify 0 into 0
6.697 * [backup-simplify]: Simplify 1 into 1
6.698 * [backup-simplify]: Simplify (/ PI 1) into PI
6.698 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
6.699 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
6.699 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
6.699 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
6.701 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.702 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
6.703 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
6.703 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
6.703 * [taylor]: Taking taylor expansion of (/ -1 k) in n
6.703 * [taylor]: Taking taylor expansion of -1 in n
6.704 * [backup-simplify]: Simplify -1 into -1
6.704 * [taylor]: Taking taylor expansion of k in n
6.704 * [backup-simplify]: Simplify k into k
6.704 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
6.704 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
6.704 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
6.704 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
6.705 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))
6.705 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
6.705 * [taylor]: Taking taylor expansion of 1.0 in k
6.706 * [backup-simplify]: Simplify 1.0 into 1.0
6.706 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
6.706 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
6.706 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
6.706 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
6.706 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
6.706 * [taylor]: Taking taylor expansion of 0.5 in k
6.706 * [backup-simplify]: Simplify 0.5 into 0.5
6.706 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
6.706 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.706 * [taylor]: Taking taylor expansion of k in k
6.706 * [backup-simplify]: Simplify 0 into 0
6.706 * [backup-simplify]: Simplify 1 into 1
6.706 * [backup-simplify]: Simplify (/ 1 1) into 1
6.706 * [taylor]: Taking taylor expansion of 1.0 in k
6.706 * [backup-simplify]: Simplify 1.0 into 1.0
6.706 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
6.706 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
6.706 * [taylor]: Taking taylor expansion of -2.0 in k
6.707 * [backup-simplify]: Simplify -2.0 into -2.0
6.707 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.707 * [taylor]: Taking taylor expansion of PI in k
6.707 * [backup-simplify]: Simplify PI into PI
6.707 * [taylor]: Taking taylor expansion of n in k
6.707 * [backup-simplify]: Simplify n into n
6.707 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.707 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
6.707 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
6.708 * [backup-simplify]: Simplify (+ 1 0) into 1
6.708 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
6.708 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
6.708 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
6.708 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
6.708 * [taylor]: Taking taylor expansion of (/ -1 k) in k
6.709 * [taylor]: Taking taylor expansion of -1 in k
6.709 * [backup-simplify]: Simplify -1 into -1
6.709 * [taylor]: Taking taylor expansion of k in k
6.709 * [backup-simplify]: Simplify 0 into 0
6.709 * [backup-simplify]: Simplify 1 into 1
6.709 * [backup-simplify]: Simplify (/ -1 1) into -1
6.709 * [backup-simplify]: Simplify (sqrt 0) into 0
6.711 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
6.711 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))
6.711 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
6.711 * [taylor]: Taking taylor expansion of 1.0 in k
6.711 * [backup-simplify]: Simplify 1.0 into 1.0
6.711 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
6.711 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
6.711 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
6.712 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
6.712 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
6.712 * [taylor]: Taking taylor expansion of 0.5 in k
6.712 * [backup-simplify]: Simplify 0.5 into 0.5
6.712 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
6.712 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.712 * [taylor]: Taking taylor expansion of k in k
6.712 * [backup-simplify]: Simplify 0 into 0
6.712 * [backup-simplify]: Simplify 1 into 1
6.712 * [backup-simplify]: Simplify (/ 1 1) into 1
6.712 * [taylor]: Taking taylor expansion of 1.0 in k
6.712 * [backup-simplify]: Simplify 1.0 into 1.0
6.712 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
6.712 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
6.712 * [taylor]: Taking taylor expansion of -2.0 in k
6.712 * [backup-simplify]: Simplify -2.0 into -2.0
6.712 * [taylor]: Taking taylor expansion of (/ PI n) in k
6.712 * [taylor]: Taking taylor expansion of PI in k
6.712 * [backup-simplify]: Simplify PI into PI
6.712 * [taylor]: Taking taylor expansion of n in k
6.713 * [backup-simplify]: Simplify n into n
6.713 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
6.713 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
6.713 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
6.713 * [backup-simplify]: Simplify (+ 1 0) into 1
6.714 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
6.714 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
6.714 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
6.714 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
6.714 * [taylor]: Taking taylor expansion of (/ -1 k) in k
6.714 * [taylor]: Taking taylor expansion of -1 in k
6.714 * [backup-simplify]: Simplify -1 into -1
6.714 * [taylor]: Taking taylor expansion of k in k
6.714 * [backup-simplify]: Simplify 0 into 0
6.714 * [backup-simplify]: Simplify 1 into 1
6.715 * [backup-simplify]: Simplify (/ -1 1) into -1
6.715 * [backup-simplify]: Simplify (sqrt 0) into 0
6.717 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
6.717 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))
6.717 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))
6.717 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
6.717 * [taylor]: Taking taylor expansion of +nan.0 in n
6.717 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.717 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
6.718 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
6.718 * [taylor]: Taking taylor expansion of 0.5 in n
6.718 * [backup-simplify]: Simplify 0.5 into 0.5
6.718 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
6.718 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
6.718 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.718 * [taylor]: Taking taylor expansion of k in n
6.718 * [backup-simplify]: Simplify k into k
6.718 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.718 * [taylor]: Taking taylor expansion of 1.0 in n
6.718 * [backup-simplify]: Simplify 1.0 into 1.0
6.718 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
6.718 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
6.718 * [taylor]: Taking taylor expansion of -2.0 in n
6.718 * [backup-simplify]: Simplify -2.0 into -2.0
6.718 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.718 * [taylor]: Taking taylor expansion of PI in n
6.718 * [backup-simplify]: Simplify PI into PI
6.718 * [taylor]: Taking taylor expansion of n in n
6.718 * [backup-simplify]: Simplify 0 into 0
6.718 * [backup-simplify]: Simplify 1 into 1
6.719 * [backup-simplify]: Simplify (/ PI 1) into PI
6.719 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
6.720 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
6.720 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
6.722 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.723 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
6.724 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
6.725 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
6.727 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
6.728 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
6.729 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
6.732 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
6.733 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))
6.734 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))
6.734 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
6.734 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
6.734 * [taylor]: Taking taylor expansion of +nan.0 in n
6.734 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.734 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
6.734 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
6.734 * [taylor]: Taking taylor expansion of 0.5 in n
6.734 * [backup-simplify]: Simplify 0.5 into 0.5
6.734 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
6.734 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
6.734 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.734 * [taylor]: Taking taylor expansion of k in n
6.735 * [backup-simplify]: Simplify k into k
6.735 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.735 * [taylor]: Taking taylor expansion of 1.0 in n
6.735 * [backup-simplify]: Simplify 1.0 into 1.0
6.735 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
6.735 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
6.735 * [taylor]: Taking taylor expansion of -2.0 in n
6.735 * [backup-simplify]: Simplify -2.0 into -2.0
6.735 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.735 * [taylor]: Taking taylor expansion of PI in n
6.735 * [backup-simplify]: Simplify PI into PI
6.735 * [taylor]: Taking taylor expansion of n in n
6.735 * [backup-simplify]: Simplify 0 into 0
6.735 * [backup-simplify]: Simplify 1 into 1
6.736 * [backup-simplify]: Simplify (/ PI 1) into PI
6.736 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
6.737 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
6.737 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
6.739 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.740 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
6.741 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
6.743 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
6.744 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
6.745 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
6.747 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
6.748 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.749 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
6.751 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
6.751 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.751 * [backup-simplify]: Simplify (+ 0 0) into 0
6.753 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.754 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
6.756 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0
6.758 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
6.760 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0
6.760 * [backup-simplify]: Simplify 0 into 0
6.761 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.769 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
6.772 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))
6.773 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))
6.773 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
6.773 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
6.773 * [taylor]: Taking taylor expansion of +nan.0 in n
6.773 * [backup-simplify]: Simplify +nan.0 into +nan.0
6.773 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
6.773 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
6.773 * [taylor]: Taking taylor expansion of 0.5 in n
6.773 * [backup-simplify]: Simplify 0.5 into 0.5
6.773 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
6.773 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
6.773 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.773 * [taylor]: Taking taylor expansion of k in n
6.773 * [backup-simplify]: Simplify k into k
6.773 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.773 * [taylor]: Taking taylor expansion of 1.0 in n
6.774 * [backup-simplify]: Simplify 1.0 into 1.0
6.774 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
6.774 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
6.774 * [taylor]: Taking taylor expansion of -2.0 in n
6.774 * [backup-simplify]: Simplify -2.0 into -2.0
6.774 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.774 * [taylor]: Taking taylor expansion of PI in n
6.774 * [backup-simplify]: Simplify PI into PI
6.774 * [taylor]: Taking taylor expansion of n in n
6.774 * [backup-simplify]: Simplify 0 into 0
6.774 * [backup-simplify]: Simplify 1 into 1
6.774 * [backup-simplify]: Simplify (/ PI 1) into PI
6.775 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
6.776 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
6.776 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
6.778 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
6.779 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
6.781 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
6.782 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
6.783 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
6.785 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
6.786 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
6.792 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))))))
6.792 * * * [progress]: simplifying candidates
6.798 * [simplify]: Simplifying:
  (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (pow (* (* 2.0 PI) n) (/ 1.0 2.0))
  (pow (* (* 2.0 PI) n) (/ k 2.0))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) 1)
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (- (log 1.0) (log (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (- 1.0)
  (- (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt 1.0) (cbrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt 1.0) (sqrt (cbrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))
  (/ (cbrt 1.0) (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) 1)
  (/ (cbrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1.0) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt 1.0) (sqrt (cbrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt 1))
  (/ (sqrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) 1)
  (/ (sqrt 1.0) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1.0 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 1)
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1.0)
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1.0 (sqrt 1))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1.0 1)
  (/ (sqrt k) (cbrt 1.0))
  (/ (sqrt k) (sqrt 1.0))
  (/ (sqrt k) 1.0)
  (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
  (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ 1.0 (sqrt k)) 1)
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
  (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
  (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0)))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
  (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))))))
6.807 * * [simplify]: iteration 0: 361 enodes
7.029 * * [simplify]: iteration 1: 997 enodes
7.876 * * [simplify]: iteration 2: 3294 enodes
9.681 * * [simplify]: iteration complete: 5001 enodes
9.681 * * [simplify]: Extracting #0: cost 117 inf + 0
9.683 * * [simplify]: Extracting #1: cost 594 inf + 43
9.689 * * [simplify]: Extracting #2: cost 1027 inf + 5201
9.705 * * [simplify]: Extracting #3: cost 1245 inf + 33021
9.763 * * [simplify]: Extracting #4: cost 832 inf + 185468
9.860 * * [simplify]: Extracting #5: cost 526 inf + 362164
10.000 * * [simplify]: Extracting #6: cost 391 inf + 508480
10.185 * * [simplify]: Extracting #7: cost 122 inf + 725100
10.395 * * [simplify]: Extracting #8: cost 24 inf + 804532
10.620 * * [simplify]: Extracting #9: cost 2 inf + 833702
10.841 * * [simplify]: Extracting #10: cost 0 inf + 833798
11.064 * [simplify]: Simplified to:
  (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0))))
  (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0))))
  (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0))))
  (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0))))
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (pow (* n (* PI 2.0)) (/ 1.0 2.0))
  (pow (* n (* PI 2.0)) (/ k 2.0))
  (pow (* n (* PI 2.0)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* n (* PI 2.0)) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* n (* PI 2.0)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0))))
  (pow (* n (* PI 2.0)) (* (/ (cbrt (- 1.0 k)) (sqrt 2.0)) (cbrt (- 1.0 k))))
  (pow (* n (* PI 2.0)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* n (* PI 2.0)) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* n (* PI 2.0)) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* n (* PI 2.0)) (sqrt (- 1.0 k)))
  (pow (* n (* PI 2.0)) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* n (* PI 2.0)) (/ 1 (sqrt 2.0)))
  (* n (* PI 2.0))
  (pow (* n (* PI 2.0)) (/ (/ (+ (sqrt k) (sqrt 1.0)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* n (* PI 2.0)) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0)))
  (pow (* n (* PI 2.0)) (+ (sqrt k) (sqrt 1.0)))
  (pow (* n (* PI 2.0)) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* n (* PI 2.0)) (/ 1 (sqrt 2.0)))
  (* n (* PI 2.0))
  (* n (* PI 2.0))
  (pow (* n (* PI 2.0)) (- 1.0 k))
  (pow (* PI 2.0) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0))))
  (exp (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))
  (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2.0) 2))
  (* n (* PI 2.0))
  (* n (* PI 2.0))
  (log (* n (* PI 2.0)))
  (log (* n (* PI 2.0)))
  (log (* n (* PI 2.0)))
  (exp (* n (* PI 2.0)))
  (* (* n (* PI 2.0)) (* (* n (* PI 2.0)) (* n (* PI 2.0))))
  (* (* n (* PI 2.0)) (* (* n (* PI 2.0)) (* n (* PI 2.0))))
  (* (cbrt (* n (* PI 2.0))) (cbrt (* n (* PI 2.0))))
  (cbrt (* n (* PI 2.0)))
  (* (* n (* PI 2.0)) (* (* n (* PI 2.0)) (* n (* PI 2.0))))
  (sqrt (* n (* PI 2.0)))
  (sqrt (* n (* PI 2.0)))
  (* (* (cbrt n) (cbrt n)) (* PI 2.0))
  (* 2.0 (* (sqrt n) PI))
  (* PI 2.0)
  (* n PI)
  (log (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (/ (* (/ (* 1.0 1.0) k) 1.0) (sqrt k))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (/ (* (/ (* 1.0 1.0) k) 1.0) (sqrt k))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (- 1.0)
  (- (sqrt k))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k))))
  (/ (cbrt 1.0) (cbrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k)))
  (/ (cbrt 1.0) (sqrt (cbrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (fabs (cbrt k)))
  (/ (sqrt 1.0) (sqrt (cbrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt k))
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ 1.0 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1.0 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1.0)
  (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ 1.0 (fabs (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1.0
  (/ 1.0 (sqrt (sqrt k)))
  1.0
  (/ (sqrt k) (cbrt 1.0))
  (/ (sqrt k) (sqrt 1.0))
  (/ (sqrt k) 1.0)
  (+ (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (log (/ 1.0 (sqrt k))))
  (+ (* (/ (- 1.0 k) 2.0) (log (* n (* PI 2.0)))) (log (/ 1.0 (sqrt k))))
  (exp (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))
  (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (* (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))))))
  (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (* (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))))))
  (* (cbrt (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))) (cbrt (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))))
  (cbrt (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))
  (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (* (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))) (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))))))
  (sqrt (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))
  (sqrt (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k))))
  (* (pow (* n (* PI 2.0)) (/ 1.0 2.0)) 1.0)
  (* (pow (* n (* PI 2.0)) (/ k 2.0)) (sqrt k))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))))
  (* (sqrt (/ 1.0 (sqrt k))) (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (sqrt (/ 1.0 (sqrt k))) (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (* (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2.0) 2))))
  (* (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (* (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2.0) 2))))
  (* (pow (* PI 2.0) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))
  (/ (* 1.0 (* (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))))) (sqrt k))
  (* (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (/ 1.0 (sqrt k)))
  (/ 1.0 (sqrt k))
  (/ (* 1.0 (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt k))
  (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (cbrt (/ 1.0 (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt k))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))
  (/ (cbrt 1.0) (/ (cbrt (sqrt k)) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))))
  (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))
  (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt k)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))
  (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (sqrt k)))
  (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (cbrt (sqrt k))))
  (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (cbrt k))))
  (/ (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (sqrt k))
  (/ (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (sqrt k)))
  (/ (* (sqrt 1.0) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (sqrt k))
  (/ 1.0 (/ (cbrt (sqrt k)) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (cbrt k)) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))))
  (/ (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt (sqrt k)))
  (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))
  (/ (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) 1.0) (sqrt (sqrt k)))
  (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))
  (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (/ 1.0 (sqrt k)))
  (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (* (pow (* n (* PI 2.0)) (/ 1.0 2.0)) (/ 1.0 (sqrt k)))
  (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) 1.0)
  (+ (+ (* (* (* (* k k) 0.125) (exp (* (log (* n (* PI 2.0))) 0.5))) (* (log (* PI 2.0)) (log (* PI 2.0)))) (* (* (* (* k k) 0.125) (exp (* (log (* n (* PI 2.0))) 0.5))) (* (log n) (log n)))) (- (+ (exp (* (log (* n (* PI 2.0))) 0.5)) (* (* 0.25 (* (* (log (* PI 2.0)) (log n)) (exp (* (log (* n (* PI 2.0))) 0.5)))) (* k k))) (* 0.5 (* k (+ (* (exp (* (log (* n (* PI 2.0))) 0.5)) (log (* PI 2.0))) (* (exp (* (log (* n (* PI 2.0))) 0.5)) (log n)))))))
  (exp (* (log (* n (* PI 2.0))) (* 0.5 (- 1.0 k))))
  (exp (* (* 0.5 (- (log (* -2.0 PI)) (log (/ -1 n)))) (- 1.0 k)))
  (* n (* PI 2.0))
  (* n (* PI 2.0))
  (* n (* PI 2.0))
  (+ (* +nan.0 (- k)) (- (* (* k k) +nan.0) +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 (* (* k (log (* PI 2.0))) (* k (log (* PI 2.0)))))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)) (- (* (* +nan.0 (* k k)) (* (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) (log (* PI 2.0)))) (+ (- (* (* +nan.0 (* k k)) (* (* (log (* PI 2.0)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (* (* (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) (* (* k k) (log n))) +nan.0)) (- (* (* +nan.0 k) (* (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) (log (* PI 2.0)))) (+ (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) (* (* k (log n)) (* k (log n))))) (* +nan.0 (* (* k (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)) (- (* (* (* k k) +nan.0) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)) (* (* k +nan.0) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)))))))))
  (- (* (- +nan.0) (/ (exp (* (log (* n (* PI 2.0))) (* 0.5 (- 1.0 k)))) (* k (* k k)))) (- (/ (* (- +nan.0) (exp (* (log (* n (* PI 2.0))) (* 0.5 (- 1.0 k))))) k) (/ (* (- +nan.0) (exp (* (log (* n (* PI 2.0))) (* 0.5 (- 1.0 k))))) (* k k))))
  (+ (* (- +nan.0) (/ (exp (* (* 0.5 (- (log (* -2.0 PI)) (log (/ -1 n)))) (- 1.0 k))) k)) (- (* (/ +nan.0 k) (/ (exp (* (* 0.5 (- (log (* -2.0 PI)) (log (/ -1 n)))) (- 1.0 k))) k)) (* (exp (* (* 0.5 (- (log (* -2.0 PI)) (log (/ -1 n)))) (- 1.0 k))) +nan.0)))
11.085 * * * [progress]: adding candidates to table
12.373 * * [progress]: iteration 2 / 4
12.373 * * * [progress]: picking best candidate
12.493 * * * * [pick]: Picked  #<alt (λ (k n) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))>
12.493 * * * [progress]: localizing error
12.536 * * * [progress]: generating rewritten candidates
12.537 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1 2)
12.589 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 2 1)
12.625 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
12.677 * * * [progress]: generating series expansions
12.677 * * * * [progress]: [ 1 / 3 ] generating series at (2 1 2)
12.678 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
12.678 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
12.678 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
12.678 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
12.678 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
12.678 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
12.678 * [taylor]: Taking taylor expansion of 0.5 in k
12.678 * [backup-simplify]: Simplify 0.5 into 0.5
12.678 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
12.678 * [taylor]: Taking taylor expansion of 1.0 in k
12.678 * [backup-simplify]: Simplify 1.0 into 1.0
12.678 * [taylor]: Taking taylor expansion of k in k
12.678 * [backup-simplify]: Simplify 0 into 0
12.678 * [backup-simplify]: Simplify 1 into 1
12.678 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
12.678 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
12.678 * [taylor]: Taking taylor expansion of 2.0 in k
12.678 * [backup-simplify]: Simplify 2.0 into 2.0
12.678 * [taylor]: Taking taylor expansion of (* n PI) in k
12.678 * [taylor]: Taking taylor expansion of n in k
12.678 * [backup-simplify]: Simplify n into n
12.678 * [taylor]: Taking taylor expansion of PI in k
12.678 * [backup-simplify]: Simplify PI into PI
12.679 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.679 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
12.679 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
12.679 * [backup-simplify]: Simplify (- 0) into 0
12.680 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
12.680 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
12.680 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
12.680 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
12.680 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
12.680 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
12.680 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
12.681 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
12.681 * [taylor]: Taking taylor expansion of 0.5 in n
12.681 * [backup-simplify]: Simplify 0.5 into 0.5
12.681 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
12.681 * [taylor]: Taking taylor expansion of 1.0 in n
12.681 * [backup-simplify]: Simplify 1.0 into 1.0
12.681 * [taylor]: Taking taylor expansion of k in n
12.681 * [backup-simplify]: Simplify k into k
12.681 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
12.681 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
12.681 * [taylor]: Taking taylor expansion of 2.0 in n
12.681 * [backup-simplify]: Simplify 2.0 into 2.0
12.681 * [taylor]: Taking taylor expansion of (* n PI) in n
12.681 * [taylor]: Taking taylor expansion of n in n
12.681 * [backup-simplify]: Simplify 0 into 0
12.681 * [backup-simplify]: Simplify 1 into 1
12.681 * [taylor]: Taking taylor expansion of PI in n
12.681 * [backup-simplify]: Simplify PI into PI
12.681 * [backup-simplify]: Simplify (* 0 PI) into 0
12.682 * [backup-simplify]: Simplify (* 2.0 0) into 0
12.684 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.685 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
12.686 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.686 * [backup-simplify]: Simplify (- k) into (- k)
12.686 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
12.686 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
12.688 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.689 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
12.691 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
12.691 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
12.691 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
12.691 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
12.691 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
12.691 * [taylor]: Taking taylor expansion of 0.5 in n
12.691 * [backup-simplify]: Simplify 0.5 into 0.5
12.691 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
12.691 * [taylor]: Taking taylor expansion of 1.0 in n
12.691 * [backup-simplify]: Simplify 1.0 into 1.0
12.691 * [taylor]: Taking taylor expansion of k in n
12.691 * [backup-simplify]: Simplify k into k
12.691 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
12.691 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
12.691 * [taylor]: Taking taylor expansion of 2.0 in n
12.691 * [backup-simplify]: Simplify 2.0 into 2.0
12.691 * [taylor]: Taking taylor expansion of (* n PI) in n
12.691 * [taylor]: Taking taylor expansion of n in n
12.691 * [backup-simplify]: Simplify 0 into 0
12.691 * [backup-simplify]: Simplify 1 into 1
12.691 * [taylor]: Taking taylor expansion of PI in n
12.691 * [backup-simplify]: Simplify PI into PI
12.692 * [backup-simplify]: Simplify (* 0 PI) into 0
12.692 * [backup-simplify]: Simplify (* 2.0 0) into 0
12.699 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.701 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
12.702 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.702 * [backup-simplify]: Simplify (- k) into (- k)
12.702 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
12.702 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
12.704 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.705 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
12.706 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
12.706 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
12.706 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
12.706 * [taylor]: Taking taylor expansion of 0.5 in k
12.706 * [backup-simplify]: Simplify 0.5 into 0.5
12.706 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
12.706 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
12.706 * [taylor]: Taking taylor expansion of 1.0 in k
12.706 * [backup-simplify]: Simplify 1.0 into 1.0
12.706 * [taylor]: Taking taylor expansion of k in k
12.706 * [backup-simplify]: Simplify 0 into 0
12.706 * [backup-simplify]: Simplify 1 into 1
12.707 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
12.707 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
12.707 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
12.707 * [taylor]: Taking taylor expansion of 2.0 in k
12.707 * [backup-simplify]: Simplify 2.0 into 2.0
12.707 * [taylor]: Taking taylor expansion of PI in k
12.707 * [backup-simplify]: Simplify PI into PI
12.707 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.708 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.708 * [taylor]: Taking taylor expansion of (log n) in k
12.708 * [taylor]: Taking taylor expansion of n in k
12.708 * [backup-simplify]: Simplify n into n
12.708 * [backup-simplify]: Simplify (log n) into (log n)
12.709 * [backup-simplify]: Simplify (- 0) into 0
12.709 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
12.710 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
12.712 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
12.713 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
12.714 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
12.716 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
12.717 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.718 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
12.720 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
12.720 * [backup-simplify]: Simplify (- 0) into 0
12.720 * [backup-simplify]: Simplify (+ 0 0) into 0
12.721 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
12.722 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.724 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
12.726 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.726 * [taylor]: Taking taylor expansion of 0 in k
12.726 * [backup-simplify]: Simplify 0 into 0
12.726 * [backup-simplify]: Simplify 0 into 0
12.727 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
12.729 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
12.729 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
12.730 * [backup-simplify]: Simplify (+ 0 0) into 0
12.730 * [backup-simplify]: Simplify (- 1) into -1
12.731 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.732 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
12.735 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
12.738 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
12.741 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
12.742 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.743 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.747 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
12.748 * [backup-simplify]: Simplify (- 0) into 0
12.748 * [backup-simplify]: Simplify (+ 0 0) into 0
12.749 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
12.750 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.752 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
12.754 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.754 * [taylor]: Taking taylor expansion of 0 in k
12.754 * [backup-simplify]: Simplify 0 into 0
12.754 * [backup-simplify]: Simplify 0 into 0
12.755 * [backup-simplify]: Simplify 0 into 0
12.756 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.759 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
12.761 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
12.762 * [backup-simplify]: Simplify (+ 0 0) into 0
12.762 * [backup-simplify]: Simplify (- 0) into 0
12.762 * [backup-simplify]: Simplify (+ 0 0) into 0
12.764 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
12.767 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
12.771 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
12.777 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
12.788 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
12.789 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))
12.789 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
12.789 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
12.789 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
12.789 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
12.789 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
12.789 * [taylor]: Taking taylor expansion of 0.5 in k
12.789 * [backup-simplify]: Simplify 0.5 into 0.5
12.789 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
12.789 * [taylor]: Taking taylor expansion of 1.0 in k
12.789 * [backup-simplify]: Simplify 1.0 into 1.0
12.789 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.789 * [taylor]: Taking taylor expansion of k in k
12.789 * [backup-simplify]: Simplify 0 into 0
12.789 * [backup-simplify]: Simplify 1 into 1
12.790 * [backup-simplify]: Simplify (/ 1 1) into 1
12.790 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
12.790 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
12.790 * [taylor]: Taking taylor expansion of 2.0 in k
12.790 * [backup-simplify]: Simplify 2.0 into 2.0
12.790 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.790 * [taylor]: Taking taylor expansion of PI in k
12.790 * [backup-simplify]: Simplify PI into PI
12.790 * [taylor]: Taking taylor expansion of n in k
12.790 * [backup-simplify]: Simplify n into n
12.790 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.790 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
12.790 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
12.791 * [backup-simplify]: Simplify (- 1) into -1
12.791 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.792 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
12.792 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
12.792 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
12.792 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
12.792 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
12.792 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
12.792 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
12.792 * [taylor]: Taking taylor expansion of 0.5 in n
12.792 * [backup-simplify]: Simplify 0.5 into 0.5
12.792 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
12.792 * [taylor]: Taking taylor expansion of 1.0 in n
12.792 * [backup-simplify]: Simplify 1.0 into 1.0
12.792 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.792 * [taylor]: Taking taylor expansion of k in n
12.792 * [backup-simplify]: Simplify k into k
12.793 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.793 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
12.793 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
12.793 * [taylor]: Taking taylor expansion of 2.0 in n
12.793 * [backup-simplify]: Simplify 2.0 into 2.0
12.793 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.793 * [taylor]: Taking taylor expansion of PI in n
12.793 * [backup-simplify]: Simplify PI into PI
12.793 * [taylor]: Taking taylor expansion of n in n
12.793 * [backup-simplify]: Simplify 0 into 0
12.793 * [backup-simplify]: Simplify 1 into 1
12.793 * [backup-simplify]: Simplify (/ PI 1) into PI
12.794 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.795 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.795 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.796 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
12.796 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
12.797 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.798 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
12.800 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
12.800 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
12.800 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
12.800 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
12.800 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
12.800 * [taylor]: Taking taylor expansion of 0.5 in n
12.800 * [backup-simplify]: Simplify 0.5 into 0.5
12.800 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
12.800 * [taylor]: Taking taylor expansion of 1.0 in n
12.800 * [backup-simplify]: Simplify 1.0 into 1.0
12.800 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.800 * [taylor]: Taking taylor expansion of k in n
12.800 * [backup-simplify]: Simplify k into k
12.800 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.800 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
12.800 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
12.800 * [taylor]: Taking taylor expansion of 2.0 in n
12.800 * [backup-simplify]: Simplify 2.0 into 2.0
12.800 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.800 * [taylor]: Taking taylor expansion of PI in n
12.801 * [backup-simplify]: Simplify PI into PI
12.801 * [taylor]: Taking taylor expansion of n in n
12.801 * [backup-simplify]: Simplify 0 into 0
12.801 * [backup-simplify]: Simplify 1 into 1
12.801 * [backup-simplify]: Simplify (/ PI 1) into PI
12.802 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.803 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.803 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.803 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
12.803 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
12.805 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.806 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
12.807 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
12.807 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
12.808 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
12.808 * [taylor]: Taking taylor expansion of 0.5 in k
12.808 * [backup-simplify]: Simplify 0.5 into 0.5
12.808 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
12.808 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
12.808 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
12.808 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
12.808 * [taylor]: Taking taylor expansion of 2.0 in k
12.808 * [backup-simplify]: Simplify 2.0 into 2.0
12.808 * [taylor]: Taking taylor expansion of PI in k
12.808 * [backup-simplify]: Simplify PI into PI
12.808 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.810 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.810 * [taylor]: Taking taylor expansion of (log n) in k
12.810 * [taylor]: Taking taylor expansion of n in k
12.810 * [backup-simplify]: Simplify n into n
12.810 * [backup-simplify]: Simplify (log n) into (log n)
12.810 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
12.810 * [taylor]: Taking taylor expansion of 1.0 in k
12.810 * [backup-simplify]: Simplify 1.0 into 1.0
12.810 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.810 * [taylor]: Taking taylor expansion of k in k
12.810 * [backup-simplify]: Simplify 0 into 0
12.810 * [backup-simplify]: Simplify 1 into 1
12.810 * [backup-simplify]: Simplify (/ 1 1) into 1
12.810 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.812 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
12.812 * [backup-simplify]: Simplify (- 1) into -1
12.813 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.814 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
12.815 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
12.816 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
12.818 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
12.819 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.820 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
12.822 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
12.822 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.822 * [backup-simplify]: Simplify (- 0) into 0
12.823 * [backup-simplify]: Simplify (+ 0 0) into 0
12.823 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
12.825 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.826 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
12.828 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.828 * [taylor]: Taking taylor expansion of 0 in k
12.828 * [backup-simplify]: Simplify 0 into 0
12.828 * [backup-simplify]: Simplify 0 into 0
12.828 * [backup-simplify]: Simplify 0 into 0
12.829 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.831 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.834 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
12.835 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.835 * [backup-simplify]: Simplify (- 0) into 0
12.835 * [backup-simplify]: Simplify (+ 0 0) into 0
12.836 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
12.838 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.839 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
12.842 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.842 * [taylor]: Taking taylor expansion of 0 in k
12.842 * [backup-simplify]: Simplify 0 into 0
12.842 * [backup-simplify]: Simplify 0 into 0
12.842 * [backup-simplify]: Simplify 0 into 0
12.842 * [backup-simplify]: Simplify 0 into 0
12.843 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.844 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.858 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
12.859 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.859 * [backup-simplify]: Simplify (- 0) into 0
12.860 * [backup-simplify]: Simplify (+ 0 0) into 0
12.861 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
12.863 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.864 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
12.868 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
12.868 * [taylor]: Taking taylor expansion of 0 in k
12.868 * [backup-simplify]: Simplify 0 into 0
12.868 * [backup-simplify]: Simplify 0 into 0
12.869 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
12.870 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))
12.870 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
12.870 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
12.870 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
12.870 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
12.870 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
12.871 * [taylor]: Taking taylor expansion of 0.5 in k
12.871 * [backup-simplify]: Simplify 0.5 into 0.5
12.871 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
12.871 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.871 * [taylor]: Taking taylor expansion of k in k
12.871 * [backup-simplify]: Simplify 0 into 0
12.871 * [backup-simplify]: Simplify 1 into 1
12.871 * [backup-simplify]: Simplify (/ 1 1) into 1
12.871 * [taylor]: Taking taylor expansion of 1.0 in k
12.871 * [backup-simplify]: Simplify 1.0 into 1.0
12.871 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
12.871 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
12.871 * [taylor]: Taking taylor expansion of -2.0 in k
12.871 * [backup-simplify]: Simplify -2.0 into -2.0
12.871 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.871 * [taylor]: Taking taylor expansion of PI in k
12.871 * [backup-simplify]: Simplify PI into PI
12.871 * [taylor]: Taking taylor expansion of n in k
12.871 * [backup-simplify]: Simplify n into n
12.872 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.872 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
12.872 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
12.872 * [backup-simplify]: Simplify (+ 1 0) into 1
12.873 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
12.873 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
12.873 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
12.873 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
12.873 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
12.873 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
12.873 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
12.873 * [taylor]: Taking taylor expansion of 0.5 in n
12.873 * [backup-simplify]: Simplify 0.5 into 0.5
12.873 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
12.873 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.873 * [taylor]: Taking taylor expansion of k in n
12.873 * [backup-simplify]: Simplify k into k
12.873 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.873 * [taylor]: Taking taylor expansion of 1.0 in n
12.874 * [backup-simplify]: Simplify 1.0 into 1.0
12.874 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
12.874 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
12.874 * [taylor]: Taking taylor expansion of -2.0 in n
12.874 * [backup-simplify]: Simplify -2.0 into -2.0
12.874 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.874 * [taylor]: Taking taylor expansion of PI in n
12.874 * [backup-simplify]: Simplify PI into PI
12.874 * [taylor]: Taking taylor expansion of n in n
12.874 * [backup-simplify]: Simplify 0 into 0
12.874 * [backup-simplify]: Simplify 1 into 1
12.874 * [backup-simplify]: Simplify (/ PI 1) into PI
12.875 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.876 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
12.876 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
12.876 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
12.878 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.879 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
12.880 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
12.880 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
12.880 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
12.880 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
12.880 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
12.880 * [taylor]: Taking taylor expansion of 0.5 in n
12.880 * [backup-simplify]: Simplify 0.5 into 0.5
12.880 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
12.880 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.880 * [taylor]: Taking taylor expansion of k in n
12.881 * [backup-simplify]: Simplify k into k
12.881 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.881 * [taylor]: Taking taylor expansion of 1.0 in n
12.881 * [backup-simplify]: Simplify 1.0 into 1.0
12.881 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
12.881 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
12.881 * [taylor]: Taking taylor expansion of -2.0 in n
12.881 * [backup-simplify]: Simplify -2.0 into -2.0
12.881 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.881 * [taylor]: Taking taylor expansion of PI in n
12.881 * [backup-simplify]: Simplify PI into PI
12.881 * [taylor]: Taking taylor expansion of n in n
12.881 * [backup-simplify]: Simplify 0 into 0
12.881 * [backup-simplify]: Simplify 1 into 1
12.881 * [backup-simplify]: Simplify (/ PI 1) into PI
12.882 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.883 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
12.883 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
12.883 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
12.885 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.886 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
12.887 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
12.888 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
12.888 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
12.888 * [taylor]: Taking taylor expansion of 0.5 in k
12.888 * [backup-simplify]: Simplify 0.5 into 0.5
12.888 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
12.888 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
12.888 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.888 * [taylor]: Taking taylor expansion of k in k
12.888 * [backup-simplify]: Simplify 0 into 0
12.888 * [backup-simplify]: Simplify 1 into 1
12.888 * [backup-simplify]: Simplify (/ 1 1) into 1
12.888 * [taylor]: Taking taylor expansion of 1.0 in k
12.888 * [backup-simplify]: Simplify 1.0 into 1.0
12.888 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
12.888 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
12.888 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
12.889 * [taylor]: Taking taylor expansion of -2.0 in k
12.889 * [backup-simplify]: Simplify -2.0 into -2.0
12.889 * [taylor]: Taking taylor expansion of PI in k
12.889 * [backup-simplify]: Simplify PI into PI
12.889 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.890 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
12.890 * [taylor]: Taking taylor expansion of (log n) in k
12.890 * [taylor]: Taking taylor expansion of n in k
12.890 * [backup-simplify]: Simplify n into n
12.890 * [backup-simplify]: Simplify (log n) into (log n)
12.891 * [backup-simplify]: Simplify (+ 1 0) into 1
12.891 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.892 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
12.893 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
12.894 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
12.896 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
12.897 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
12.898 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.899 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
12.901 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
12.901 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.902 * [backup-simplify]: Simplify (+ 0 0) into 0
12.902 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
12.904 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.905 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
12.907 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.907 * [taylor]: Taking taylor expansion of 0 in k
12.907 * [backup-simplify]: Simplify 0 into 0
12.907 * [backup-simplify]: Simplify 0 into 0
12.907 * [backup-simplify]: Simplify 0 into 0
12.909 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.910 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.913 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
12.914 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.914 * [backup-simplify]: Simplify (+ 0 0) into 0
12.915 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
12.917 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.918 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
12.921 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.921 * [taylor]: Taking taylor expansion of 0 in k
12.921 * [backup-simplify]: Simplify 0 into 0
12.921 * [backup-simplify]: Simplify 0 into 0
12.921 * [backup-simplify]: Simplify 0 into 0
12.921 * [backup-simplify]: Simplify 0 into 0
12.922 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.924 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.931 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0
12.931 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.931 * [backup-simplify]: Simplify (+ 0 0) into 0
12.933 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
12.934 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.936 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
12.939 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
12.939 * [taylor]: Taking taylor expansion of 0 in k
12.939 * [backup-simplify]: Simplify 0 into 0
12.939 * [backup-simplify]: Simplify 0 into 0
12.940 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
12.941 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 2 1)
12.941 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
12.941 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
12.941 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
12.941 * [taylor]: Taking taylor expansion of 2.0 in n
12.941 * [backup-simplify]: Simplify 2.0 into 2.0
12.941 * [taylor]: Taking taylor expansion of (* n PI) in n
12.941 * [taylor]: Taking taylor expansion of n in n
12.941 * [backup-simplify]: Simplify 0 into 0
12.941 * [backup-simplify]: Simplify 1 into 1
12.941 * [taylor]: Taking taylor expansion of PI in n
12.941 * [backup-simplify]: Simplify PI into PI
12.941 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
12.941 * [taylor]: Taking taylor expansion of 2.0 in n
12.941 * [backup-simplify]: Simplify 2.0 into 2.0
12.941 * [taylor]: Taking taylor expansion of (* n PI) in n
12.942 * [taylor]: Taking taylor expansion of n in n
12.942 * [backup-simplify]: Simplify 0 into 0
12.942 * [backup-simplify]: Simplify 1 into 1
12.942 * [taylor]: Taking taylor expansion of PI in n
12.942 * [backup-simplify]: Simplify PI into PI
12.942 * [backup-simplify]: Simplify (* 0 PI) into 0
12.942 * [backup-simplify]: Simplify (* 2.0 0) into 0
12.943 * [backup-simplify]: Simplify 0 into 0
12.944 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.946 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
12.946 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.948 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.949 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
12.949 * [backup-simplify]: Simplify 0 into 0
12.950 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.951 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.951 * [backup-simplify]: Simplify 0 into 0
12.953 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.954 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
12.954 * [backup-simplify]: Simplify 0 into 0
12.956 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.957 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
12.958 * [backup-simplify]: Simplify 0 into 0
12.959 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.961 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
12.961 * [backup-simplify]: Simplify 0 into 0
12.963 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
12.965 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
12.965 * [backup-simplify]: Simplify 0 into 0
12.966 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
12.966 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
12.967 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
12.967 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
12.967 * [taylor]: Taking taylor expansion of 2.0 in n
12.967 * [backup-simplify]: Simplify 2.0 into 2.0
12.967 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.967 * [taylor]: Taking taylor expansion of PI in n
12.967 * [backup-simplify]: Simplify PI into PI
12.967 * [taylor]: Taking taylor expansion of n in n
12.967 * [backup-simplify]: Simplify 0 into 0
12.967 * [backup-simplify]: Simplify 1 into 1
12.967 * [backup-simplify]: Simplify (/ PI 1) into PI
12.967 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
12.967 * [taylor]: Taking taylor expansion of 2.0 in n
12.967 * [backup-simplify]: Simplify 2.0 into 2.0
12.967 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.968 * [taylor]: Taking taylor expansion of PI in n
12.968 * [backup-simplify]: Simplify PI into PI
12.968 * [taylor]: Taking taylor expansion of n in n
12.968 * [backup-simplify]: Simplify 0 into 0
12.968 * [backup-simplify]: Simplify 1 into 1
12.968 * [backup-simplify]: Simplify (/ PI 1) into PI
12.969 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.969 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.970 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.971 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
12.971 * [backup-simplify]: Simplify 0 into 0
12.972 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.973 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.973 * [backup-simplify]: Simplify 0 into 0
12.974 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.976 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.976 * [backup-simplify]: Simplify 0 into 0
12.977 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.978 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.978 * [backup-simplify]: Simplify 0 into 0
12.980 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.981 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
12.981 * [backup-simplify]: Simplify 0 into 0
12.982 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.984 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
12.984 * [backup-simplify]: Simplify 0 into 0
12.985 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
12.986 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
12.986 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
12.986 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
12.986 * [taylor]: Taking taylor expansion of -2.0 in n
12.986 * [backup-simplify]: Simplify -2.0 into -2.0
12.986 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.986 * [taylor]: Taking taylor expansion of PI in n
12.986 * [backup-simplify]: Simplify PI into PI
12.986 * [taylor]: Taking taylor expansion of n in n
12.986 * [backup-simplify]: Simplify 0 into 0
12.986 * [backup-simplify]: Simplify 1 into 1
12.987 * [backup-simplify]: Simplify (/ PI 1) into PI
12.987 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
12.987 * [taylor]: Taking taylor expansion of -2.0 in n
12.987 * [backup-simplify]: Simplify -2.0 into -2.0
12.987 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.987 * [taylor]: Taking taylor expansion of PI in n
12.987 * [backup-simplify]: Simplify PI into PI
12.987 * [taylor]: Taking taylor expansion of n in n
12.987 * [backup-simplify]: Simplify 0 into 0
12.987 * [backup-simplify]: Simplify 1 into 1
12.987 * [backup-simplify]: Simplify (/ PI 1) into PI
12.988 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.988 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.989 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.990 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
12.990 * [backup-simplify]: Simplify 0 into 0
12.991 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.992 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.992 * [backup-simplify]: Simplify 0 into 0
12.994 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.995 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.995 * [backup-simplify]: Simplify 0 into 0
12.996 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.997 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.997 * [backup-simplify]: Simplify 0 into 0
12.998 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.000 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.000 * [backup-simplify]: Simplify 0 into 0
13.001 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.003 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.003 * [backup-simplify]: Simplify 0 into 0
13.004 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
13.004 * * * * [progress]: [ 3 / 3 ] generating series at (2)
13.005 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))))
13.005 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (n k) around 0
13.005 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
13.005 * [taylor]: Taking taylor expansion of 1.0 in k
13.005 * [backup-simplify]: Simplify 1.0 into 1.0
13.005 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
13.005 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
13.005 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
13.005 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
13.005 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
13.005 * [taylor]: Taking taylor expansion of 0.5 in k
13.005 * [backup-simplify]: Simplify 0.5 into 0.5
13.005 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
13.005 * [taylor]: Taking taylor expansion of 1.0 in k
13.005 * [backup-simplify]: Simplify 1.0 into 1.0
13.005 * [taylor]: Taking taylor expansion of k in k
13.005 * [backup-simplify]: Simplify 0 into 0
13.005 * [backup-simplify]: Simplify 1 into 1
13.005 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
13.005 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
13.005 * [taylor]: Taking taylor expansion of 2.0 in k
13.006 * [backup-simplify]: Simplify 2.0 into 2.0
13.006 * [taylor]: Taking taylor expansion of (* n PI) in k
13.006 * [taylor]: Taking taylor expansion of n in k
13.006 * [backup-simplify]: Simplify n into n
13.006 * [taylor]: Taking taylor expansion of PI in k
13.006 * [backup-simplify]: Simplify PI into PI
13.006 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.006 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
13.006 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
13.006 * [backup-simplify]: Simplify (- 0) into 0
13.007 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
13.007 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
13.007 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
13.008 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
13.008 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
13.008 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.008 * [taylor]: Taking taylor expansion of k in k
13.008 * [backup-simplify]: Simplify 0 into 0
13.008 * [backup-simplify]: Simplify 1 into 1
13.008 * [backup-simplify]: Simplify (/ 1 1) into 1
13.009 * [backup-simplify]: Simplify (sqrt 0) into 0
13.010 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.010 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
13.010 * [taylor]: Taking taylor expansion of 1.0 in n
13.010 * [backup-simplify]: Simplify 1.0 into 1.0
13.010 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
13.010 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
13.010 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
13.010 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
13.010 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
13.010 * [taylor]: Taking taylor expansion of 0.5 in n
13.010 * [backup-simplify]: Simplify 0.5 into 0.5
13.010 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
13.010 * [taylor]: Taking taylor expansion of 1.0 in n
13.010 * [backup-simplify]: Simplify 1.0 into 1.0
13.010 * [taylor]: Taking taylor expansion of k in n
13.010 * [backup-simplify]: Simplify k into k
13.011 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
13.011 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.011 * [taylor]: Taking taylor expansion of 2.0 in n
13.011 * [backup-simplify]: Simplify 2.0 into 2.0
13.011 * [taylor]: Taking taylor expansion of (* n PI) in n
13.011 * [taylor]: Taking taylor expansion of n in n
13.011 * [backup-simplify]: Simplify 0 into 0
13.011 * [backup-simplify]: Simplify 1 into 1
13.011 * [taylor]: Taking taylor expansion of PI in n
13.011 * [backup-simplify]: Simplify PI into PI
13.011 * [backup-simplify]: Simplify (* 0 PI) into 0
13.012 * [backup-simplify]: Simplify (* 2.0 0) into 0
13.013 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.015 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
13.016 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.016 * [backup-simplify]: Simplify (- k) into (- k)
13.016 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
13.016 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
13.017 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.027 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
13.028 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
13.029 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
13.029 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.029 * [taylor]: Taking taylor expansion of k in n
13.029 * [backup-simplify]: Simplify k into k
13.029 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.029 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
13.029 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.029 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
13.029 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
13.029 * [taylor]: Taking taylor expansion of 1.0 in n
13.029 * [backup-simplify]: Simplify 1.0 into 1.0
13.029 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
13.029 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
13.029 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
13.029 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
13.029 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
13.029 * [taylor]: Taking taylor expansion of 0.5 in n
13.029 * [backup-simplify]: Simplify 0.5 into 0.5
13.029 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
13.030 * [taylor]: Taking taylor expansion of 1.0 in n
13.030 * [backup-simplify]: Simplify 1.0 into 1.0
13.030 * [taylor]: Taking taylor expansion of k in n
13.030 * [backup-simplify]: Simplify k into k
13.030 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
13.030 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
13.030 * [taylor]: Taking taylor expansion of 2.0 in n
13.030 * [backup-simplify]: Simplify 2.0 into 2.0
13.030 * [taylor]: Taking taylor expansion of (* n PI) in n
13.030 * [taylor]: Taking taylor expansion of n in n
13.030 * [backup-simplify]: Simplify 0 into 0
13.030 * [backup-simplify]: Simplify 1 into 1
13.030 * [taylor]: Taking taylor expansion of PI in n
13.030 * [backup-simplify]: Simplify PI into PI
13.030 * [backup-simplify]: Simplify (* 0 PI) into 0
13.031 * [backup-simplify]: Simplify (* 2.0 0) into 0
13.032 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.034 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
13.035 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.035 * [backup-simplify]: Simplify (- k) into (- k)
13.035 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
13.035 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
13.037 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.038 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
13.039 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
13.039 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
13.039 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.039 * [taylor]: Taking taylor expansion of k in n
13.039 * [backup-simplify]: Simplify k into k
13.039 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.040 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
13.040 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.040 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
13.041 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) into (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))
13.043 * [backup-simplify]: Simplify (* 1.0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))) into (* 1.0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))))
13.043 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))) in k
13.043 * [taylor]: Taking taylor expansion of 1.0 in k
13.043 * [backup-simplify]: Simplify 1.0 into 1.0
13.043 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) in k
13.043 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
13.043 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.043 * [taylor]: Taking taylor expansion of k in k
13.043 * [backup-simplify]: Simplify 0 into 0
13.043 * [backup-simplify]: Simplify 1 into 1
13.044 * [backup-simplify]: Simplify (/ 1 1) into 1
13.044 * [backup-simplify]: Simplify (sqrt 0) into 0
13.045 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.045 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
13.046 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
13.046 * [taylor]: Taking taylor expansion of 0.5 in k
13.046 * [backup-simplify]: Simplify 0.5 into 0.5
13.046 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
13.046 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
13.046 * [taylor]: Taking taylor expansion of 1.0 in k
13.046 * [backup-simplify]: Simplify 1.0 into 1.0
13.046 * [taylor]: Taking taylor expansion of k in k
13.046 * [backup-simplify]: Simplify 0 into 0
13.046 * [backup-simplify]: Simplify 1 into 1
13.046 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
13.046 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
13.046 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
13.046 * [taylor]: Taking taylor expansion of 2.0 in k
13.046 * [backup-simplify]: Simplify 2.0 into 2.0
13.046 * [taylor]: Taking taylor expansion of PI in k
13.046 * [backup-simplify]: Simplify PI into PI
13.047 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.048 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.048 * [taylor]: Taking taylor expansion of (log n) in k
13.048 * [taylor]: Taking taylor expansion of n in k
13.048 * [backup-simplify]: Simplify n into n
13.048 * [backup-simplify]: Simplify (log n) into (log n)
13.048 * [backup-simplify]: Simplify (- 0) into 0
13.049 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
13.050 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
13.051 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
13.052 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
13.053 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
13.054 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) into 0
13.055 * [backup-simplify]: Simplify (* 1.0 0) into 0
13.055 * [backup-simplify]: Simplify 0 into 0
13.056 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.057 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
13.059 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.060 * [backup-simplify]: Simplify (- 0) into 0
13.060 * [backup-simplify]: Simplify (+ 0 0) into 0
13.061 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
13.062 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.063 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
13.065 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.067 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
13.069 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))))) into 0
13.069 * [taylor]: Taking taylor expansion of 0 in k
13.069 * [backup-simplify]: Simplify 0 into 0
13.070 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
13.072 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.073 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
13.073 * [backup-simplify]: Simplify (+ 0 0) into 0
13.073 * [backup-simplify]: Simplify (- 1) into -1
13.074 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.075 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
13.078 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
13.081 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
13.085 * [backup-simplify]: Simplify (+ (* 0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
13.087 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
13.088 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
13.089 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.089 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
13.091 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.092 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.096 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
13.097 * [backup-simplify]: Simplify (- 0) into 0
13.097 * [backup-simplify]: Simplify (+ 0 0) into 0
13.098 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
13.099 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.101 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
13.104 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.106 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
13.108 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))))) into 0
13.108 * [taylor]: Taking taylor expansion of 0 in k
13.109 * [backup-simplify]: Simplify 0 into 0
13.109 * [backup-simplify]: Simplify 0 into 0
13.110 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.113 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
13.116 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
13.116 * [backup-simplify]: Simplify (+ 0 0) into 0
13.116 * [backup-simplify]: Simplify (- 0) into 0
13.117 * [backup-simplify]: Simplify (+ 0 0) into 0
13.119 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
13.122 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.127 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
13.128 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
13.131 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.142 * [backup-simplify]: Simplify (+ (* 0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))) (+ (* +nan.0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))))
13.149 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))))
13.155 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))))
13.155 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.156 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
13.158 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.159 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
13.166 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
13.166 * [backup-simplify]: Simplify (- 0) into 0
13.167 * [backup-simplify]: Simplify (+ 0 0) into 0
13.168 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
13.169 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
13.171 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.174 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.176 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
13.179 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt (/ 1 k)) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))))))) into 0
13.179 * [taylor]: Taking taylor expansion of 0 in k
13.179 * [backup-simplify]: Simplify 0 into 0
13.179 * [backup-simplify]: Simplify 0 into 0
13.179 * [backup-simplify]: Simplify 0 into 0
13.180 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.194 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
13.198 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
13.198 * [backup-simplify]: Simplify (+ 0 0) into 0
13.199 * [backup-simplify]: Simplify (- 0) into 0
13.199 * [backup-simplify]: Simplify (+ 0 0) into 0
13.201 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
13.204 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))))) into 0
13.211 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n))) (* 0.020833333333333332 (pow (log n) 3)))))))
13.212 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.216 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.235 * [backup-simplify]: Simplify (+ (* 0 (* -1 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n))) (* 0.020833333333333332 (pow (log n) 3)))))))) (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))) (+ (* +nan.0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))
13.260 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) (+ (* 0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))))))))))
13.274 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))))))))))
13.295 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (pow k 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))))))))))
13.297 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) (sqrt (/ 1 k))) into (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))))
13.297 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (n k) around 0
13.297 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
13.297 * [taylor]: Taking taylor expansion of 1.0 in k
13.297 * [backup-simplify]: Simplify 1.0 into 1.0
13.297 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
13.297 * [taylor]: Taking taylor expansion of (sqrt k) in k
13.297 * [taylor]: Taking taylor expansion of k in k
13.297 * [backup-simplify]: Simplify 0 into 0
13.297 * [backup-simplify]: Simplify 1 into 1
13.297 * [backup-simplify]: Simplify (sqrt 0) into 0
13.299 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.299 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
13.299 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
13.299 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
13.299 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
13.299 * [taylor]: Taking taylor expansion of 0.5 in k
13.299 * [backup-simplify]: Simplify 0.5 into 0.5
13.299 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
13.299 * [taylor]: Taking taylor expansion of 1.0 in k
13.299 * [backup-simplify]: Simplify 1.0 into 1.0
13.299 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.299 * [taylor]: Taking taylor expansion of k in k
13.299 * [backup-simplify]: Simplify 0 into 0
13.299 * [backup-simplify]: Simplify 1 into 1
13.300 * [backup-simplify]: Simplify (/ 1 1) into 1
13.300 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
13.300 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
13.300 * [taylor]: Taking taylor expansion of 2.0 in k
13.300 * [backup-simplify]: Simplify 2.0 into 2.0
13.300 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.300 * [taylor]: Taking taylor expansion of PI in k
13.300 * [backup-simplify]: Simplify PI into PI
13.300 * [taylor]: Taking taylor expansion of n in k
13.300 * [backup-simplify]: Simplify n into n
13.300 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.300 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
13.300 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
13.301 * [backup-simplify]: Simplify (- 1) into -1
13.301 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.301 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
13.302 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
13.302 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
13.302 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n
13.302 * [taylor]: Taking taylor expansion of 1.0 in n
13.302 * [backup-simplify]: Simplify 1.0 into 1.0
13.302 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
13.302 * [taylor]: Taking taylor expansion of (sqrt k) in n
13.302 * [taylor]: Taking taylor expansion of k in n
13.302 * [backup-simplify]: Simplify k into k
13.302 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
13.302 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
13.302 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
13.302 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
13.302 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
13.302 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
13.303 * [taylor]: Taking taylor expansion of 0.5 in n
13.303 * [backup-simplify]: Simplify 0.5 into 0.5
13.303 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
13.303 * [taylor]: Taking taylor expansion of 1.0 in n
13.303 * [backup-simplify]: Simplify 1.0 into 1.0
13.303 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.303 * [taylor]: Taking taylor expansion of k in n
13.303 * [backup-simplify]: Simplify k into k
13.303 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.303 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
13.303 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.303 * [taylor]: Taking taylor expansion of 2.0 in n
13.303 * [backup-simplify]: Simplify 2.0 into 2.0
13.303 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.303 * [taylor]: Taking taylor expansion of PI in n
13.303 * [backup-simplify]: Simplify PI into PI
13.303 * [taylor]: Taking taylor expansion of n in n
13.303 * [backup-simplify]: Simplify 0 into 0
13.303 * [backup-simplify]: Simplify 1 into 1
13.304 * [backup-simplify]: Simplify (/ PI 1) into PI
13.304 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.305 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.305 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.305 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
13.306 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
13.307 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.308 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
13.310 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
13.310 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n
13.310 * [taylor]: Taking taylor expansion of 1.0 in n
13.310 * [backup-simplify]: Simplify 1.0 into 1.0
13.310 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
13.310 * [taylor]: Taking taylor expansion of (sqrt k) in n
13.310 * [taylor]: Taking taylor expansion of k in n
13.310 * [backup-simplify]: Simplify k into k
13.310 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
13.310 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
13.310 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
13.310 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
13.310 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
13.310 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
13.310 * [taylor]: Taking taylor expansion of 0.5 in n
13.310 * [backup-simplify]: Simplify 0.5 into 0.5
13.310 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
13.310 * [taylor]: Taking taylor expansion of 1.0 in n
13.310 * [backup-simplify]: Simplify 1.0 into 1.0
13.310 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.310 * [taylor]: Taking taylor expansion of k in n
13.310 * [backup-simplify]: Simplify k into k
13.310 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.310 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
13.310 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
13.311 * [taylor]: Taking taylor expansion of 2.0 in n
13.311 * [backup-simplify]: Simplify 2.0 into 2.0
13.311 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.311 * [taylor]: Taking taylor expansion of PI in n
13.311 * [backup-simplify]: Simplify PI into PI
13.311 * [taylor]: Taking taylor expansion of n in n
13.311 * [backup-simplify]: Simplify 0 into 0
13.311 * [backup-simplify]: Simplify 1 into 1
13.311 * [backup-simplify]: Simplify (/ PI 1) into PI
13.312 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.313 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.313 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
13.313 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
13.313 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
13.315 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.316 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
13.317 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
13.319 * [backup-simplify]: Simplify (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
13.320 * [backup-simplify]: Simplify (* 1.0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (* 1.0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
13.320 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) in k
13.320 * [taylor]: Taking taylor expansion of 1.0 in k
13.320 * [backup-simplify]: Simplify 1.0 into 1.0
13.320 * [taylor]: Taking taylor expansion of (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) in k
13.320 * [taylor]: Taking taylor expansion of (sqrt k) in k
13.320 * [taylor]: Taking taylor expansion of k in k
13.320 * [backup-simplify]: Simplify 0 into 0
13.320 * [backup-simplify]: Simplify 1 into 1
13.321 * [backup-simplify]: Simplify (sqrt 0) into 0
13.322 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
13.322 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
13.322 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
13.322 * [taylor]: Taking taylor expansion of 0.5 in k
13.322 * [backup-simplify]: Simplify 0.5 into 0.5
13.322 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
13.322 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
13.322 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
13.322 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
13.323 * [taylor]: Taking taylor expansion of 2.0 in k
13.323 * [backup-simplify]: Simplify 2.0 into 2.0
13.323 * [taylor]: Taking taylor expansion of PI in k
13.323 * [backup-simplify]: Simplify PI into PI
13.323 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
13.324 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
13.324 * [taylor]: Taking taylor expansion of (log n) in k
13.324 * [taylor]: Taking taylor expansion of n in k
13.324 * [backup-simplify]: Simplify n into n
13.324 * [backup-simplify]: Simplify (log n) into (log n)
13.324 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
13.324 * [taylor]: Taking taylor expansion of 1.0 in k
13.324 * [backup-simplify]: Simplify 1.0 into 1.0
13.324 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.324 * [taylor]: Taking taylor expansion of k in k
13.325 * [backup-simplify]: Simplify 0 into 0
13.325 * [backup-simplify]: Simplify 1 into 1
13.325 * [backup-simplify]: Simplify (/ 1 1) into 1
13.325 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.326 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
13.327 * [backup-simplify]: Simplify (- 1) into -1
13.327 * [backup-simplify]: Simplify (+ 0 -1) into -1
13.328 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
13.329 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
13.330 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
13.332 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into 0
13.332 * [backup-simplify]: Simplify (* 1.0 0) into 0
13.332 * [backup-simplify]: Simplify 0 into 0
13.333 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.334 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
13.336 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
13.336 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.336 * [backup-simplify]: Simplify (- 0) into 0
13.337 * [backup-simplify]: Simplify (+ 0 0) into 0
13.337 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
13.339 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.340 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
13.342 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.343 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0
13.345 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0
13.345 * [taylor]: Taking taylor expansion of 0 in k
13.345 * [backup-simplify]: Simplify 0 into 0
13.345 * [backup-simplify]: Simplify 0 into 0
13.354 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
13.356 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
13.357 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
13.359 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.360 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.363 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
13.364 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.364 * [backup-simplify]: Simplify (- 0) into 0
13.365 * [backup-simplify]: Simplify (+ 0 0) into 0
13.365 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
13.367 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.369 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
13.371 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.372 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
13.374 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0
13.377 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into 0
13.377 * [taylor]: Taking taylor expansion of 0 in k
13.377 * [backup-simplify]: Simplify 0 into 0
13.377 * [backup-simplify]: Simplify 0 into 0
13.377 * [backup-simplify]: Simplify 0 into 0
13.380 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.382 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
13.385 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
13.386 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
13.388 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.389 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.395 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
13.396 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.396 * [backup-simplify]: Simplify (- 0) into 0
13.397 * [backup-simplify]: Simplify (+ 0 0) into 0
13.398 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
13.399 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
13.401 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
13.404 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.406 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
13.408 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into 0
13.410 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (sqrt k) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))))) into 0
13.410 * [taylor]: Taking taylor expansion of 0 in k
13.410 * [backup-simplify]: Simplify 0 into 0
13.410 * [backup-simplify]: Simplify 0 into 0
13.410 * [backup-simplify]: Simplify 0 into 0
13.411 * [backup-simplify]: Simplify 0 into 0
13.415 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.418 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
13.422 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
13.424 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
13.429 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2))))))))
13.430 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) (sqrt (/ 1 (- k)))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))))
13.430 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (n k) around 0
13.430 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
13.430 * [taylor]: Taking taylor expansion of 1.0 in k
13.430 * [backup-simplify]: Simplify 1.0 into 1.0
13.430 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
13.430 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
13.430 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
13.430 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
13.430 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
13.430 * [taylor]: Taking taylor expansion of 0.5 in k
13.430 * [backup-simplify]: Simplify 0.5 into 0.5
13.431 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
13.431 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.431 * [taylor]: Taking taylor expansion of k in k
13.431 * [backup-simplify]: Simplify 0 into 0
13.431 * [backup-simplify]: Simplify 1 into 1
13.431 * [backup-simplify]: Simplify (/ 1 1) into 1
13.431 * [taylor]: Taking taylor expansion of 1.0 in k
13.431 * [backup-simplify]: Simplify 1.0 into 1.0
13.431 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
13.431 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
13.432 * [taylor]: Taking taylor expansion of -2.0 in k
13.432 * [backup-simplify]: Simplify -2.0 into -2.0
13.432 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.432 * [taylor]: Taking taylor expansion of PI in k
13.432 * [backup-simplify]: Simplify PI into PI
13.432 * [taylor]: Taking taylor expansion of n in k
13.432 * [backup-simplify]: Simplify n into n
13.432 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.432 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
13.432 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
13.433 * [backup-simplify]: Simplify (+ 1 0) into 1
13.433 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
13.433 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
13.433 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
13.433 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
13.433 * [taylor]: Taking taylor expansion of (/ -1 k) in k
13.433 * [taylor]: Taking taylor expansion of -1 in k
13.434 * [backup-simplify]: Simplify -1 into -1
13.434 * [taylor]: Taking taylor expansion of k in k
13.434 * [backup-simplify]: Simplify 0 into 0
13.434 * [backup-simplify]: Simplify 1 into 1
13.434 * [backup-simplify]: Simplify (/ -1 1) into -1
13.434 * [backup-simplify]: Simplify (sqrt 0) into 0
13.436 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
13.436 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))
13.436 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
13.436 * [taylor]: Taking taylor expansion of 1.0 in n
13.437 * [backup-simplify]: Simplify 1.0 into 1.0
13.437 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
13.437 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
13.437 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
13.437 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
13.437 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
13.437 * [taylor]: Taking taylor expansion of 0.5 in n
13.437 * [backup-simplify]: Simplify 0.5 into 0.5
13.437 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
13.437 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.437 * [taylor]: Taking taylor expansion of k in n
13.437 * [backup-simplify]: Simplify k into k
13.437 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.437 * [taylor]: Taking taylor expansion of 1.0 in n
13.437 * [backup-simplify]: Simplify 1.0 into 1.0
13.437 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
13.437 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.437 * [taylor]: Taking taylor expansion of -2.0 in n
13.437 * [backup-simplify]: Simplify -2.0 into -2.0
13.437 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.437 * [taylor]: Taking taylor expansion of PI in n
13.437 * [backup-simplify]: Simplify PI into PI
13.437 * [taylor]: Taking taylor expansion of n in n
13.437 * [backup-simplify]: Simplify 0 into 0
13.437 * [backup-simplify]: Simplify 1 into 1
13.438 * [backup-simplify]: Simplify (/ PI 1) into PI
13.439 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.441 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.441 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
13.441 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
13.443 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.444 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
13.446 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
13.446 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
13.446 * [taylor]: Taking taylor expansion of (/ -1 k) in n
13.446 * [taylor]: Taking taylor expansion of -1 in n
13.446 * [backup-simplify]: Simplify -1 into -1
13.446 * [taylor]: Taking taylor expansion of k in n
13.446 * [backup-simplify]: Simplify k into k
13.446 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
13.446 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
13.446 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
13.446 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
13.448 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))
13.448 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
13.448 * [taylor]: Taking taylor expansion of 1.0 in n
13.448 * [backup-simplify]: Simplify 1.0 into 1.0
13.448 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
13.448 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
13.448 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
13.448 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
13.448 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
13.448 * [taylor]: Taking taylor expansion of 0.5 in n
13.448 * [backup-simplify]: Simplify 0.5 into 0.5
13.448 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
13.448 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.448 * [taylor]: Taking taylor expansion of k in n
13.448 * [backup-simplify]: Simplify k into k
13.448 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.449 * [taylor]: Taking taylor expansion of 1.0 in n
13.449 * [backup-simplify]: Simplify 1.0 into 1.0
13.449 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
13.449 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
13.449 * [taylor]: Taking taylor expansion of -2.0 in n
13.449 * [backup-simplify]: Simplify -2.0 into -2.0
13.449 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.449 * [taylor]: Taking taylor expansion of PI in n
13.449 * [backup-simplify]: Simplify PI into PI
13.449 * [taylor]: Taking taylor expansion of n in n
13.449 * [backup-simplify]: Simplify 0 into 0
13.449 * [backup-simplify]: Simplify 1 into 1
13.450 * [backup-simplify]: Simplify (/ PI 1) into PI
13.450 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.451 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.452 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
13.452 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
13.458 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.460 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
13.461 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
13.461 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
13.461 * [taylor]: Taking taylor expansion of (/ -1 k) in n
13.461 * [taylor]: Taking taylor expansion of -1 in n
13.461 * [backup-simplify]: Simplify -1 into -1
13.461 * [taylor]: Taking taylor expansion of k in n
13.461 * [backup-simplify]: Simplify k into k
13.461 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
13.461 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
13.462 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
13.462 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
13.463 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))
13.465 * [backup-simplify]: Simplify (* 1.0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))) into (* 1.0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))))
13.465 * [taylor]: Taking taylor expansion of (* 1.0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))) in k
13.465 * [taylor]: Taking taylor expansion of 1.0 in k
13.465 * [backup-simplify]: Simplify 1.0 into 1.0
13.465 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) in k
13.465 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
13.465 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
13.465 * [taylor]: Taking taylor expansion of 0.5 in k
13.465 * [backup-simplify]: Simplify 0.5 into 0.5
13.465 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
13.466 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
13.466 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.466 * [taylor]: Taking taylor expansion of k in k
13.466 * [backup-simplify]: Simplify 0 into 0
13.466 * [backup-simplify]: Simplify 1 into 1
13.466 * [backup-simplify]: Simplify (/ 1 1) into 1
13.466 * [taylor]: Taking taylor expansion of 1.0 in k
13.466 * [backup-simplify]: Simplify 1.0 into 1.0
13.466 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
13.466 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
13.466 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
13.466 * [taylor]: Taking taylor expansion of -2.0 in k
13.466 * [backup-simplify]: Simplify -2.0 into -2.0
13.466 * [taylor]: Taking taylor expansion of PI in k
13.466 * [backup-simplify]: Simplify PI into PI
13.467 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
13.468 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
13.468 * [taylor]: Taking taylor expansion of (log n) in k
13.468 * [taylor]: Taking taylor expansion of n in k
13.468 * [backup-simplify]: Simplify n into n
13.468 * [backup-simplify]: Simplify (log n) into (log n)
13.469 * [backup-simplify]: Simplify (+ 1 0) into 1
13.469 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.470 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
13.471 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
13.472 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
13.474 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
13.474 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
13.474 * [taylor]: Taking taylor expansion of (/ -1 k) in k
13.474 * [taylor]: Taking taylor expansion of -1 in k
13.474 * [backup-simplify]: Simplify -1 into -1
13.474 * [taylor]: Taking taylor expansion of k in k
13.474 * [backup-simplify]: Simplify 0 into 0
13.474 * [backup-simplify]: Simplify 1 into 1
13.474 * [backup-simplify]: Simplify (/ -1 1) into -1
13.475 * [backup-simplify]: Simplify (sqrt 0) into 0
13.476 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
13.477 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
13.479 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
13.480 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
13.481 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.482 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
13.484 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
13.484 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.485 * [backup-simplify]: Simplify (+ 0 0) into 0
13.485 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
13.487 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.488 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
13.490 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.492 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
13.494 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))))) into 0
13.494 * [taylor]: Taking taylor expansion of 0 in k
13.494 * [backup-simplify]: Simplify 0 into 0
13.494 * [backup-simplify]: Simplify 0 into 0
13.495 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
13.499 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
13.501 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
13.504 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
13.505 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
13.507 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.508 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
13.511 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
13.512 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.512 * [backup-simplify]: Simplify (+ 0 0) into 0
13.513 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
13.515 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
13.517 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
13.531 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.532 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.532 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
13.534 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
13.536 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))))) into 0
13.536 * [taylor]: Taking taylor expansion of 0 in k
13.536 * [backup-simplify]: Simplify 0 into 0
13.537 * [backup-simplify]: Simplify 0 into 0
13.537 * [backup-simplify]: Simplify 0 into 0
13.538 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.542 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
13.546 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
13.550 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
13.552 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
13.557 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))))))
13.557 * * * [progress]: simplifying candidates
13.560 * [simplify]: Simplifying:
  (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (pow (* (* 2.0 PI) n) (/ 1.0 2.0))
  (pow (* (* 2.0 PI) n) (/ k 2.0))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) 1)
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (- (+ (log 1.0) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k)))
  (- (log (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k)))
  (log (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (exp (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (/ (* (* (* 1.0 1.0) 1.0) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (/ (* (* (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (* (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (- (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- (sqrt k))
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 (sqrt 1))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 1)
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt 1))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1)
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
  (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (+ (* +nan.0 (* (pow k 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* k (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))))))
13.566 * * [simplify]: iteration 0: 264 enodes
13.729 * * [simplify]: iteration 1: 743 enodes
14.303 * * [simplify]: iteration 2: 2402 enodes
16.333 * * [simplify]: iteration complete: 5001 enodes
16.333 * * [simplify]: Extracting #0: cost 67 inf + 0
16.335 * * [simplify]: Extracting #1: cost 579 inf + 1
16.341 * * [simplify]: Extracting #2: cost 1200 inf + 1481
16.357 * * [simplify]: Extracting #3: cost 1547 inf + 29577
16.407 * * [simplify]: Extracting #4: cost 1071 inf + 194042
16.546 * * [simplify]: Extracting #5: cost 485 inf + 458796
16.736 * * [simplify]: Extracting #6: cost 192 inf + 603042
16.957 * * [simplify]: Extracting #7: cost 32 inf + 693723
17.211 * * [simplify]: Extracting #8: cost 0 inf + 711655
17.466 * * [simplify]: Extracting #9: cost 0 inf + 708433
17.692 * * [simplify]: Extracting #10: cost 0 inf + 706019
17.939 * * [simplify]: Extracting #11: cost 0 inf + 705489
18.190 * [simplify]: Simplified to:
  (* (log (* n (* PI 2.0))) (/ (- 1.0 k) 2.0))
  (* (log (* n (* PI 2.0))) (/ (- 1.0 k) 2.0))
  (* (log (* n (* PI 2.0))) (/ (- 1.0 k) 2.0))
  (* (log (* n (* PI 2.0))) (/ (- 1.0 k) 2.0))
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (pow (* n (* PI 2.0)) (/ 1.0 2.0))
  (pow (* n (* PI 2.0)) (/ k 2.0))
  (pow (* n (* PI 2.0)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* n (* PI 2.0)) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* n (* PI 2.0)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0))))
  (pow (* n (* PI 2.0)) (/ (cbrt (- 1.0 k)) (/ (sqrt 2.0) (cbrt (- 1.0 k)))))
  (pow (* n (* PI 2.0)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* n (* PI 2.0)) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* n (* PI 2.0)) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* n (* PI 2.0)) (sqrt (- 1.0 k)))
  (pow (* n (* PI 2.0)) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* n (* PI 2.0)) (/ 1 (sqrt 2.0)))
  (* n (* PI 2.0))
  (pow (* n (* PI 2.0)) (/ (+ (sqrt k) (sqrt 1.0)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* n (* PI 2.0)) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0)))
  (pow (* n (* PI 2.0)) (+ (sqrt k) (sqrt 1.0)))
  (pow (* n (* PI 2.0)) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* n (* PI 2.0)) (/ 1 (sqrt 2.0)))
  (* n (* PI 2.0))
  (* n (* PI 2.0))
  (pow (* n (* PI 2.0)) (- 1.0 k))
  (pow (* PI 2.0) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (* (log (* n (* PI 2.0))) (/ (- 1.0 k) 2.0))
  (exp (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))
  (pow (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) 3)
  (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))
  (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2) 2.0))
  (pow (* n (* PI 2.0)) (/ (/ (- 1.0 k) 2) 2.0))
  (* n (* PI 2.0))
  (* n (* PI 2.0))
  (log (* n (* PI 2.0)))
  (log (* n (* PI 2.0)))
  (log (* n (* PI 2.0)))
  (exp (* n (* PI 2.0)))
  (* (* n (* PI 2.0)) (* (* n (* PI 2.0)) (* n (* PI 2.0))))
  (* (* n (* PI 2.0)) (* (* n (* PI 2.0)) (* n (* PI 2.0))))
  (* (cbrt (* n (* PI 2.0))) (cbrt (* n (* PI 2.0))))
  (cbrt (* n (* PI 2.0)))
  (* (* n (* PI 2.0)) (* (* n (* PI 2.0)) (* n (* PI 2.0))))
  (sqrt (* n (* PI 2.0)))
  (sqrt (* n (* PI 2.0)))
  (* (* PI 2.0) (* (cbrt n) (cbrt n)))
  (* (* PI 2.0) (sqrt n))
  (* PI 2.0)
  (* n PI)
  (+ (log (/ 1.0 (sqrt k))) (* (log (* n (* PI 2.0))) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* n (* PI 2.0))) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* n (* PI 2.0))) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* n (* PI 2.0))) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* n (* PI 2.0))) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* n (* PI 2.0))) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* n (* PI 2.0))) (/ (- 1.0 k) 2.0)))
  (exp (/ 1.0 (/ (sqrt k) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))))
  (* (/ 1.0 (/ (sqrt k) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (/ (sqrt k) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))) (/ 1.0 (/ (sqrt k) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))))))
  (* (/ 1.0 (/ (sqrt k) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (/ (sqrt k) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))) (/ 1.0 (/ (sqrt k) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))))))
  (* (cbrt (/ 1.0 (/ (sqrt k) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))))) (cbrt (/ 1.0 (/ (sqrt k) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))))))
  (cbrt (/ 1.0 (/ (sqrt k) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))))
  (* (/ 1.0 (/ (sqrt k) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (/ (sqrt k) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))) (/ 1.0 (/ (sqrt k) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))))))
  (sqrt (/ 1.0 (/ (sqrt k) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))))
  (sqrt (/ 1.0 (/ (sqrt k) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))))
  (* (- 1.0) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))
  (- (sqrt k))
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (fabs (cbrt k)))
  (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) 1.0))
  (* (/ (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k))) (/ 1.0 (cbrt (sqrt k))))
  (* (/ 1.0 (fabs (cbrt k))) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))))
  (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) 1.0)
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0))))
  (* (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)) 1.0)
  (/ (sqrt k) (pow (* n (* PI 2.0)) (/ (- 1.0 k) 2.0)))
  (* (pow (* n (* PI 2.0)) (/ k 2.0)) (sqrt k))
  (+ (* (* (* (* k k) 0.125) (exp (* 0.5 (log (* n (* PI 2.0)))))) (+ (* (log n) (log n)) (* (log (* PI 2.0)) (log (* PI 2.0))))) (- (+ (* (* (* k k) (* (log (* PI 2.0)) (* (exp (* 0.5 (log (* n (* PI 2.0))))) (log n)))) 0.25) (exp (* 0.5 (log (* n (* PI 2.0)))))) (* 0.5 (* k (* (exp (* 0.5 (log (* n (* PI 2.0))))) (+ (log (* PI 2.0)) (log n)))))))
  (exp (* (* 0.5 (log (* n (* PI 2.0)))) (- 1.0 k)))
  (exp (* (* 0.5 (- (log (* PI -2.0)) (log (/ -1 n)))) (- 1.0 k)))
  (* n (* PI 2.0))
  (* n (* PI 2.0))
  (* n (* PI 2.0))
  (- (- (* (* (* k k) +nan.0) (exp (* 0.5 (log (* n (* PI 2.0)))))) (- (* (* (* (* k k) +nan.0) (exp (* 0.5 (log (* n (* PI 2.0)))))) (- (log n) (log (* PI 2.0)))) (+ (+ (* (* +nan.0 (exp (* 0.5 (log (* n (* PI 2.0)))))) (- (* (* (log (* PI 2.0)) k) (* (log (* PI 2.0)) k)) k)) (+ (- (* +nan.0 (* (* k k) (* (log (* PI 2.0)) (* (exp (* 0.5 (log (* n (* PI 2.0))))) (log n))))) (* (* k (* +nan.0 (exp (* 0.5 (log (* n (* PI 2.0))))))) (log (* PI 2.0)))) (* +nan.0 (- (* (* k k) (* (exp (* 0.5 (log (* n (* PI 2.0))))) (* (log n) (log n)))) (exp (* 0.5 (log (* n (* PI 2.0))))))))) (* (- k) (* (* (exp (* 0.5 (log (* n (* PI 2.0))))) (log n)) +nan.0))))))
  (+ (* (/ (exp (* (* 0.5 (log (* n (* PI 2.0)))) (- 1.0 k))) (* (* k k) k)) (- +nan.0)) (- (* +nan.0 (/ (exp (* (* 0.5 (log (* n (* PI 2.0)))) (- 1.0 k))) k)) (* (/ (exp (* (* 0.5 (log (* n (* PI 2.0)))) (- 1.0 k))) k) (/ +nan.0 k))))
  (+ (/ (* (- +nan.0) (exp (* (* 0.5 (- (log (* PI -2.0)) (log (/ -1 n)))) (- 1.0 k)))) k) (* +nan.0 (- (/ (exp (* (* 0.5 (- (log (* PI -2.0)) (log (/ -1 n)))) (- 1.0 k))) (* k k)) (exp (* (* 0.5 (- (log (* PI -2.0)) (log (/ -1 n)))) (- 1.0 k))))))
18.205 * * * [progress]: adding candidates to table
19.011 * * [progress]: iteration 3 / 4
19.011 * * * [progress]: picking best candidate
19.102 * * * * [pick]: Picked  #<alt (λ (k n) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))>
19.102 * * * [progress]: localizing error
19.150 * * * [progress]: generating rewritten candidates
19.150 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2)
19.205 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1)
19.241 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2)
19.267 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
19.368 * * * [progress]: generating series expansions
19.368 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2)
19.369 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
19.369 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
19.369 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
19.369 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
19.369 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
19.369 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
19.369 * [taylor]: Taking taylor expansion of 0.5 in k
19.369 * [backup-simplify]: Simplify 0.5 into 0.5
19.369 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
19.369 * [taylor]: Taking taylor expansion of 1.0 in k
19.369 * [backup-simplify]: Simplify 1.0 into 1.0
19.369 * [taylor]: Taking taylor expansion of k in k
19.369 * [backup-simplify]: Simplify 0 into 0
19.369 * [backup-simplify]: Simplify 1 into 1
19.369 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
19.369 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
19.369 * [taylor]: Taking taylor expansion of 2.0 in k
19.369 * [backup-simplify]: Simplify 2.0 into 2.0
19.369 * [taylor]: Taking taylor expansion of (* n PI) in k
19.370 * [taylor]: Taking taylor expansion of n in k
19.370 * [backup-simplify]: Simplify n into n
19.370 * [taylor]: Taking taylor expansion of PI in k
19.370 * [backup-simplify]: Simplify PI into PI
19.370 * [backup-simplify]: Simplify (* n PI) into (* n PI)
19.370 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
19.370 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
19.371 * [backup-simplify]: Simplify (- 0) into 0
19.371 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
19.372 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
19.372 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
19.372 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
19.372 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
19.372 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
19.372 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
19.372 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
19.372 * [taylor]: Taking taylor expansion of 0.5 in n
19.372 * [backup-simplify]: Simplify 0.5 into 0.5
19.372 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
19.372 * [taylor]: Taking taylor expansion of 1.0 in n
19.372 * [backup-simplify]: Simplify 1.0 into 1.0
19.372 * [taylor]: Taking taylor expansion of k in n
19.372 * [backup-simplify]: Simplify k into k
19.372 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
19.372 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
19.372 * [taylor]: Taking taylor expansion of 2.0 in n
19.372 * [backup-simplify]: Simplify 2.0 into 2.0
19.372 * [taylor]: Taking taylor expansion of (* n PI) in n
19.372 * [taylor]: Taking taylor expansion of n in n
19.372 * [backup-simplify]: Simplify 0 into 0
19.372 * [backup-simplify]: Simplify 1 into 1
19.373 * [taylor]: Taking taylor expansion of PI in n
19.373 * [backup-simplify]: Simplify PI into PI
19.373 * [backup-simplify]: Simplify (* 0 PI) into 0
19.374 * [backup-simplify]: Simplify (* 2.0 0) into 0
19.375 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.377 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
19.378 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.378 * [backup-simplify]: Simplify (- k) into (- k)
19.378 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
19.378 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
19.380 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
19.381 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
19.382 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
19.382 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
19.382 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
19.382 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
19.382 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
19.382 * [taylor]: Taking taylor expansion of 0.5 in n
19.383 * [backup-simplify]: Simplify 0.5 into 0.5
19.383 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
19.383 * [taylor]: Taking taylor expansion of 1.0 in n
19.383 * [backup-simplify]: Simplify 1.0 into 1.0
19.383 * [taylor]: Taking taylor expansion of k in n
19.383 * [backup-simplify]: Simplify k into k
19.383 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
19.383 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
19.383 * [taylor]: Taking taylor expansion of 2.0 in n
19.383 * [backup-simplify]: Simplify 2.0 into 2.0
19.383 * [taylor]: Taking taylor expansion of (* n PI) in n
19.383 * [taylor]: Taking taylor expansion of n in n
19.383 * [backup-simplify]: Simplify 0 into 0
19.383 * [backup-simplify]: Simplify 1 into 1
19.383 * [taylor]: Taking taylor expansion of PI in n
19.383 * [backup-simplify]: Simplify PI into PI
19.384 * [backup-simplify]: Simplify (* 0 PI) into 0
19.384 * [backup-simplify]: Simplify (* 2.0 0) into 0
19.386 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.387 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
19.388 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.389 * [backup-simplify]: Simplify (- k) into (- k)
19.389 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
19.389 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
19.390 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
19.391 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
19.393 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
19.393 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
19.393 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
19.393 * [taylor]: Taking taylor expansion of 0.5 in k
19.393 * [backup-simplify]: Simplify 0.5 into 0.5
19.393 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
19.393 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
19.393 * [taylor]: Taking taylor expansion of 1.0 in k
19.393 * [backup-simplify]: Simplify 1.0 into 1.0
19.393 * [taylor]: Taking taylor expansion of k in k
19.393 * [backup-simplify]: Simplify 0 into 0
19.393 * [backup-simplify]: Simplify 1 into 1
19.393 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
19.393 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
19.393 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
19.393 * [taylor]: Taking taylor expansion of 2.0 in k
19.393 * [backup-simplify]: Simplify 2.0 into 2.0
19.393 * [taylor]: Taking taylor expansion of PI in k
19.393 * [backup-simplify]: Simplify PI into PI
19.394 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
19.395 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.395 * [taylor]: Taking taylor expansion of (log n) in k
19.395 * [taylor]: Taking taylor expansion of n in k
19.395 * [backup-simplify]: Simplify n into n
19.395 * [backup-simplify]: Simplify (log n) into (log n)
19.396 * [backup-simplify]: Simplify (- 0) into 0
19.396 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
19.397 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
19.398 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
19.400 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
19.401 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
19.402 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
19.403 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
19.404 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
19.406 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
19.407 * [backup-simplify]: Simplify (- 0) into 0
19.407 * [backup-simplify]: Simplify (+ 0 0) into 0
19.408 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
19.409 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
19.410 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
19.413 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
19.413 * [taylor]: Taking taylor expansion of 0 in k
19.413 * [backup-simplify]: Simplify 0 into 0
19.413 * [backup-simplify]: Simplify 0 into 0
19.414 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
19.416 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
19.417 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
19.417 * [backup-simplify]: Simplify (+ 0 0) into 0
19.417 * [backup-simplify]: Simplify (- 1) into -1
19.418 * [backup-simplify]: Simplify (+ 0 -1) into -1
19.419 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
19.422 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
19.426 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
19.429 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
19.431 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
19.432 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
19.436 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
19.436 * [backup-simplify]: Simplify (- 0) into 0
19.437 * [backup-simplify]: Simplify (+ 0 0) into 0
19.438 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
19.439 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
19.441 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
19.443 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
19.444 * [taylor]: Taking taylor expansion of 0 in k
19.444 * [backup-simplify]: Simplify 0 into 0
19.444 * [backup-simplify]: Simplify 0 into 0
19.444 * [backup-simplify]: Simplify 0 into 0
19.445 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
19.448 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
19.451 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
19.451 * [backup-simplify]: Simplify (+ 0 0) into 0
19.452 * [backup-simplify]: Simplify (- 0) into 0
19.452 * [backup-simplify]: Simplify (+ 0 0) into 0
19.454 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
19.457 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
19.461 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
19.467 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
19.478 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
19.479 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))
19.479 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
19.479 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
19.479 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
19.480 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
19.480 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
19.480 * [taylor]: Taking taylor expansion of 0.5 in k
19.480 * [backup-simplify]: Simplify 0.5 into 0.5
19.480 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
19.480 * [taylor]: Taking taylor expansion of 1.0 in k
19.480 * [backup-simplify]: Simplify 1.0 into 1.0
19.480 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.480 * [taylor]: Taking taylor expansion of k in k
19.480 * [backup-simplify]: Simplify 0 into 0
19.480 * [backup-simplify]: Simplify 1 into 1
19.480 * [backup-simplify]: Simplify (/ 1 1) into 1
19.480 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
19.480 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
19.480 * [taylor]: Taking taylor expansion of 2.0 in k
19.480 * [backup-simplify]: Simplify 2.0 into 2.0
19.480 * [taylor]: Taking taylor expansion of (/ PI n) in k
19.480 * [taylor]: Taking taylor expansion of PI in k
19.481 * [backup-simplify]: Simplify PI into PI
19.481 * [taylor]: Taking taylor expansion of n in k
19.481 * [backup-simplify]: Simplify n into n
19.481 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
19.481 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
19.481 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
19.481 * [backup-simplify]: Simplify (- 1) into -1
19.482 * [backup-simplify]: Simplify (+ 0 -1) into -1
19.482 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
19.482 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
19.483 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
19.483 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
19.483 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
19.483 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
19.483 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
19.483 * [taylor]: Taking taylor expansion of 0.5 in n
19.483 * [backup-simplify]: Simplify 0.5 into 0.5
19.483 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
19.483 * [taylor]: Taking taylor expansion of 1.0 in n
19.483 * [backup-simplify]: Simplify 1.0 into 1.0
19.483 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.483 * [taylor]: Taking taylor expansion of k in n
19.483 * [backup-simplify]: Simplify k into k
19.483 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.483 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
19.483 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
19.483 * [taylor]: Taking taylor expansion of 2.0 in n
19.483 * [backup-simplify]: Simplify 2.0 into 2.0
19.483 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.483 * [taylor]: Taking taylor expansion of PI in n
19.483 * [backup-simplify]: Simplify PI into PI
19.483 * [taylor]: Taking taylor expansion of n in n
19.483 * [backup-simplify]: Simplify 0 into 0
19.483 * [backup-simplify]: Simplify 1 into 1
19.484 * [backup-simplify]: Simplify (/ PI 1) into PI
19.485 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
19.486 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.486 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
19.486 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
19.486 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
19.487 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
19.489 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
19.490 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
19.490 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
19.490 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
19.490 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
19.490 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
19.490 * [taylor]: Taking taylor expansion of 0.5 in n
19.490 * [backup-simplify]: Simplify 0.5 into 0.5
19.490 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
19.490 * [taylor]: Taking taylor expansion of 1.0 in n
19.490 * [backup-simplify]: Simplify 1.0 into 1.0
19.490 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.490 * [taylor]: Taking taylor expansion of k in n
19.490 * [backup-simplify]: Simplify k into k
19.491 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.491 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
19.491 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
19.491 * [taylor]: Taking taylor expansion of 2.0 in n
19.491 * [backup-simplify]: Simplify 2.0 into 2.0
19.491 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.491 * [taylor]: Taking taylor expansion of PI in n
19.491 * [backup-simplify]: Simplify PI into PI
19.491 * [taylor]: Taking taylor expansion of n in n
19.491 * [backup-simplify]: Simplify 0 into 0
19.491 * [backup-simplify]: Simplify 1 into 1
19.491 * [backup-simplify]: Simplify (/ PI 1) into PI
19.492 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
19.517 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.517 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
19.517 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
19.517 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
19.519 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
19.520 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
19.521 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
19.522 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
19.522 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
19.522 * [taylor]: Taking taylor expansion of 0.5 in k
19.522 * [backup-simplify]: Simplify 0.5 into 0.5
19.522 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
19.522 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
19.522 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
19.522 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
19.522 * [taylor]: Taking taylor expansion of 2.0 in k
19.522 * [backup-simplify]: Simplify 2.0 into 2.0
19.522 * [taylor]: Taking taylor expansion of PI in k
19.522 * [backup-simplify]: Simplify PI into PI
19.523 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
19.524 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.524 * [taylor]: Taking taylor expansion of (log n) in k
19.524 * [taylor]: Taking taylor expansion of n in k
19.524 * [backup-simplify]: Simplify n into n
19.524 * [backup-simplify]: Simplify (log n) into (log n)
19.524 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
19.524 * [taylor]: Taking taylor expansion of 1.0 in k
19.524 * [backup-simplify]: Simplify 1.0 into 1.0
19.524 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.524 * [taylor]: Taking taylor expansion of k in k
19.524 * [backup-simplify]: Simplify 0 into 0
19.524 * [backup-simplify]: Simplify 1 into 1
19.525 * [backup-simplify]: Simplify (/ 1 1) into 1
19.525 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
19.526 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
19.526 * [backup-simplify]: Simplify (- 1) into -1
19.527 * [backup-simplify]: Simplify (+ 0 -1) into -1
19.528 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
19.529 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
19.530 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
19.532 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
19.533 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
19.533 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
19.535 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
19.535 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
19.536 * [backup-simplify]: Simplify (- 0) into 0
19.536 * [backup-simplify]: Simplify (+ 0 0) into 0
19.537 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
19.538 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
19.540 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
19.542 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
19.542 * [taylor]: Taking taylor expansion of 0 in k
19.542 * [backup-simplify]: Simplify 0 into 0
19.542 * [backup-simplify]: Simplify 0 into 0
19.542 * [backup-simplify]: Simplify 0 into 0
19.543 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.544 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
19.548 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
19.548 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.549 * [backup-simplify]: Simplify (- 0) into 0
19.549 * [backup-simplify]: Simplify (+ 0 0) into 0
19.550 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
19.552 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
19.553 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
19.556 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
19.556 * [taylor]: Taking taylor expansion of 0 in k
19.556 * [backup-simplify]: Simplify 0 into 0
19.556 * [backup-simplify]: Simplify 0 into 0
19.556 * [backup-simplify]: Simplify 0 into 0
19.556 * [backup-simplify]: Simplify 0 into 0
19.557 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.558 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
19.565 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
19.565 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.565 * [backup-simplify]: Simplify (- 0) into 0
19.566 * [backup-simplify]: Simplify (+ 0 0) into 0
19.567 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
19.568 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
19.571 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
19.573 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
19.574 * [taylor]: Taking taylor expansion of 0 in k
19.574 * [backup-simplify]: Simplify 0 into 0
19.574 * [backup-simplify]: Simplify 0 into 0
19.575 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
19.576 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))
19.576 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
19.576 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
19.576 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
19.576 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
19.576 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
19.576 * [taylor]: Taking taylor expansion of 0.5 in k
19.576 * [backup-simplify]: Simplify 0.5 into 0.5
19.576 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
19.576 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.576 * [taylor]: Taking taylor expansion of k in k
19.576 * [backup-simplify]: Simplify 0 into 0
19.576 * [backup-simplify]: Simplify 1 into 1
19.577 * [backup-simplify]: Simplify (/ 1 1) into 1
19.577 * [taylor]: Taking taylor expansion of 1.0 in k
19.577 * [backup-simplify]: Simplify 1.0 into 1.0
19.577 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
19.577 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
19.577 * [taylor]: Taking taylor expansion of -2.0 in k
19.577 * [backup-simplify]: Simplify -2.0 into -2.0
19.577 * [taylor]: Taking taylor expansion of (/ PI n) in k
19.577 * [taylor]: Taking taylor expansion of PI in k
19.577 * [backup-simplify]: Simplify PI into PI
19.577 * [taylor]: Taking taylor expansion of n in k
19.577 * [backup-simplify]: Simplify n into n
19.577 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
19.577 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
19.578 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
19.578 * [backup-simplify]: Simplify (+ 1 0) into 1
19.578 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
19.579 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
19.579 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
19.579 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
19.579 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
19.579 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
19.579 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
19.579 * [taylor]: Taking taylor expansion of 0.5 in n
19.579 * [backup-simplify]: Simplify 0.5 into 0.5
19.579 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
19.579 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.579 * [taylor]: Taking taylor expansion of k in n
19.579 * [backup-simplify]: Simplify k into k
19.579 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.579 * [taylor]: Taking taylor expansion of 1.0 in n
19.579 * [backup-simplify]: Simplify 1.0 into 1.0
19.579 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
19.580 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
19.580 * [taylor]: Taking taylor expansion of -2.0 in n
19.580 * [backup-simplify]: Simplify -2.0 into -2.0
19.580 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.580 * [taylor]: Taking taylor expansion of PI in n
19.580 * [backup-simplify]: Simplify PI into PI
19.580 * [taylor]: Taking taylor expansion of n in n
19.580 * [backup-simplify]: Simplify 0 into 0
19.580 * [backup-simplify]: Simplify 1 into 1
19.580 * [backup-simplify]: Simplify (/ PI 1) into PI
19.581 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
19.582 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
19.582 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
19.582 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
19.584 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
19.585 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
19.587 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
19.587 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
19.587 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
19.587 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
19.587 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
19.587 * [taylor]: Taking taylor expansion of 0.5 in n
19.587 * [backup-simplify]: Simplify 0.5 into 0.5
19.587 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
19.587 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.587 * [taylor]: Taking taylor expansion of k in n
19.587 * [backup-simplify]: Simplify k into k
19.587 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.587 * [taylor]: Taking taylor expansion of 1.0 in n
19.587 * [backup-simplify]: Simplify 1.0 into 1.0
19.587 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
19.587 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
19.587 * [taylor]: Taking taylor expansion of -2.0 in n
19.587 * [backup-simplify]: Simplify -2.0 into -2.0
19.587 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.587 * [taylor]: Taking taylor expansion of PI in n
19.587 * [backup-simplify]: Simplify PI into PI
19.587 * [taylor]: Taking taylor expansion of n in n
19.587 * [backup-simplify]: Simplify 0 into 0
19.587 * [backup-simplify]: Simplify 1 into 1
19.588 * [backup-simplify]: Simplify (/ PI 1) into PI
19.588 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
19.589 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
19.590 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
19.590 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
19.591 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
19.593 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
19.594 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
19.594 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
19.594 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
19.594 * [taylor]: Taking taylor expansion of 0.5 in k
19.594 * [backup-simplify]: Simplify 0.5 into 0.5
19.594 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
19.595 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
19.595 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.595 * [taylor]: Taking taylor expansion of k in k
19.595 * [backup-simplify]: Simplify 0 into 0
19.595 * [backup-simplify]: Simplify 1 into 1
19.595 * [backup-simplify]: Simplify (/ 1 1) into 1
19.595 * [taylor]: Taking taylor expansion of 1.0 in k
19.596 * [backup-simplify]: Simplify 1.0 into 1.0
19.596 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
19.596 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
19.596 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
19.596 * [taylor]: Taking taylor expansion of -2.0 in k
19.596 * [backup-simplify]: Simplify -2.0 into -2.0
19.596 * [taylor]: Taking taylor expansion of PI in k
19.596 * [backup-simplify]: Simplify PI into PI
19.596 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
19.597 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
19.598 * [taylor]: Taking taylor expansion of (log n) in k
19.598 * [taylor]: Taking taylor expansion of n in k
19.598 * [backup-simplify]: Simplify n into n
19.598 * [backup-simplify]: Simplify (log n) into (log n)
19.598 * [backup-simplify]: Simplify (+ 1 0) into 1
19.598 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
19.599 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
19.600 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
19.601 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
19.603 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
19.604 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
19.605 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
19.606 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
19.608 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
19.608 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
19.609 * [backup-simplify]: Simplify (+ 0 0) into 0
19.609 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
19.611 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
19.612 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
19.614 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
19.614 * [taylor]: Taking taylor expansion of 0 in k
19.614 * [backup-simplify]: Simplify 0 into 0
19.615 * [backup-simplify]: Simplify 0 into 0
19.615 * [backup-simplify]: Simplify 0 into 0
19.616 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.617 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
19.620 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
19.621 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.621 * [backup-simplify]: Simplify (+ 0 0) into 0
19.622 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
19.624 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
19.625 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
19.628 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
19.628 * [taylor]: Taking taylor expansion of 0 in k
19.628 * [backup-simplify]: Simplify 0 into 0
19.628 * [backup-simplify]: Simplify 0 into 0
19.628 * [backup-simplify]: Simplify 0 into 0
19.628 * [backup-simplify]: Simplify 0 into 0
19.630 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.632 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
19.639 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0
19.639 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.640 * [backup-simplify]: Simplify (+ 0 0) into 0
19.641 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
19.643 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
19.645 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
19.648 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
19.648 * [taylor]: Taking taylor expansion of 0 in k
19.648 * [backup-simplify]: Simplify 0 into 0
19.648 * [backup-simplify]: Simplify 0 into 0
19.650 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
19.650 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1)
19.650 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
19.651 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
19.651 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
19.651 * [taylor]: Taking taylor expansion of 2.0 in n
19.651 * [backup-simplify]: Simplify 2.0 into 2.0
19.651 * [taylor]: Taking taylor expansion of (* n PI) in n
19.651 * [taylor]: Taking taylor expansion of n in n
19.651 * [backup-simplify]: Simplify 0 into 0
19.651 * [backup-simplify]: Simplify 1 into 1
19.651 * [taylor]: Taking taylor expansion of PI in n
19.651 * [backup-simplify]: Simplify PI into PI
19.651 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
19.651 * [taylor]: Taking taylor expansion of 2.0 in n
19.651 * [backup-simplify]: Simplify 2.0 into 2.0
19.651 * [taylor]: Taking taylor expansion of (* n PI) in n
19.651 * [taylor]: Taking taylor expansion of n in n
19.651 * [backup-simplify]: Simplify 0 into 0
19.651 * [backup-simplify]: Simplify 1 into 1
19.651 * [taylor]: Taking taylor expansion of PI in n
19.651 * [backup-simplify]: Simplify PI into PI
19.652 * [backup-simplify]: Simplify (* 0 PI) into 0
19.652 * [backup-simplify]: Simplify (* 2.0 0) into 0
19.652 * [backup-simplify]: Simplify 0 into 0
19.654 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.656 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
19.657 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
19.658 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
19.659 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
19.659 * [backup-simplify]: Simplify 0 into 0
19.661 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
19.662 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
19.662 * [backup-simplify]: Simplify 0 into 0
19.664 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
19.665 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
19.665 * [backup-simplify]: Simplify 0 into 0
19.667 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
19.669 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
19.669 * [backup-simplify]: Simplify 0 into 0
19.671 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
19.673 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
19.673 * [backup-simplify]: Simplify 0 into 0
19.675 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
19.678 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
19.678 * [backup-simplify]: Simplify 0 into 0
19.679 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
19.679 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
19.679 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
19.679 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
19.679 * [taylor]: Taking taylor expansion of 2.0 in n
19.679 * [backup-simplify]: Simplify 2.0 into 2.0
19.679 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.679 * [taylor]: Taking taylor expansion of PI in n
19.679 * [backup-simplify]: Simplify PI into PI
19.679 * [taylor]: Taking taylor expansion of n in n
19.680 * [backup-simplify]: Simplify 0 into 0
19.680 * [backup-simplify]: Simplify 1 into 1
19.680 * [backup-simplify]: Simplify (/ PI 1) into PI
19.680 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
19.680 * [taylor]: Taking taylor expansion of 2.0 in n
19.680 * [backup-simplify]: Simplify 2.0 into 2.0
19.680 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.680 * [taylor]: Taking taylor expansion of PI in n
19.680 * [backup-simplify]: Simplify PI into PI
19.680 * [taylor]: Taking taylor expansion of n in n
19.680 * [backup-simplify]: Simplify 0 into 0
19.680 * [backup-simplify]: Simplify 1 into 1
19.681 * [backup-simplify]: Simplify (/ PI 1) into PI
19.686 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
19.687 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
19.688 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
19.689 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
19.689 * [backup-simplify]: Simplify 0 into 0
19.690 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.691 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
19.691 * [backup-simplify]: Simplify 0 into 0
19.692 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.693 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
19.693 * [backup-simplify]: Simplify 0 into 0
19.695 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.696 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
19.696 * [backup-simplify]: Simplify 0 into 0
19.697 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.699 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
19.699 * [backup-simplify]: Simplify 0 into 0
19.700 * [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
19.702 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
19.702 * [backup-simplify]: Simplify 0 into 0
19.703 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
19.703 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
19.703 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
19.704 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
19.704 * [taylor]: Taking taylor expansion of -2.0 in n
19.704 * [backup-simplify]: Simplify -2.0 into -2.0
19.704 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.704 * [taylor]: Taking taylor expansion of PI in n
19.704 * [backup-simplify]: Simplify PI into PI
19.704 * [taylor]: Taking taylor expansion of n in n
19.704 * [backup-simplify]: Simplify 0 into 0
19.704 * [backup-simplify]: Simplify 1 into 1
19.704 * [backup-simplify]: Simplify (/ PI 1) into PI
19.704 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
19.704 * [taylor]: Taking taylor expansion of -2.0 in n
19.704 * [backup-simplify]: Simplify -2.0 into -2.0
19.704 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.704 * [taylor]: Taking taylor expansion of PI in n
19.705 * [backup-simplify]: Simplify PI into PI
19.705 * [taylor]: Taking taylor expansion of n in n
19.705 * [backup-simplify]: Simplify 0 into 0
19.705 * [backup-simplify]: Simplify 1 into 1
19.705 * [backup-simplify]: Simplify (/ PI 1) into PI
19.706 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
19.706 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
19.707 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
19.708 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
19.708 * [backup-simplify]: Simplify 0 into 0
19.709 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.710 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
19.710 * [backup-simplify]: Simplify 0 into 0
19.711 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.713 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
19.713 * [backup-simplify]: Simplify 0 into 0
19.714 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.716 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
19.716 * [backup-simplify]: Simplify 0 into 0
19.717 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.719 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
19.719 * [backup-simplify]: Simplify 0 into 0
19.720 * [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
19.722 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
19.722 * [backup-simplify]: Simplify 0 into 0
19.722 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
19.723 * * * * [progress]: [ 3 / 4 ] generating series at (2 2)
19.724 * [backup-simplify]: Simplify (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))))
19.724 * [approximate]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0
19.724 * [taylor]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n
19.724 * [taylor]: Taking taylor expansion of (sqrt k) in n
19.724 * [taylor]: Taking taylor expansion of k in n
19.724 * [backup-simplify]: Simplify k into k
19.724 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
19.724 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
19.724 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n
19.724 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
19.724 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
19.724 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
19.724 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
19.724 * [taylor]: Taking taylor expansion of 0.5 in n
19.724 * [backup-simplify]: Simplify 0.5 into 0.5
19.724 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
19.724 * [taylor]: Taking taylor expansion of 1.0 in n
19.724 * [backup-simplify]: Simplify 1.0 into 1.0
19.724 * [taylor]: Taking taylor expansion of k in n
19.724 * [backup-simplify]: Simplify k into k
19.724 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
19.724 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
19.724 * [taylor]: Taking taylor expansion of 2.0 in n
19.724 * [backup-simplify]: Simplify 2.0 into 2.0
19.724 * [taylor]: Taking taylor expansion of (* n PI) in n
19.724 * [taylor]: Taking taylor expansion of n in n
19.725 * [backup-simplify]: Simplify 0 into 0
19.725 * [backup-simplify]: Simplify 1 into 1
19.725 * [taylor]: Taking taylor expansion of PI in n
19.725 * [backup-simplify]: Simplify PI into PI
19.725 * [backup-simplify]: Simplify (* 0 PI) into 0
19.726 * [backup-simplify]: Simplify (* 2.0 0) into 0
19.727 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.729 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
19.730 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.730 * [backup-simplify]: Simplify (- k) into (- k)
19.730 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
19.730 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
19.732 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
19.733 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
19.734 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
19.736 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) into (/ 1 (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))
19.736 * [taylor]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
19.736 * [taylor]: Taking taylor expansion of (sqrt k) in k
19.736 * [taylor]: Taking taylor expansion of k in k
19.736 * [backup-simplify]: Simplify 0 into 0
19.736 * [backup-simplify]: Simplify 1 into 1
19.736 * [backup-simplify]: Simplify (sqrt 0) into 0
19.738 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
19.738 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
19.738 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
19.738 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
19.738 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
19.739 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
19.739 * [taylor]: Taking taylor expansion of 0.5 in k
19.739 * [backup-simplify]: Simplify 0.5 into 0.5
19.739 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
19.739 * [taylor]: Taking taylor expansion of 1.0 in k
19.739 * [backup-simplify]: Simplify 1.0 into 1.0
19.739 * [taylor]: Taking taylor expansion of k in k
19.739 * [backup-simplify]: Simplify 0 into 0
19.739 * [backup-simplify]: Simplify 1 into 1
19.739 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
19.739 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
19.739 * [taylor]: Taking taylor expansion of 2.0 in k
19.739 * [backup-simplify]: Simplify 2.0 into 2.0
19.739 * [taylor]: Taking taylor expansion of (* n PI) in k
19.739 * [taylor]: Taking taylor expansion of n in k
19.739 * [backup-simplify]: Simplify n into n
19.739 * [taylor]: Taking taylor expansion of PI in k
19.739 * [backup-simplify]: Simplify PI into PI
19.739 * [backup-simplify]: Simplify (* n PI) into (* n PI)
19.739 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
19.740 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
19.740 * [backup-simplify]: Simplify (- 0) into 0
19.741 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
19.741 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
19.741 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
19.741 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
19.742 * [backup-simplify]: Simplify (/ 1 (pow (* 2.0 (* n PI)) 0.5)) into (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)
19.742 * [taylor]: Taking taylor expansion of (* (sqrt k) (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
19.742 * [taylor]: Taking taylor expansion of (sqrt k) in k
19.742 * [taylor]: Taking taylor expansion of k in k
19.742 * [backup-simplify]: Simplify 0 into 0
19.742 * [backup-simplify]: Simplify 1 into 1
19.742 * [backup-simplify]: Simplify (sqrt 0) into 0
19.744 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
19.744 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
19.744 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
19.744 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
19.744 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
19.744 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
19.744 * [taylor]: Taking taylor expansion of 0.5 in k
19.744 * [backup-simplify]: Simplify 0.5 into 0.5
19.744 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
19.744 * [taylor]: Taking taylor expansion of 1.0 in k
19.744 * [backup-simplify]: Simplify 1.0 into 1.0
19.744 * [taylor]: Taking taylor expansion of k in k
19.744 * [backup-simplify]: Simplify 0 into 0
19.744 * [backup-simplify]: Simplify 1 into 1
19.744 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
19.744 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
19.744 * [taylor]: Taking taylor expansion of 2.0 in k
19.744 * [backup-simplify]: Simplify 2.0 into 2.0
19.744 * [taylor]: Taking taylor expansion of (* n PI) in k
19.744 * [taylor]: Taking taylor expansion of n in k
19.744 * [backup-simplify]: Simplify n into n
19.744 * [taylor]: Taking taylor expansion of PI in k
19.744 * [backup-simplify]: Simplify PI into PI
19.744 * [backup-simplify]: Simplify (* n PI) into (* n PI)
19.744 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
19.745 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
19.745 * [backup-simplify]: Simplify (- 0) into 0
19.745 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
19.746 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
19.746 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
19.746 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
19.746 * [backup-simplify]: Simplify (/ 1 (pow (* 2.0 (* n PI)) 0.5)) into (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)
19.748 * [backup-simplify]: Simplify (* 0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) into 0
19.748 * [taylor]: Taking taylor expansion of 0 in n
19.748 * [backup-simplify]: Simplify 0 into 0
19.748 * [backup-simplify]: Simplify 0 into 0
19.749 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
19.749 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0
19.750 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0
19.751 * [backup-simplify]: Simplify (- 1) into -1
19.751 * [backup-simplify]: Simplify (+ 0 -1) into -1
19.753 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5)
19.754 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI)))))
19.755 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
19.758 * [backup-simplify]: Simplify (- (+ (* (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) (/ (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (pow (* 2.0 (* n PI)) 0.5))))) into (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI)))))
19.762 * [backup-simplify]: Simplify (+ (* 0 (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI)))))) (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))
19.762 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) in n
19.762 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n
19.762 * [taylor]: Taking taylor expansion of +nan.0 in n
19.762 * [backup-simplify]: Simplify +nan.0 into +nan.0
19.762 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n
19.762 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n
19.762 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
19.762 * [taylor]: Taking taylor expansion of 0.5 in n
19.762 * [backup-simplify]: Simplify 0.5 into 0.5
19.762 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
19.762 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
19.762 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
19.762 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
19.762 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
19.763 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
19.763 * [taylor]: Taking taylor expansion of 1.0 in n
19.763 * [backup-simplify]: Simplify 1.0 into 1.0
19.763 * [taylor]: Taking taylor expansion of (log PI) in n
19.763 * [taylor]: Taking taylor expansion of PI in n
19.763 * [backup-simplify]: Simplify PI into PI
19.763 * [backup-simplify]: Simplify (log PI) into (log PI)
19.764 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
19.766 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
19.766 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
19.766 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
19.766 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
19.766 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
19.766 * [taylor]: Taking taylor expansion of 1.0 in n
19.766 * [backup-simplify]: Simplify 1.0 into 1.0
19.766 * [taylor]: Taking taylor expansion of (log n) in n
19.766 * [taylor]: Taking taylor expansion of n in n
19.766 * [backup-simplify]: Simplify 0 into 0
19.766 * [backup-simplify]: Simplify 1 into 1
19.767 * [backup-simplify]: Simplify (log 1) into 0
19.767 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
19.768 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
19.768 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
19.768 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
19.768 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
19.768 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
19.768 * [taylor]: Taking taylor expansion of 1.0 in n
19.768 * [backup-simplify]: Simplify 1.0 into 1.0
19.768 * [taylor]: Taking taylor expansion of (log 2.0) in n
19.768 * [taylor]: Taking taylor expansion of 2.0 in n
19.768 * [backup-simplify]: Simplify 2.0 into 2.0
19.768 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
19.769 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
19.771 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
19.771 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
19.773 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
19.774 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)
19.776 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))
19.777 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))
19.779 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
19.781 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))
19.782 * [backup-simplify]: Simplify (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))
19.784 * [backup-simplify]: Simplify (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))
19.784 * [backup-simplify]: Simplify 0 into 0
19.785 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
19.786 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
19.788 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0
19.788 * [backup-simplify]: Simplify (- 0) into 0
19.788 * [backup-simplify]: Simplify (+ 0 0) into 0
19.789 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0
19.791 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0
19.792 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
19.799 * [backup-simplify]: Simplify (- (+ (* (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) (/ (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (pow (* 2.0 (* n PI)) 0.5))) (* (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI))))) (/ (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (pow (* 2.0 (* n PI)) 0.5))))) into (- (* 0.25 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 0.125 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))
19.802 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
19.809 * [backup-simplify]: Simplify (+ (* 0 (- (* 0.25 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 0.125 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) (+ (* +nan.0 (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI)))))) (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))) into (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))
19.810 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))) in n
19.810 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))) in n
19.810 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) in n
19.810 * [taylor]: Taking taylor expansion of +nan.0 in n
19.810 * [backup-simplify]: Simplify +nan.0 into +nan.0
19.810 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5) in n
19.810 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))))) in n
19.810 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n
19.810 * [taylor]: Taking taylor expansion of 0.5 in n
19.810 * [backup-simplify]: Simplify 0.5 into 0.5
19.810 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n
19.810 * [taylor]: Taking taylor expansion of (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n
19.810 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n
19.810 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
19.810 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
19.810 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
19.810 * [taylor]: Taking taylor expansion of 1.0 in n
19.810 * [backup-simplify]: Simplify 1.0 into 1.0
19.810 * [taylor]: Taking taylor expansion of (log 2.0) in n
19.810 * [taylor]: Taking taylor expansion of 2.0 in n
19.810 * [backup-simplify]: Simplify 2.0 into 2.0
19.811 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
19.812 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
19.813 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
19.813 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n
19.813 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
19.813 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
19.813 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
19.813 * [taylor]: Taking taylor expansion of 1.0 in n
19.814 * [backup-simplify]: Simplify 1.0 into 1.0
19.814 * [taylor]: Taking taylor expansion of (log n) in n
19.814 * [taylor]: Taking taylor expansion of n in n
19.814 * [backup-simplify]: Simplify 0 into 0
19.814 * [backup-simplify]: Simplify 1 into 1
19.814 * [backup-simplify]: Simplify (log 1) into 0
19.815 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
19.815 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
19.815 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
19.815 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
19.815 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
19.815 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
19.815 * [taylor]: Taking taylor expansion of 1.0 in n
19.815 * [backup-simplify]: Simplify 1.0 into 1.0
19.815 * [taylor]: Taking taylor expansion of (log PI) in n
19.815 * [taylor]: Taking taylor expansion of PI in n
19.815 * [backup-simplify]: Simplify PI into PI
19.815 * [backup-simplify]: Simplify (log PI) into (log PI)
19.816 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
19.818 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
19.819 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
19.820 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)
19.821 * [backup-simplify]: Simplify (/ 1 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0)
19.823 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0))
19.824 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0)))
19.826 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
19.826 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))) in n
19.826 * [taylor]: Taking taylor expansion of (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) in n
19.826 * [taylor]: Taking taylor expansion of +nan.0 in n
19.827 * [backup-simplify]: Simplify +nan.0 into +nan.0
19.827 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n
19.827 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
19.827 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
19.827 * [taylor]: Taking taylor expansion of 2.0 in n
19.827 * [backup-simplify]: Simplify 2.0 into 2.0
19.827 * [taylor]: Taking taylor expansion of (* n PI) in n
19.827 * [taylor]: Taking taylor expansion of n in n
19.827 * [backup-simplify]: Simplify 0 into 0
19.827 * [backup-simplify]: Simplify 1 into 1
19.827 * [taylor]: Taking taylor expansion of PI in n
19.827 * [backup-simplify]: Simplify PI into PI
19.827 * [backup-simplify]: Simplify (* 0 PI) into 0
19.828 * [backup-simplify]: Simplify (* 2.0 0) into 0
19.829 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.831 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
19.832 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.832 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n
19.832 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n
19.832 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
19.832 * [taylor]: Taking taylor expansion of 0.5 in n
19.832 * [backup-simplify]: Simplify 0.5 into 0.5
19.832 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
19.832 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
19.832 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
19.833 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
19.833 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
19.833 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
19.833 * [taylor]: Taking taylor expansion of 1.0 in n
19.833 * [backup-simplify]: Simplify 1.0 into 1.0
19.833 * [taylor]: Taking taylor expansion of (log PI) in n
19.833 * [taylor]: Taking taylor expansion of PI in n
19.833 * [backup-simplify]: Simplify PI into PI
19.833 * [backup-simplify]: Simplify (log PI) into (log PI)
19.834 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
19.836 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
19.836 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
19.836 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
19.836 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
19.837 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
19.837 * [taylor]: Taking taylor expansion of 1.0 in n
19.837 * [backup-simplify]: Simplify 1.0 into 1.0
19.837 * [taylor]: Taking taylor expansion of (log n) in n
19.837 * [taylor]: Taking taylor expansion of n in n
19.837 * [backup-simplify]: Simplify 0 into 0
19.837 * [backup-simplify]: Simplify 1 into 1
19.837 * [backup-simplify]: Simplify (log 1) into 0
19.838 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
19.838 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
19.838 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
19.838 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
19.838 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
19.838 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
19.838 * [taylor]: Taking taylor expansion of 1.0 in n
19.838 * [backup-simplify]: Simplify 1.0 into 1.0
19.838 * [taylor]: Taking taylor expansion of (log 2.0) in n
19.838 * [taylor]: Taking taylor expansion of 2.0 in n
19.838 * [backup-simplify]: Simplify 2.0 into 2.0
19.838 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
19.839 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
19.841 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
19.842 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
19.843 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
19.844 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)
19.846 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))
19.847 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))
19.849 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
19.856 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))
19.858 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
19.861 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))
19.864 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))
19.867 * [backup-simplify]: Simplify (- (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))
19.874 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))
19.882 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))
19.889 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))
19.891 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0
19.892 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0
19.893 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0
19.897 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
19.898 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
19.899 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0
19.900 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0
19.901 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0
19.903 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
19.904 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0
19.905 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
19.907 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0
19.910 * [backup-simplify]: Simplify (- (+ (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) (/ 0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0))))) into 0
19.912 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1)))) 1) into 0
19.914 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0)))) into 0
19.916 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
19.919 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0
19.919 * [backup-simplify]: Simplify (- 0) into 0
19.919 * [backup-simplify]: Simplify 0 into 0
19.919 * [backup-simplify]: Simplify 0 into 0
19.920 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
19.921 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
19.925 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0
19.925 * [backup-simplify]: Simplify (- 0) into 0
19.925 * [backup-simplify]: Simplify (+ 0 0) into 0
19.927 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0
19.928 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0
19.931 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
19.944 * [backup-simplify]: Simplify (- (+ (* (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) (/ (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (pow (* 2.0 (* n PI)) 0.5))) (* (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI))))) (/ (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (pow (* 2.0 (* n PI)) 0.5))) (* (- (* 0.25 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 0.125 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) (/ (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (pow (* 2.0 (* n PI)) 0.5))))) into (* 0.020833333333333332 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 3)))
19.948 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
19.958 * [backup-simplify]: Simplify (+ (* 0 (* 0.020833333333333332 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 3)))) (+ (* +nan.0 (- (* 0.25 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 0.125 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) (+ (* +nan.0 (* 0.5 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (log (* 2.0 (* n PI)))))) (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))) into (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))
19.959 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))) in n
19.959 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))) in n
19.959 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n
19.959 * [taylor]: Taking taylor expansion of +nan.0 in n
19.959 * [backup-simplify]: Simplify +nan.0 into +nan.0
19.959 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n
19.959 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n
19.959 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
19.959 * [taylor]: Taking taylor expansion of 0.5 in n
19.959 * [backup-simplify]: Simplify 0.5 into 0.5
19.959 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
19.959 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
19.959 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
19.959 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
19.959 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
19.959 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
19.959 * [taylor]: Taking taylor expansion of 1.0 in n
19.959 * [backup-simplify]: Simplify 1.0 into 1.0
19.959 * [taylor]: Taking taylor expansion of (log PI) in n
19.959 * [taylor]: Taking taylor expansion of PI in n
19.959 * [backup-simplify]: Simplify PI into PI
19.960 * [backup-simplify]: Simplify (log PI) into (log PI)
19.961 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
19.963 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
19.963 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
19.963 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
19.963 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
19.963 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
19.963 * [taylor]: Taking taylor expansion of 1.0 in n
19.963 * [backup-simplify]: Simplify 1.0 into 1.0
19.963 * [taylor]: Taking taylor expansion of (log n) in n
19.963 * [taylor]: Taking taylor expansion of n in n
19.963 * [backup-simplify]: Simplify 0 into 0
19.963 * [backup-simplify]: Simplify 1 into 1
19.963 * [backup-simplify]: Simplify (log 1) into 0
19.964 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
19.964 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
19.964 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
19.964 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
19.964 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
19.964 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
19.964 * [taylor]: Taking taylor expansion of 1.0 in n
19.964 * [backup-simplify]: Simplify 1.0 into 1.0
19.964 * [taylor]: Taking taylor expansion of (log 2.0) in n
19.964 * [taylor]: Taking taylor expansion of 2.0 in n
19.964 * [backup-simplify]: Simplify 2.0 into 2.0
19.965 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
19.966 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
19.967 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
19.968 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
19.969 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
19.971 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)
19.972 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))
19.974 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))
19.975 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
19.976 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))) in n
19.976 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))) in n
19.976 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n
19.976 * [taylor]: Taking taylor expansion of +nan.0 in n
19.976 * [backup-simplify]: Simplify +nan.0 into +nan.0
19.976 * [taylor]: Taking taylor expansion of (* (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n
19.976 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5) in n
19.976 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))))) in n
19.976 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
19.976 * [taylor]: Taking taylor expansion of 0.5 in n
19.976 * [backup-simplify]: Simplify 0.5 into 0.5
19.976 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
19.976 * [taylor]: Taking taylor expansion of (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
19.976 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
19.976 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
19.976 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
19.976 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
19.976 * [taylor]: Taking taylor expansion of 1.0 in n
19.976 * [backup-simplify]: Simplify 1.0 into 1.0
19.976 * [taylor]: Taking taylor expansion of (log 2.0) in n
19.976 * [taylor]: Taking taylor expansion of 2.0 in n
19.976 * [backup-simplify]: Simplify 2.0 into 2.0
19.977 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
19.978 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
19.979 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
19.980 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
19.980 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
19.980 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
19.980 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
19.980 * [taylor]: Taking taylor expansion of 1.0 in n
19.980 * [backup-simplify]: Simplify 1.0 into 1.0
19.980 * [taylor]: Taking taylor expansion of (log PI) in n
19.980 * [taylor]: Taking taylor expansion of PI in n
19.980 * [backup-simplify]: Simplify PI into PI
19.980 * [backup-simplify]: Simplify (log PI) into (log PI)
19.981 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
19.983 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
19.983 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
19.983 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
19.983 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
19.983 * [taylor]: Taking taylor expansion of 1.0 in n
19.983 * [backup-simplify]: Simplify 1.0 into 1.0
19.983 * [taylor]: Taking taylor expansion of (log n) in n
19.983 * [taylor]: Taking taylor expansion of n in n
19.983 * [backup-simplify]: Simplify 0 into 0
19.983 * [backup-simplify]: Simplify 1 into 1
19.984 * [backup-simplify]: Simplify (log 1) into 0
19.984 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
19.984 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
19.984 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
19.985 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
19.986 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)
19.988 * [backup-simplify]: Simplify (/ 1 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0)
19.989 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0))
19.991 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0)))
19.992 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
19.992 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n
19.992 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
19.992 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
19.993 * [taylor]: Taking taylor expansion of 2.0 in n
19.993 * [backup-simplify]: Simplify 2.0 into 2.0
19.993 * [taylor]: Taking taylor expansion of (* n PI) in n
19.993 * [taylor]: Taking taylor expansion of n in n
19.993 * [backup-simplify]: Simplify 0 into 0
19.993 * [backup-simplify]: Simplify 1 into 1
19.993 * [taylor]: Taking taylor expansion of PI in n
19.993 * [backup-simplify]: Simplify PI into PI
19.993 * [backup-simplify]: Simplify (* 0 PI) into 0
19.994 * [backup-simplify]: Simplify (* 2.0 0) into 0
19.995 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.997 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
19.998 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.000 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.000 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))) in n
20.000 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))) in n
20.000 * [taylor]: Taking taylor expansion of (* +nan.0 (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) in n
20.000 * [taylor]: Taking taylor expansion of +nan.0 in n
20.000 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.000 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (* n PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n
20.000 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
20.000 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.000 * [taylor]: Taking taylor expansion of 2.0 in n
20.000 * [backup-simplify]: Simplify 2.0 into 2.0
20.000 * [taylor]: Taking taylor expansion of (* n PI) in n
20.000 * [taylor]: Taking taylor expansion of n in n
20.000 * [backup-simplify]: Simplify 0 into 0
20.000 * [backup-simplify]: Simplify 1 into 1
20.000 * [taylor]: Taking taylor expansion of PI in n
20.000 * [backup-simplify]: Simplify PI into PI
20.001 * [backup-simplify]: Simplify (* 0 PI) into 0
20.001 * [backup-simplify]: Simplify (* 2.0 0) into 0
20.003 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.004 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
20.006 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.006 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n
20.006 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n
20.006 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
20.006 * [taylor]: Taking taylor expansion of 0.5 in n
20.006 * [backup-simplify]: Simplify 0.5 into 0.5
20.006 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
20.006 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
20.006 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
20.006 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.006 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.006 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.006 * [taylor]: Taking taylor expansion of 1.0 in n
20.006 * [backup-simplify]: Simplify 1.0 into 1.0
20.006 * [taylor]: Taking taylor expansion of (log PI) in n
20.006 * [taylor]: Taking taylor expansion of PI in n
20.006 * [backup-simplify]: Simplify PI into PI
20.007 * [backup-simplify]: Simplify (log PI) into (log PI)
20.008 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.010 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.010 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
20.010 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.010 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.010 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.010 * [taylor]: Taking taylor expansion of 1.0 in n
20.010 * [backup-simplify]: Simplify 1.0 into 1.0
20.010 * [taylor]: Taking taylor expansion of (log n) in n
20.010 * [taylor]: Taking taylor expansion of n in n
20.010 * [backup-simplify]: Simplify 0 into 0
20.010 * [backup-simplify]: Simplify 1 into 1
20.010 * [backup-simplify]: Simplify (log 1) into 0
20.011 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.011 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.011 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.011 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.011 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.011 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.011 * [taylor]: Taking taylor expansion of 1.0 in n
20.011 * [backup-simplify]: Simplify 1.0 into 1.0
20.011 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.011 * [taylor]: Taking taylor expansion of 2.0 in n
20.011 * [backup-simplify]: Simplify 2.0 into 2.0
20.012 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.013 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.014 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.015 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
20.016 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
20.018 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)
20.025 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))
20.026 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))
20.028 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.028 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))) in n
20.028 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) in n
20.028 * [taylor]: Taking taylor expansion of +nan.0 in n
20.028 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.028 * [taylor]: Taking taylor expansion of (* (pow (log (* 2.0 (* n PI))) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) in n
20.028 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n
20.028 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
20.028 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.028 * [taylor]: Taking taylor expansion of 2.0 in n
20.028 * [backup-simplify]: Simplify 2.0 into 2.0
20.028 * [taylor]: Taking taylor expansion of (* n PI) in n
20.028 * [taylor]: Taking taylor expansion of n in n
20.028 * [backup-simplify]: Simplify 0 into 0
20.028 * [backup-simplify]: Simplify 1 into 1
20.028 * [taylor]: Taking taylor expansion of PI in n
20.028 * [backup-simplify]: Simplify PI into PI
20.029 * [backup-simplify]: Simplify (* 0 PI) into 0
20.029 * [backup-simplify]: Simplify (* 2.0 0) into 0
20.031 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.033 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
20.034 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.035 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.035 * [taylor]: Taking taylor expansion of (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5) in n
20.035 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))))) in n
20.035 * [taylor]: Taking taylor expansion of (* 0.5 (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
20.035 * [taylor]: Taking taylor expansion of 0.5 in n
20.035 * [backup-simplify]: Simplify 0.5 into 0.5
20.036 * [taylor]: Taking taylor expansion of (log (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
20.036 * [taylor]: Taking taylor expansion of (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
20.036 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
20.036 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.036 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.036 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.036 * [taylor]: Taking taylor expansion of 1.0 in n
20.036 * [backup-simplify]: Simplify 1.0 into 1.0
20.036 * [taylor]: Taking taylor expansion of (log PI) in n
20.036 * [taylor]: Taking taylor expansion of PI in n
20.036 * [backup-simplify]: Simplify PI into PI
20.036 * [backup-simplify]: Simplify (log PI) into (log PI)
20.037 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.039 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.039 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
20.039 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.039 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.039 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.039 * [taylor]: Taking taylor expansion of 1.0 in n
20.039 * [backup-simplify]: Simplify 1.0 into 1.0
20.039 * [taylor]: Taking taylor expansion of (log n) in n
20.039 * [taylor]: Taking taylor expansion of n in n
20.040 * [backup-simplify]: Simplify 0 into 0
20.040 * [backup-simplify]: Simplify 1 into 1
20.040 * [backup-simplify]: Simplify (log 1) into 0
20.040 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.040 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.041 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.041 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.041 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.041 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.041 * [taylor]: Taking taylor expansion of 1.0 in n
20.041 * [backup-simplify]: Simplify 1.0 into 1.0
20.041 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.041 * [taylor]: Taking taylor expansion of 2.0 in n
20.041 * [backup-simplify]: Simplify 2.0 into 2.0
20.041 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.042 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.044 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.044 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
20.046 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
20.047 * [backup-simplify]: Simplify (/ 1 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)
20.049 * [backup-simplify]: Simplify (log (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0)) into (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))
20.050 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))
20.052 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.054 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))
20.055 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.057 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.059 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2)
20.062 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))
20.065 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) into (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)))
20.066 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.070 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))
20.072 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))
20.074 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.080 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.082 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2)
20.085 * [backup-simplify]: Simplify (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (pow (pow (pow (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))
20.104 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) into (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))
20.116 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))) into (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))
20.159 * [backup-simplify]: Simplify (+ (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))
20.176 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))
20.197 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))
20.220 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))
20.249 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))))
20.276 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))))
20.302 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))))))))))))))))
20.339 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5)) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))))))))))) (pow (* 1 k) 3)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)) (- (* +nan.0 (* (log n) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5)))))))) (pow (* 1 k) 2)) (* (- (* +nan.0 (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (* 1 k)))) into (- (+ (* +nan.0 (* (pow k 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log (* 2.0 PI)) 2)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow k 3) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log (* 2.0 PI)) 2)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (log (* 2.0 PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* k (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (log n)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log n) 2)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (* (pow k 3) (* (log (* 2.0 PI)) (log n))) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))))))))))))))))))))))))
20.340 * [backup-simplify]: Simplify (/ (sqrt (/ 1 k)) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))))
20.340 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0
20.340 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n
20.340 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
20.341 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.341 * [taylor]: Taking taylor expansion of k in n
20.341 * [backup-simplify]: Simplify k into k
20.341 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.341 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
20.341 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.341 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
20.341 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
20.341 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
20.341 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
20.341 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
20.341 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
20.341 * [taylor]: Taking taylor expansion of 0.5 in n
20.341 * [backup-simplify]: Simplify 0.5 into 0.5
20.341 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
20.341 * [taylor]: Taking taylor expansion of 1.0 in n
20.341 * [backup-simplify]: Simplify 1.0 into 1.0
20.341 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.341 * [taylor]: Taking taylor expansion of k in n
20.341 * [backup-simplify]: Simplify k into k
20.342 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.342 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
20.342 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.342 * [taylor]: Taking taylor expansion of 2.0 in n
20.342 * [backup-simplify]: Simplify 2.0 into 2.0
20.342 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.342 * [taylor]: Taking taylor expansion of PI in n
20.342 * [backup-simplify]: Simplify PI into PI
20.342 * [taylor]: Taking taylor expansion of n in n
20.342 * [backup-simplify]: Simplify 0 into 0
20.342 * [backup-simplify]: Simplify 1 into 1
20.343 * [backup-simplify]: Simplify (/ PI 1) into PI
20.343 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.344 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.344 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.345 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
20.345 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
20.346 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.348 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
20.349 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
20.351 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
20.351 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
20.351 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
20.351 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.351 * [taylor]: Taking taylor expansion of k in k
20.351 * [backup-simplify]: Simplify 0 into 0
20.351 * [backup-simplify]: Simplify 1 into 1
20.352 * [backup-simplify]: Simplify (/ 1 1) into 1
20.352 * [backup-simplify]: Simplify (sqrt 0) into 0
20.353 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.353 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
20.353 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
20.353 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
20.354 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
20.354 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
20.354 * [taylor]: Taking taylor expansion of 0.5 in k
20.354 * [backup-simplify]: Simplify 0.5 into 0.5
20.354 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
20.354 * [taylor]: Taking taylor expansion of 1.0 in k
20.354 * [backup-simplify]: Simplify 1.0 into 1.0
20.354 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.354 * [taylor]: Taking taylor expansion of k in k
20.354 * [backup-simplify]: Simplify 0 into 0
20.354 * [backup-simplify]: Simplify 1 into 1
20.354 * [backup-simplify]: Simplify (/ 1 1) into 1
20.354 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
20.354 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
20.354 * [taylor]: Taking taylor expansion of 2.0 in k
20.354 * [backup-simplify]: Simplify 2.0 into 2.0
20.354 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.354 * [taylor]: Taking taylor expansion of PI in k
20.355 * [backup-simplify]: Simplify PI into PI
20.355 * [taylor]: Taking taylor expansion of n in k
20.355 * [backup-simplify]: Simplify n into n
20.355 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.355 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
20.355 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
20.355 * [backup-simplify]: Simplify (- 1) into -1
20.356 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.356 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
20.356 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
20.357 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
20.357 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))
20.357 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
20.357 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
20.357 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.357 * [taylor]: Taking taylor expansion of k in k
20.357 * [backup-simplify]: Simplify 0 into 0
20.357 * [backup-simplify]: Simplify 1 into 1
20.358 * [backup-simplify]: Simplify (/ 1 1) into 1
20.358 * [backup-simplify]: Simplify (sqrt 0) into 0
20.360 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.360 * [taylor]: Taking taylor expansion of (/ 1 (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
20.360 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
20.360 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
20.360 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
20.360 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
20.360 * [taylor]: Taking taylor expansion of 0.5 in k
20.360 * [backup-simplify]: Simplify 0.5 into 0.5
20.360 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
20.360 * [taylor]: Taking taylor expansion of 1.0 in k
20.360 * [backup-simplify]: Simplify 1.0 into 1.0
20.360 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.360 * [taylor]: Taking taylor expansion of k in k
20.360 * [backup-simplify]: Simplify 0 into 0
20.360 * [backup-simplify]: Simplify 1 into 1
20.360 * [backup-simplify]: Simplify (/ 1 1) into 1
20.360 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
20.361 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
20.361 * [taylor]: Taking taylor expansion of 2.0 in k
20.361 * [backup-simplify]: Simplify 2.0 into 2.0
20.361 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.361 * [taylor]: Taking taylor expansion of PI in k
20.361 * [backup-simplify]: Simplify PI into PI
20.361 * [taylor]: Taking taylor expansion of n in k
20.361 * [backup-simplify]: Simplify n into n
20.361 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.361 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
20.361 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
20.361 * [backup-simplify]: Simplify (- 1) into -1
20.362 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.362 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
20.362 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
20.363 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
20.363 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))
20.364 * [backup-simplify]: Simplify (* 0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) into 0
20.364 * [taylor]: Taking taylor expansion of 0 in n
20.364 * [backup-simplify]: Simplify 0 into 0
20.364 * [backup-simplify]: Simplify 0 into 0
20.364 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into 0
20.365 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))
20.365 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) in n
20.365 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
20.365 * [taylor]: Taking taylor expansion of +nan.0 in n
20.365 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.365 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
20.366 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
20.366 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
20.366 * [taylor]: Taking taylor expansion of 0.5 in n
20.366 * [backup-simplify]: Simplify 0.5 into 0.5
20.366 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
20.366 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
20.366 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.366 * [taylor]: Taking taylor expansion of 2.0 in n
20.366 * [backup-simplify]: Simplify 2.0 into 2.0
20.366 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.366 * [taylor]: Taking taylor expansion of PI in n
20.366 * [backup-simplify]: Simplify PI into PI
20.366 * [taylor]: Taking taylor expansion of n in n
20.366 * [backup-simplify]: Simplify 0 into 0
20.366 * [backup-simplify]: Simplify 1 into 1
20.367 * [backup-simplify]: Simplify (/ PI 1) into PI
20.367 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.368 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.368 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
20.368 * [taylor]: Taking taylor expansion of 1.0 in n
20.368 * [backup-simplify]: Simplify 1.0 into 1.0
20.368 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.368 * [taylor]: Taking taylor expansion of k in n
20.368 * [backup-simplify]: Simplify k into k
20.369 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.370 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.370 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.370 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
20.372 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
20.373 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
20.374 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
20.376 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
20.377 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (/ +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
20.379 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))
20.381 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))
20.381 * [backup-simplify]: Simplify 0 into 0
20.382 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) (* 0 (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into 0
20.383 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
20.386 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
20.387 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))
20.388 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) in n
20.388 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
20.388 * [taylor]: Taking taylor expansion of +nan.0 in n
20.388 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.388 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
20.388 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
20.388 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
20.388 * [taylor]: Taking taylor expansion of 0.5 in n
20.388 * [backup-simplify]: Simplify 0.5 into 0.5
20.388 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
20.388 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
20.388 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.388 * [taylor]: Taking taylor expansion of 2.0 in n
20.388 * [backup-simplify]: Simplify 2.0 into 2.0
20.388 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.388 * [taylor]: Taking taylor expansion of PI in n
20.388 * [backup-simplify]: Simplify PI into PI
20.388 * [taylor]: Taking taylor expansion of n in n
20.388 * [backup-simplify]: Simplify 0 into 0
20.388 * [backup-simplify]: Simplify 1 into 1
20.389 * [backup-simplify]: Simplify (/ PI 1) into PI
20.389 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.390 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.390 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
20.390 * [taylor]: Taking taylor expansion of 1.0 in n
20.390 * [backup-simplify]: Simplify 1.0 into 1.0
20.390 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.391 * [taylor]: Taking taylor expansion of k in n
20.391 * [backup-simplify]: Simplify k into k
20.391 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.392 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.392 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.392 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
20.394 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
20.395 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
20.396 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
20.397 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
20.399 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (/ +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
20.405 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))
20.407 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))
20.409 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.409 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.410 * [backup-simplify]: Simplify (- 0) into 0
20.410 * [backup-simplify]: Simplify (+ 0 0) into 0
20.411 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.412 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
20.414 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
20.415 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0
20.417 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0
20.419 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
20.421 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) (/ 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))) into 0
20.423 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into 0
20.423 * [backup-simplify]: Simplify (- 0) into 0
20.424 * [backup-simplify]: Simplify 0 into 0
20.424 * [backup-simplify]: Simplify 0 into 0
20.425 * [backup-simplify]: Simplify (- (+ (* (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) (* 0 (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) (* 0 (/ 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into 0
20.426 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.430 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
20.432 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))
20.432 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) in n
20.432 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
20.432 * [taylor]: Taking taylor expansion of +nan.0 in n
20.432 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.432 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
20.432 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
20.432 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
20.432 * [taylor]: Taking taylor expansion of 0.5 in n
20.432 * [backup-simplify]: Simplify 0.5 into 0.5
20.432 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
20.432 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
20.432 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.432 * [taylor]: Taking taylor expansion of 2.0 in n
20.432 * [backup-simplify]: Simplify 2.0 into 2.0
20.432 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.432 * [taylor]: Taking taylor expansion of PI in n
20.432 * [backup-simplify]: Simplify PI into PI
20.432 * [taylor]: Taking taylor expansion of n in n
20.432 * [backup-simplify]: Simplify 0 into 0
20.432 * [backup-simplify]: Simplify 1 into 1
20.433 * [backup-simplify]: Simplify (/ PI 1) into PI
20.433 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.435 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.435 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
20.435 * [taylor]: Taking taylor expansion of 1.0 in n
20.435 * [backup-simplify]: Simplify 1.0 into 1.0
20.435 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.435 * [taylor]: Taking taylor expansion of k in n
20.435 * [backup-simplify]: Simplify k into k
20.435 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.436 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.436 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.437 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
20.438 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
20.439 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
20.440 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
20.442 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
20.443 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (/ +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
20.445 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))
20.446 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))))
20.451 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k))))))))) (pow (* 1 (/ 1 k)) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k))))))))) (* 1 (/ 1 k))) (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k))))))))))) into (- (+ (* +nan.0 (/ 1 (* k (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))))) (- (+ (* +nan.0 (/ 1 (* (pow k 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))))) (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))))))))))
20.452 * [backup-simplify]: Simplify (/ (sqrt (/ 1 (- k))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))))
20.452 * [approximate]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in (k n) around 0
20.452 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in n
20.452 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
20.452 * [taylor]: Taking taylor expansion of (/ -1 k) in n
20.452 * [taylor]: Taking taylor expansion of -1 in n
20.453 * [backup-simplify]: Simplify -1 into -1
20.453 * [taylor]: Taking taylor expansion of k in n
20.453 * [backup-simplify]: Simplify k into k
20.453 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
20.453 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
20.453 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
20.453 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
20.453 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
20.453 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
20.453 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
20.453 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
20.453 * [taylor]: Taking taylor expansion of 0.5 in n
20.453 * [backup-simplify]: Simplify 0.5 into 0.5
20.453 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
20.453 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.453 * [taylor]: Taking taylor expansion of k in n
20.453 * [backup-simplify]: Simplify k into k
20.453 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.454 * [taylor]: Taking taylor expansion of 1.0 in n
20.454 * [backup-simplify]: Simplify 1.0 into 1.0
20.454 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
20.454 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
20.454 * [taylor]: Taking taylor expansion of -2.0 in n
20.454 * [backup-simplify]: Simplify -2.0 into -2.0
20.454 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.454 * [taylor]: Taking taylor expansion of PI in n
20.454 * [backup-simplify]: Simplify PI into PI
20.454 * [taylor]: Taking taylor expansion of n in n
20.454 * [backup-simplify]: Simplify 0 into 0
20.454 * [backup-simplify]: Simplify 1 into 1
20.454 * [backup-simplify]: Simplify (/ PI 1) into PI
20.455 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
20.456 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
20.456 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
20.456 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
20.458 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
20.459 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
20.460 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
20.462 * [backup-simplify]: Simplify (/ (sqrt (/ -1 k)) (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (/ (sqrt (/ -1 k)) (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
20.462 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in k
20.462 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
20.462 * [taylor]: Taking taylor expansion of (/ -1 k) in k
20.462 * [taylor]: Taking taylor expansion of -1 in k
20.462 * [backup-simplify]: Simplify -1 into -1
20.462 * [taylor]: Taking taylor expansion of k in k
20.462 * [backup-simplify]: Simplify 0 into 0
20.462 * [backup-simplify]: Simplify 1 into 1
20.463 * [backup-simplify]: Simplify (/ -1 1) into -1
20.463 * [backup-simplify]: Simplify (sqrt 0) into 0
20.465 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
20.465 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
20.465 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
20.465 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
20.465 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
20.465 * [taylor]: Taking taylor expansion of 0.5 in k
20.465 * [backup-simplify]: Simplify 0.5 into 0.5
20.465 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
20.465 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.465 * [taylor]: Taking taylor expansion of k in k
20.465 * [backup-simplify]: Simplify 0 into 0
20.465 * [backup-simplify]: Simplify 1 into 1
20.465 * [backup-simplify]: Simplify (/ 1 1) into 1
20.465 * [taylor]: Taking taylor expansion of 1.0 in k
20.465 * [backup-simplify]: Simplify 1.0 into 1.0
20.465 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
20.465 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
20.465 * [taylor]: Taking taylor expansion of -2.0 in k
20.466 * [backup-simplify]: Simplify -2.0 into -2.0
20.466 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.466 * [taylor]: Taking taylor expansion of PI in k
20.466 * [backup-simplify]: Simplify PI into PI
20.466 * [taylor]: Taking taylor expansion of n in k
20.466 * [backup-simplify]: Simplify n into n
20.466 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.466 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
20.466 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
20.466 * [backup-simplify]: Simplify (+ 1 0) into 1
20.467 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
20.467 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
20.467 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
20.468 * [backup-simplify]: Simplify (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) into (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))
20.468 * [taylor]: Taking taylor expansion of (/ (sqrt (/ -1 k)) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in k
20.468 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
20.468 * [taylor]: Taking taylor expansion of (/ -1 k) in k
20.468 * [taylor]: Taking taylor expansion of -1 in k
20.468 * [backup-simplify]: Simplify -1 into -1
20.468 * [taylor]: Taking taylor expansion of k in k
20.468 * [backup-simplify]: Simplify 0 into 0
20.468 * [backup-simplify]: Simplify 1 into 1
20.468 * [backup-simplify]: Simplify (/ -1 1) into -1
20.469 * [backup-simplify]: Simplify (sqrt 0) into 0
20.470 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
20.470 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
20.470 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
20.470 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
20.470 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
20.470 * [taylor]: Taking taylor expansion of 0.5 in k
20.470 * [backup-simplify]: Simplify 0.5 into 0.5
20.470 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
20.470 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.470 * [taylor]: Taking taylor expansion of k in k
20.470 * [backup-simplify]: Simplify 0 into 0
20.470 * [backup-simplify]: Simplify 1 into 1
20.471 * [backup-simplify]: Simplify (/ 1 1) into 1
20.471 * [taylor]: Taking taylor expansion of 1.0 in k
20.471 * [backup-simplify]: Simplify 1.0 into 1.0
20.471 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
20.471 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
20.471 * [taylor]: Taking taylor expansion of -2.0 in k
20.471 * [backup-simplify]: Simplify -2.0 into -2.0
20.471 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.471 * [taylor]: Taking taylor expansion of PI in k
20.471 * [backup-simplify]: Simplify PI into PI
20.471 * [taylor]: Taking taylor expansion of n in k
20.471 * [backup-simplify]: Simplify n into n
20.471 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.471 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
20.472 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
20.472 * [backup-simplify]: Simplify (+ 1 0) into 1
20.473 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
20.473 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
20.473 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
20.473 * [backup-simplify]: Simplify (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) into (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))
20.473 * [taylor]: Taking taylor expansion of (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
20.473 * [taylor]: Taking taylor expansion of +nan.0 in n
20.473 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.474 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
20.474 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
20.474 * [taylor]: Taking taylor expansion of 0.5 in n
20.474 * [backup-simplify]: Simplify 0.5 into 0.5
20.474 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
20.474 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
20.474 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.474 * [taylor]: Taking taylor expansion of k in n
20.474 * [backup-simplify]: Simplify k into k
20.474 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.474 * [taylor]: Taking taylor expansion of 1.0 in n
20.474 * [backup-simplify]: Simplify 1.0 into 1.0
20.474 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
20.474 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
20.474 * [taylor]: Taking taylor expansion of -2.0 in n
20.474 * [backup-simplify]: Simplify -2.0 into -2.0
20.474 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.474 * [taylor]: Taking taylor expansion of PI in n
20.474 * [backup-simplify]: Simplify PI into PI
20.474 * [taylor]: Taking taylor expansion of n in n
20.474 * [backup-simplify]: Simplify 0 into 0
20.474 * [backup-simplify]: Simplify 1 into 1
20.475 * [backup-simplify]: Simplify (/ PI 1) into PI
20.475 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
20.476 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
20.477 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
20.478 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
20.480 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
20.481 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
20.482 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
20.483 * [backup-simplify]: Simplify (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
20.485 * [backup-simplify]: Simplify (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
20.486 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
20.489 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
20.490 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (+ (* (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))
20.490 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) in n
20.490 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
20.490 * [taylor]: Taking taylor expansion of +nan.0 in n
20.490 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.490 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
20.490 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
20.490 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
20.490 * [taylor]: Taking taylor expansion of 0.5 in n
20.490 * [backup-simplify]: Simplify 0.5 into 0.5
20.490 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
20.490 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
20.490 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.490 * [taylor]: Taking taylor expansion of k in n
20.490 * [backup-simplify]: Simplify k into k
20.490 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.490 * [taylor]: Taking taylor expansion of 1.0 in n
20.490 * [backup-simplify]: Simplify 1.0 into 1.0
20.490 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
20.490 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
20.491 * [taylor]: Taking taylor expansion of -2.0 in n
20.491 * [backup-simplify]: Simplify -2.0 into -2.0
20.491 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.491 * [taylor]: Taking taylor expansion of PI in n
20.491 * [backup-simplify]: Simplify PI into PI
20.491 * [taylor]: Taking taylor expansion of n in n
20.491 * [backup-simplify]: Simplify 0 into 0
20.491 * [backup-simplify]: Simplify 1 into 1
20.491 * [backup-simplify]: Simplify (/ PI 1) into PI
20.492 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
20.493 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
20.493 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
20.495 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
20.496 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
20.497 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
20.498 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
20.500 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
20.501 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
20.503 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))
20.504 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))
20.505 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.506 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
20.508 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
20.508 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.508 * [backup-simplify]: Simplify (+ 0 0) into 0
20.510 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
20.512 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
20.513 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0
20.515 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
20.519 * [backup-simplify]: Simplify (- (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) (+ (* (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))) into 0
20.519 * [backup-simplify]: Simplify 0 into 0
20.520 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.525 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
20.526 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (+ (* (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) (* (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (/ 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))
20.526 * [taylor]: Taking taylor expansion of (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) in n
20.526 * [taylor]: Taking taylor expansion of (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
20.526 * [taylor]: Taking taylor expansion of +nan.0 in n
20.526 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.526 * [taylor]: Taking taylor expansion of (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
20.526 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
20.526 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
20.526 * [taylor]: Taking taylor expansion of 0.5 in n
20.527 * [backup-simplify]: Simplify 0.5 into 0.5
20.527 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
20.527 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
20.527 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.527 * [taylor]: Taking taylor expansion of k in n
20.527 * [backup-simplify]: Simplify k into k
20.527 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.527 * [taylor]: Taking taylor expansion of 1.0 in n
20.527 * [backup-simplify]: Simplify 1.0 into 1.0
20.527 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
20.527 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
20.527 * [taylor]: Taking taylor expansion of -2.0 in n
20.527 * [backup-simplify]: Simplify -2.0 into -2.0
20.527 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.527 * [taylor]: Taking taylor expansion of PI in n
20.527 * [backup-simplify]: Simplify PI into PI
20.527 * [taylor]: Taking taylor expansion of n in n
20.527 * [backup-simplify]: Simplify 0 into 0
20.527 * [backup-simplify]: Simplify 1 into 1
20.528 * [backup-simplify]: Simplify (/ PI 1) into PI
20.528 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
20.529 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
20.529 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
20.531 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
20.532 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
20.533 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
20.534 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
20.536 * [backup-simplify]: Simplify (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
20.537 * [backup-simplify]: Simplify (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
20.539 * [backup-simplify]: Simplify (- (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))
20.540 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))) into (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))))
20.545 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (/ 1 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) (* 1 (/ 1 (- k)))) (/ +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ 1 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ 1 (* k (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))) (- (* +nan.0 (/ 1 (* (pow k 2) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))))))))
20.546 * * * * [progress]: [ 4 / 4 ] generating series at (2)
20.547 * [backup-simplify]: Simplify (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) into (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))))
20.547 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in (k n) around 0
20.547 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in n
20.547 * [taylor]: Taking taylor expansion of 1.0 in n
20.547 * [backup-simplify]: Simplify 1.0 into 1.0
20.547 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in n
20.547 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
20.547 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.547 * [taylor]: Taking taylor expansion of k in n
20.547 * [backup-simplify]: Simplify k into k
20.547 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.547 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
20.547 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.547 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
20.547 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
20.547 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
20.548 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
20.548 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
20.548 * [taylor]: Taking taylor expansion of 0.5 in n
20.548 * [backup-simplify]: Simplify 0.5 into 0.5
20.548 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
20.548 * [taylor]: Taking taylor expansion of 1.0 in n
20.548 * [backup-simplify]: Simplify 1.0 into 1.0
20.548 * [taylor]: Taking taylor expansion of k in n
20.548 * [backup-simplify]: Simplify k into k
20.548 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
20.548 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.548 * [taylor]: Taking taylor expansion of 2.0 in n
20.548 * [backup-simplify]: Simplify 2.0 into 2.0
20.548 * [taylor]: Taking taylor expansion of (* n PI) in n
20.548 * [taylor]: Taking taylor expansion of n in n
20.548 * [backup-simplify]: Simplify 0 into 0
20.548 * [backup-simplify]: Simplify 1 into 1
20.548 * [taylor]: Taking taylor expansion of PI in n
20.548 * [backup-simplify]: Simplify PI into PI
20.549 * [backup-simplify]: Simplify (* 0 PI) into 0
20.549 * [backup-simplify]: Simplify (* 2.0 0) into 0
20.551 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.553 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
20.554 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.554 * [backup-simplify]: Simplify (- k) into (- k)
20.554 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
20.554 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
20.556 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.557 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
20.558 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
20.558 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
20.558 * [taylor]: Taking taylor expansion of 1.0 in k
20.559 * [backup-simplify]: Simplify 1.0 into 1.0
20.559 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
20.559 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
20.559 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.559 * [taylor]: Taking taylor expansion of k in k
20.559 * [backup-simplify]: Simplify 0 into 0
20.559 * [backup-simplify]: Simplify 1 into 1
20.559 * [backup-simplify]: Simplify (/ 1 1) into 1
20.560 * [backup-simplify]: Simplify (sqrt 0) into 0
20.561 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.561 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
20.561 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
20.561 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
20.561 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
20.561 * [taylor]: Taking taylor expansion of 0.5 in k
20.561 * [backup-simplify]: Simplify 0.5 into 0.5
20.561 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
20.561 * [taylor]: Taking taylor expansion of 1.0 in k
20.561 * [backup-simplify]: Simplify 1.0 into 1.0
20.561 * [taylor]: Taking taylor expansion of k in k
20.561 * [backup-simplify]: Simplify 0 into 0
20.561 * [backup-simplify]: Simplify 1 into 1
20.561 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
20.561 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
20.561 * [taylor]: Taking taylor expansion of 2.0 in k
20.562 * [backup-simplify]: Simplify 2.0 into 2.0
20.562 * [taylor]: Taking taylor expansion of (* n PI) in k
20.562 * [taylor]: Taking taylor expansion of n in k
20.562 * [backup-simplify]: Simplify n into n
20.562 * [taylor]: Taking taylor expansion of PI in k
20.562 * [backup-simplify]: Simplify PI into PI
20.562 * [backup-simplify]: Simplify (* n PI) into (* n PI)
20.562 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
20.562 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
20.562 * [backup-simplify]: Simplify (- 0) into 0
20.563 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
20.563 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
20.564 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
20.564 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
20.564 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))))) in k
20.564 * [taylor]: Taking taylor expansion of 1.0 in k
20.564 * [backup-simplify]: Simplify 1.0 into 1.0
20.564 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))) in k
20.564 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
20.564 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.564 * [taylor]: Taking taylor expansion of k in k
20.564 * [backup-simplify]: Simplify 0 into 0
20.564 * [backup-simplify]: Simplify 1 into 1
20.564 * [backup-simplify]: Simplify (/ 1 1) into 1
20.565 * [backup-simplify]: Simplify (sqrt 0) into 0
20.571 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.571 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
20.571 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
20.571 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
20.571 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
20.571 * [taylor]: Taking taylor expansion of 0.5 in k
20.571 * [backup-simplify]: Simplify 0.5 into 0.5
20.571 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
20.571 * [taylor]: Taking taylor expansion of 1.0 in k
20.571 * [backup-simplify]: Simplify 1.0 into 1.0
20.571 * [taylor]: Taking taylor expansion of k in k
20.571 * [backup-simplify]: Simplify 0 into 0
20.571 * [backup-simplify]: Simplify 1 into 1
20.571 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
20.571 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
20.571 * [taylor]: Taking taylor expansion of 2.0 in k
20.571 * [backup-simplify]: Simplify 2.0 into 2.0
20.571 * [taylor]: Taking taylor expansion of (* n PI) in k
20.571 * [taylor]: Taking taylor expansion of n in k
20.572 * [backup-simplify]: Simplify n into n
20.572 * [taylor]: Taking taylor expansion of PI in k
20.572 * [backup-simplify]: Simplify PI into PI
20.572 * [backup-simplify]: Simplify (* n PI) into (* n PI)
20.572 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
20.572 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
20.572 * [backup-simplify]: Simplify (- 0) into 0
20.573 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
20.573 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
20.573 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
20.573 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
20.574 * [backup-simplify]: Simplify (* 0 (pow (* 2.0 (* n PI)) 0.5)) into 0
20.574 * [backup-simplify]: Simplify (* 1.0 0) into 0
20.574 * [taylor]: Taking taylor expansion of 0 in n
20.574 * [backup-simplify]: Simplify 0 into 0
20.574 * [backup-simplify]: Simplify 0 into 0
20.575 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
20.575 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0
20.576 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0
20.576 * [backup-simplify]: Simplify (- 1) into -1
20.577 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.578 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5)
20.579 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI)))))
20.580 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
20.581 * [backup-simplify]: Simplify (+ (* 0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))
20.583 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
20.583 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n
20.583 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n
20.583 * [taylor]: Taking taylor expansion of +nan.0 in n
20.583 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.583 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
20.583 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
20.583 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
20.583 * [taylor]: Taking taylor expansion of 0.5 in n
20.583 * [backup-simplify]: Simplify 0.5 into 0.5
20.583 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
20.583 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
20.583 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.583 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.583 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.583 * [taylor]: Taking taylor expansion of 1.0 in n
20.583 * [backup-simplify]: Simplify 1.0 into 1.0
20.583 * [taylor]: Taking taylor expansion of (log PI) in n
20.583 * [taylor]: Taking taylor expansion of PI in n
20.583 * [backup-simplify]: Simplify PI into PI
20.584 * [backup-simplify]: Simplify (log PI) into (log PI)
20.585 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.586 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.586 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
20.586 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.586 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.586 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.586 * [taylor]: Taking taylor expansion of 1.0 in n
20.586 * [backup-simplify]: Simplify 1.0 into 1.0
20.586 * [taylor]: Taking taylor expansion of (log n) in n
20.586 * [taylor]: Taking taylor expansion of n in n
20.586 * [backup-simplify]: Simplify 0 into 0
20.587 * [backup-simplify]: Simplify 1 into 1
20.587 * [backup-simplify]: Simplify (log 1) into 0
20.587 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.587 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.587 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.587 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.588 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.588 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.588 * [taylor]: Taking taylor expansion of 1.0 in n
20.588 * [backup-simplify]: Simplify 1.0 into 1.0
20.588 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.588 * [taylor]: Taking taylor expansion of 2.0 in n
20.588 * [backup-simplify]: Simplify 2.0 into 2.0
20.588 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.589 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.590 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.591 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
20.592 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
20.593 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))
20.594 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))
20.596 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.597 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))
20.598 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))
20.600 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
20.600 * [backup-simplify]: Simplify 0 into 0
20.601 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
20.601 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
20.603 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0
20.604 * [backup-simplify]: Simplify (- 0) into 0
20.604 * [backup-simplify]: Simplify (+ 0 0) into 0
20.605 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0
20.606 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0
20.607 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
20.608 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
20.611 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
20.614 * [backup-simplify]: Simplify (+ (* 0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5)))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))
20.619 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))
20.620 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))))) in n
20.620 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))) in n
20.620 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n
20.620 * [taylor]: Taking taylor expansion of +nan.0 in n
20.620 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.620 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
20.620 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
20.620 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
20.620 * [taylor]: Taking taylor expansion of 0.5 in n
20.620 * [backup-simplify]: Simplify 0.5 into 0.5
20.620 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
20.620 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
20.620 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.620 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.620 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.620 * [taylor]: Taking taylor expansion of 1.0 in n
20.620 * [backup-simplify]: Simplify 1.0 into 1.0
20.620 * [taylor]: Taking taylor expansion of (log PI) in n
20.620 * [taylor]: Taking taylor expansion of PI in n
20.620 * [backup-simplify]: Simplify PI into PI
20.621 * [backup-simplify]: Simplify (log PI) into (log PI)
20.621 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.623 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.623 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
20.623 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.623 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.623 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.623 * [taylor]: Taking taylor expansion of 1.0 in n
20.623 * [backup-simplify]: Simplify 1.0 into 1.0
20.623 * [taylor]: Taking taylor expansion of (log n) in n
20.623 * [taylor]: Taking taylor expansion of n in n
20.623 * [backup-simplify]: Simplify 0 into 0
20.623 * [backup-simplify]: Simplify 1 into 1
20.624 * [backup-simplify]: Simplify (log 1) into 0
20.624 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.624 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.624 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.624 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.624 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.624 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.624 * [taylor]: Taking taylor expansion of 1.0 in n
20.624 * [backup-simplify]: Simplify 1.0 into 1.0
20.624 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.624 * [taylor]: Taking taylor expansion of 2.0 in n
20.624 * [backup-simplify]: Simplify 2.0 into 2.0
20.625 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.626 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.627 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.628 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
20.629 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
20.630 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))
20.632 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))
20.634 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.634 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))))) in n
20.634 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n
20.634 * [taylor]: Taking taylor expansion of +nan.0 in n
20.634 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.634 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n
20.634 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
20.634 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
20.634 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
20.634 * [taylor]: Taking taylor expansion of 0.5 in n
20.634 * [backup-simplify]: Simplify 0.5 into 0.5
20.634 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
20.634 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
20.634 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.634 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.634 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.634 * [taylor]: Taking taylor expansion of 1.0 in n
20.634 * [backup-simplify]: Simplify 1.0 into 1.0
20.635 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.635 * [taylor]: Taking taylor expansion of 2.0 in n
20.635 * [backup-simplify]: Simplify 2.0 into 2.0
20.635 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.637 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.638 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.638 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
20.638 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.638 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.638 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.638 * [taylor]: Taking taylor expansion of 1.0 in n
20.638 * [backup-simplify]: Simplify 1.0 into 1.0
20.638 * [taylor]: Taking taylor expansion of (log PI) in n
20.639 * [taylor]: Taking taylor expansion of PI in n
20.639 * [backup-simplify]: Simplify PI into PI
20.639 * [backup-simplify]: Simplify (log PI) into (log PI)
20.640 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.642 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.642 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.642 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.642 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.642 * [taylor]: Taking taylor expansion of 1.0 in n
20.642 * [backup-simplify]: Simplify 1.0 into 1.0
20.642 * [taylor]: Taking taylor expansion of (log n) in n
20.642 * [taylor]: Taking taylor expansion of n in n
20.642 * [backup-simplify]: Simplify 0 into 0
20.642 * [backup-simplify]: Simplify 1 into 1
20.643 * [backup-simplify]: Simplify (log 1) into 0
20.643 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.643 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.643 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.644 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
20.645 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)
20.646 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))
20.648 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))
20.649 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.649 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
20.649 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.649 * [taylor]: Taking taylor expansion of 2.0 in n
20.650 * [backup-simplify]: Simplify 2.0 into 2.0
20.650 * [taylor]: Taking taylor expansion of (* n PI) in n
20.650 * [taylor]: Taking taylor expansion of n in n
20.650 * [backup-simplify]: Simplify 0 into 0
20.650 * [backup-simplify]: Simplify 1 into 1
20.650 * [taylor]: Taking taylor expansion of PI in n
20.650 * [backup-simplify]: Simplify PI into PI
20.650 * [backup-simplify]: Simplify (* 0 PI) into 0
20.651 * [backup-simplify]: Simplify (* 2.0 0) into 0
20.652 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.654 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
20.655 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.656 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))
20.658 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.660 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))
20.663 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
20.665 * [backup-simplify]: Simplify (- (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))
20.670 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))
20.676 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))
20.682 * [backup-simplify]: Simplify (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))
20.684 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0
20.685 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0
20.686 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0
20.688 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
20.688 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.688 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0
20.689 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0
20.690 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0
20.692 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
20.693 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0
20.694 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
20.696 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0
20.697 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1)))) 1) into 0
20.699 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)))) into 0
20.701 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
20.703 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0
20.703 * [backup-simplify]: Simplify (- 0) into 0
20.703 * [backup-simplify]: Simplify 0 into 0
20.703 * [backup-simplify]: Simplify 0 into 0
20.704 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
20.706 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
20.709 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0
20.710 * [backup-simplify]: Simplify (- 0) into 0
20.710 * [backup-simplify]: Simplify (+ 0 0) into 0
20.711 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0
20.713 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0
20.715 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
20.720 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
20.725 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
20.730 * [backup-simplify]: Simplify (+ (* 0 (* -0.020833333333333332 (* (pow (log (* 2.0 (* n PI))) 3) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* 0.125 (* (pow (log (* 2.0 (* n PI))) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (+ (* +nan.0 (* -0.5 (* (log (* 2.0 (* n PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) (* +nan.0 (pow (* 2.0 (* n PI)) 0.5))))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))
20.741 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))) (+ (* 0 (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))
20.742 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n
20.742 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n
20.742 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n
20.742 * [taylor]: Taking taylor expansion of +nan.0 in n
20.742 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.742 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n
20.742 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n
20.742 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n
20.742 * [taylor]: Taking taylor expansion of 0.5 in n
20.742 * [backup-simplify]: Simplify 0.5 into 0.5
20.742 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n
20.742 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n
20.742 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.742 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.742 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.742 * [taylor]: Taking taylor expansion of 1.0 in n
20.742 * [backup-simplify]: Simplify 1.0 into 1.0
20.742 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.742 * [taylor]: Taking taylor expansion of 2.0 in n
20.742 * [backup-simplify]: Simplify 2.0 into 2.0
20.743 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.744 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.745 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.745 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n
20.745 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.745 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.745 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.745 * [taylor]: Taking taylor expansion of 1.0 in n
20.745 * [backup-simplify]: Simplify 1.0 into 1.0
20.745 * [taylor]: Taking taylor expansion of (log n) in n
20.745 * [taylor]: Taking taylor expansion of n in n
20.745 * [backup-simplify]: Simplify 0 into 0
20.745 * [backup-simplify]: Simplify 1 into 1
20.746 * [backup-simplify]: Simplify (log 1) into 0
20.746 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.746 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.746 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.746 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.746 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.747 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.747 * [taylor]: Taking taylor expansion of 1.0 in n
20.747 * [backup-simplify]: Simplify 1.0 into 1.0
20.747 * [taylor]: Taking taylor expansion of (log PI) in n
20.747 * [taylor]: Taking taylor expansion of PI in n
20.747 * [backup-simplify]: Simplify PI into PI
20.747 * [backup-simplify]: Simplify (log PI) into (log PI)
20.748 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.750 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.751 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
20.752 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)
20.754 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))
20.755 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))
20.756 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.757 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n
20.757 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n
20.757 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n
20.757 * [taylor]: Taking taylor expansion of +nan.0 in n
20.757 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.757 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n
20.757 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
20.757 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
20.757 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
20.757 * [taylor]: Taking taylor expansion of 0.5 in n
20.757 * [backup-simplify]: Simplify 0.5 into 0.5
20.757 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
20.757 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
20.757 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.757 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.757 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.757 * [taylor]: Taking taylor expansion of 1.0 in n
20.757 * [backup-simplify]: Simplify 1.0 into 1.0
20.757 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.757 * [taylor]: Taking taylor expansion of 2.0 in n
20.757 * [backup-simplify]: Simplify 2.0 into 2.0
20.758 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.759 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.760 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.760 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
20.760 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.760 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.760 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.760 * [taylor]: Taking taylor expansion of 1.0 in n
20.760 * [backup-simplify]: Simplify 1.0 into 1.0
20.760 * [taylor]: Taking taylor expansion of (log PI) in n
20.760 * [taylor]: Taking taylor expansion of PI in n
20.760 * [backup-simplify]: Simplify PI into PI
20.761 * [backup-simplify]: Simplify (log PI) into (log PI)
20.762 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.764 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.764 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.764 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.764 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.764 * [taylor]: Taking taylor expansion of 1.0 in n
20.764 * [backup-simplify]: Simplify 1.0 into 1.0
20.764 * [taylor]: Taking taylor expansion of (log n) in n
20.764 * [taylor]: Taking taylor expansion of n in n
20.764 * [backup-simplify]: Simplify 0 into 0
20.764 * [backup-simplify]: Simplify 1 into 1
20.764 * [backup-simplify]: Simplify (log 1) into 0
20.765 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.765 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.765 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.766 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
20.767 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)
20.768 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))
20.770 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))
20.771 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.771 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
20.771 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.771 * [taylor]: Taking taylor expansion of 2.0 in n
20.771 * [backup-simplify]: Simplify 2.0 into 2.0
20.771 * [taylor]: Taking taylor expansion of (* n PI) in n
20.771 * [taylor]: Taking taylor expansion of n in n
20.771 * [backup-simplify]: Simplify 0 into 0
20.771 * [backup-simplify]: Simplify 1 into 1
20.771 * [taylor]: Taking taylor expansion of PI in n
20.771 * [backup-simplify]: Simplify PI into PI
20.772 * [backup-simplify]: Simplify (* 0 PI) into 0
20.772 * [backup-simplify]: Simplify (* 2.0 0) into 0
20.774 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.775 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
20.776 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.776 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n
20.776 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n
20.776 * [taylor]: Taking taylor expansion of +nan.0 in n
20.777 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.777 * [taylor]: Taking taylor expansion of (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n
20.777 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) in n
20.777 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))))) in n
20.777 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))))) in n
20.777 * [taylor]: Taking taylor expansion of 0.5 in n
20.777 * [backup-simplify]: Simplify 0.5 into 0.5
20.777 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) in n
20.777 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) in n
20.777 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
20.777 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
20.777 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
20.777 * [taylor]: Taking taylor expansion of 1.0 in n
20.777 * [backup-simplify]: Simplify 1.0 into 1.0
20.777 * [taylor]: Taking taylor expansion of (log 2.0) in n
20.777 * [taylor]: Taking taylor expansion of 2.0 in n
20.777 * [backup-simplify]: Simplify 2.0 into 2.0
20.777 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
20.778 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
20.780 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
20.780 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (pow n 1.0)) in n
20.780 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
20.780 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
20.780 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
20.780 * [taylor]: Taking taylor expansion of 1.0 in n
20.780 * [backup-simplify]: Simplify 1.0 into 1.0
20.780 * [taylor]: Taking taylor expansion of (log PI) in n
20.780 * [taylor]: Taking taylor expansion of PI in n
20.780 * [backup-simplify]: Simplify PI into PI
20.780 * [backup-simplify]: Simplify (log PI) into (log PI)
20.782 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
20.784 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
20.784 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
20.784 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
20.784 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
20.784 * [taylor]: Taking taylor expansion of 1.0 in n
20.784 * [backup-simplify]: Simplify 1.0 into 1.0
20.784 * [taylor]: Taking taylor expansion of (log n) in n
20.784 * [taylor]: Taking taylor expansion of n in n
20.784 * [backup-simplify]: Simplify 0 into 0
20.784 * [backup-simplify]: Simplify 1 into 1
20.785 * [backup-simplify]: Simplify (log 1) into 0
20.785 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
20.785 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
20.785 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
20.786 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow n 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
20.787 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)
20.788 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))
20.790 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))
20.791 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
20.791 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n
20.791 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
20.791 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
20.791 * [taylor]: Taking taylor expansion of 2.0 in n
20.792 * [backup-simplify]: Simplify 2.0 into 2.0
20.792 * [taylor]: Taking taylor expansion of (* n PI) in n
20.792 * [taylor]: Taking taylor expansion of n in n
20.792 * [backup-simplify]: Simplify 0 into 0
20.792 * [backup-simplify]: Simplify 1 into 1
20.792 * [taylor]: Taking taylor expansion of PI in n
20.792 * [backup-simplify]: Simplify PI into PI
20.792 * [backup-simplify]: Simplify (* 0 PI) into 0
20.793 * [backup-simplify]: Simplify (* 2.0 0) into 0
20.794 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
20.796 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
20.797 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.798 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.800 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))
20.801 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.804 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))
20.806 * [backup-simplify]: Simplify (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
20.808 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.809 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
20.812 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2)
20.815 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))
20.817 * [backup-simplify]: Simplify (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
20.820 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (+ (log (* 2.0 PI)) (log n)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))
20.832 * [backup-simplify]: Simplify (+ (* +nan.0 (* (+ (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))))))))))))
20.847 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))
20.863 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))
20.886 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))
20.902 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))))))))))))
20.929 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (log n) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (* (log (* 2.0 PI)) (log n)) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (log n) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))))))))))))
20.931 * [backup-simplify]: Simplify (/ 1.0 (/ (sqrt (/ 1 k)) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)))) into (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))))
20.931 * [approximate]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in (k n) around 0
20.931 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in n
20.931 * [taylor]: Taking taylor expansion of 1.0 in n
20.931 * [backup-simplify]: Simplify 1.0 into 1.0
20.931 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
20.931 * [taylor]: Taking taylor expansion of (sqrt k) in n
20.931 * [taylor]: Taking taylor expansion of k in n
20.931 * [backup-simplify]: Simplify k into k
20.932 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
20.932 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
20.932 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
20.932 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
20.932 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
20.932 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
20.932 * [taylor]: Taking taylor expansion of 0.5 in n
20.932 * [backup-simplify]: Simplify 0.5 into 0.5
20.932 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
20.932 * [taylor]: Taking taylor expansion of 1.0 in n
20.932 * [backup-simplify]: Simplify 1.0 into 1.0
20.932 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.932 * [taylor]: Taking taylor expansion of k in n
20.932 * [backup-simplify]: Simplify k into k
20.932 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.932 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
20.932 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.932 * [taylor]: Taking taylor expansion of 2.0 in n
20.932 * [backup-simplify]: Simplify 2.0 into 2.0
20.932 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.932 * [taylor]: Taking taylor expansion of PI in n
20.932 * [backup-simplify]: Simplify PI into PI
20.932 * [taylor]: Taking taylor expansion of n in n
20.932 * [backup-simplify]: Simplify 0 into 0
20.932 * [backup-simplify]: Simplify 1 into 1
20.933 * [backup-simplify]: Simplify (/ PI 1) into PI
20.933 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.935 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.935 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.935 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
20.935 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
20.936 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.938 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
20.939 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
20.939 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
20.939 * [taylor]: Taking taylor expansion of 1.0 in k
20.939 * [backup-simplify]: Simplify 1.0 into 1.0
20.939 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
20.939 * [taylor]: Taking taylor expansion of (sqrt k) in k
20.939 * [taylor]: Taking taylor expansion of k in k
20.939 * [backup-simplify]: Simplify 0 into 0
20.939 * [backup-simplify]: Simplify 1 into 1
20.940 * [backup-simplify]: Simplify (sqrt 0) into 0
20.941 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.941 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
20.941 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
20.941 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
20.941 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
20.941 * [taylor]: Taking taylor expansion of 0.5 in k
20.941 * [backup-simplify]: Simplify 0.5 into 0.5
20.941 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
20.941 * [taylor]: Taking taylor expansion of 1.0 in k
20.942 * [backup-simplify]: Simplify 1.0 into 1.0
20.942 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.942 * [taylor]: Taking taylor expansion of k in k
20.942 * [backup-simplify]: Simplify 0 into 0
20.942 * [backup-simplify]: Simplify 1 into 1
20.942 * [backup-simplify]: Simplify (/ 1 1) into 1
20.942 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
20.942 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
20.942 * [taylor]: Taking taylor expansion of 2.0 in k
20.942 * [backup-simplify]: Simplify 2.0 into 2.0
20.942 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.942 * [taylor]: Taking taylor expansion of PI in k
20.942 * [backup-simplify]: Simplify PI into PI
20.942 * [taylor]: Taking taylor expansion of n in k
20.942 * [backup-simplify]: Simplify n into n
20.942 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.942 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
20.943 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
20.943 * [backup-simplify]: Simplify (- 1) into -1
20.943 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.944 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
20.944 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
20.944 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
20.944 * [taylor]: Taking taylor expansion of (* 1.0 (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))))) in k
20.944 * [taylor]: Taking taylor expansion of 1.0 in k
20.944 * [backup-simplify]: Simplify 1.0 into 1.0
20.944 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
20.944 * [taylor]: Taking taylor expansion of (sqrt k) in k
20.944 * [taylor]: Taking taylor expansion of k in k
20.944 * [backup-simplify]: Simplify 0 into 0
20.945 * [backup-simplify]: Simplify 1 into 1
20.945 * [backup-simplify]: Simplify (sqrt 0) into 0
20.946 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
20.946 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
20.946 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
20.946 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
20.946 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
20.946 * [taylor]: Taking taylor expansion of 0.5 in k
20.946 * [backup-simplify]: Simplify 0.5 into 0.5
20.946 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
20.947 * [taylor]: Taking taylor expansion of 1.0 in k
20.947 * [backup-simplify]: Simplify 1.0 into 1.0
20.947 * [taylor]: Taking taylor expansion of (/ 1 k) in k
20.947 * [taylor]: Taking taylor expansion of k in k
20.947 * [backup-simplify]: Simplify 0 into 0
20.947 * [backup-simplify]: Simplify 1 into 1
20.947 * [backup-simplify]: Simplify (/ 1 1) into 1
20.947 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
20.947 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
20.947 * [taylor]: Taking taylor expansion of 2.0 in k
20.947 * [backup-simplify]: Simplify 2.0 into 2.0
20.947 * [taylor]: Taking taylor expansion of (/ PI n) in k
20.947 * [taylor]: Taking taylor expansion of PI in k
20.947 * [backup-simplify]: Simplify PI into PI
20.947 * [taylor]: Taking taylor expansion of n in k
20.947 * [backup-simplify]: Simplify n into n
20.947 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
20.947 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
20.948 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
20.948 * [backup-simplify]: Simplify (- 1) into -1
20.948 * [backup-simplify]: Simplify (+ 0 -1) into -1
20.949 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
20.949 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
20.949 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
20.949 * [backup-simplify]: Simplify (* 0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) into 0
20.950 * [backup-simplify]: Simplify (* 1.0 0) into 0
20.950 * [taylor]: Taking taylor expansion of 0 in n
20.950 * [backup-simplify]: Simplify 0 into 0
20.950 * [backup-simplify]: Simplify 0 into 0
20.951 * [backup-simplify]: Simplify (+ (* 0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))
20.951 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))
20.952 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
20.952 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
20.952 * [taylor]: Taking taylor expansion of +nan.0 in n
20.952 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.952 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
20.952 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
20.952 * [taylor]: Taking taylor expansion of 0.5 in n
20.952 * [backup-simplify]: Simplify 0.5 into 0.5
20.952 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
20.952 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
20.952 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.952 * [taylor]: Taking taylor expansion of 2.0 in n
20.952 * [backup-simplify]: Simplify 2.0 into 2.0
20.952 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.952 * [taylor]: Taking taylor expansion of PI in n
20.952 * [backup-simplify]: Simplify PI into PI
20.952 * [taylor]: Taking taylor expansion of n in n
20.952 * [backup-simplify]: Simplify 0 into 0
20.952 * [backup-simplify]: Simplify 1 into 1
20.953 * [backup-simplify]: Simplify (/ PI 1) into PI
20.953 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.954 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.954 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
20.954 * [taylor]: Taking taylor expansion of 1.0 in n
20.954 * [backup-simplify]: Simplify 1.0 into 1.0
20.954 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.954 * [taylor]: Taking taylor expansion of k in n
20.954 * [backup-simplify]: Simplify k into k
20.954 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.956 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.956 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.956 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
20.957 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
20.958 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
20.959 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
20.960 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
20.961 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
20.963 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
20.963 * [backup-simplify]: Simplify 0 into 0
20.966 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
20.967 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))
20.968 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))
20.968 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
20.968 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
20.968 * [taylor]: Taking taylor expansion of +nan.0 in n
20.968 * [backup-simplify]: Simplify +nan.0 into +nan.0
20.968 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
20.968 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
20.968 * [taylor]: Taking taylor expansion of 0.5 in n
20.968 * [backup-simplify]: Simplify 0.5 into 0.5
20.968 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
20.968 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
20.968 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
20.968 * [taylor]: Taking taylor expansion of 2.0 in n
20.968 * [backup-simplify]: Simplify 2.0 into 2.0
20.968 * [taylor]: Taking taylor expansion of (/ PI n) in n
20.968 * [taylor]: Taking taylor expansion of PI in n
20.968 * [backup-simplify]: Simplify PI into PI
20.968 * [taylor]: Taking taylor expansion of n in n
20.968 * [backup-simplify]: Simplify 0 into 0
20.968 * [backup-simplify]: Simplify 1 into 1
20.969 * [backup-simplify]: Simplify (/ PI 1) into PI
20.969 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
20.970 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
20.970 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
20.970 * [taylor]: Taking taylor expansion of 1.0 in n
20.970 * [backup-simplify]: Simplify 1.0 into 1.0
20.970 * [taylor]: Taking taylor expansion of (/ 1 k) in n
20.970 * [taylor]: Taking taylor expansion of k in n
20.970 * [backup-simplify]: Simplify k into k
20.970 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
20.972 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.972 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
20.972 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
20.973 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
20.974 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
20.975 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
20.980 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
20.981 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
20.983 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
20.984 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
20.984 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
20.985 * [backup-simplify]: Simplify (- 0) into 0
20.985 * [backup-simplify]: Simplify (+ 0 0) into 0
20.986 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
20.986 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
20.988 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
20.989 * [backup-simplify]: Simplify (+ (* (- (log (* 2.0 PI)) (log n)) 0) (* 0 (- 1.0 (/ 1 k)))) into 0
20.991 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into 0
20.993 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
20.994 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into 0
20.995 * [backup-simplify]: Simplify (- 0) into 0
20.995 * [backup-simplify]: Simplify 0 into 0
20.995 * [backup-simplify]: Simplify 0 into 0
20.998 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
21.000 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* +nan.0 0) (+ (* +nan.0 0) (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))
21.001 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))))
21.001 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))))) in n
21.001 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))) in n
21.001 * [taylor]: Taking taylor expansion of +nan.0 in n
21.001 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.001 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))))) in n
21.001 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))) in n
21.001 * [taylor]: Taking taylor expansion of 0.5 in n
21.001 * [backup-simplify]: Simplify 0.5 into 0.5
21.001 * [taylor]: Taking taylor expansion of (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k))) in n
21.001 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
21.001 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
21.001 * [taylor]: Taking taylor expansion of 2.0 in n
21.001 * [backup-simplify]: Simplify 2.0 into 2.0
21.001 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.002 * [taylor]: Taking taylor expansion of PI in n
21.002 * [backup-simplify]: Simplify PI into PI
21.002 * [taylor]: Taking taylor expansion of n in n
21.002 * [backup-simplify]: Simplify 0 into 0
21.002 * [backup-simplify]: Simplify 1 into 1
21.002 * [backup-simplify]: Simplify (/ PI 1) into PI
21.003 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
21.004 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
21.004 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
21.004 * [taylor]: Taking taylor expansion of 1.0 in n
21.004 * [backup-simplify]: Simplify 1.0 into 1.0
21.004 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.004 * [taylor]: Taking taylor expansion of k in n
21.004 * [backup-simplify]: Simplify k into k
21.004 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.005 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
21.005 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
21.005 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
21.006 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) into (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))
21.007 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
21.009 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
21.010 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))
21.011 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
21.012 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))))
21.016 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2))))))))
21.017 * [backup-simplify]: Simplify (/ 1.0 (/ (sqrt (/ 1 (- k))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))))
21.017 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0
21.017 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
21.017 * [taylor]: Taking taylor expansion of 1.0 in n
21.017 * [backup-simplify]: Simplify 1.0 into 1.0
21.017 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
21.017 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
21.017 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
21.017 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
21.017 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
21.017 * [taylor]: Taking taylor expansion of 0.5 in n
21.018 * [backup-simplify]: Simplify 0.5 into 0.5
21.018 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.018 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.018 * [taylor]: Taking taylor expansion of k in n
21.018 * [backup-simplify]: Simplify k into k
21.018 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.018 * [taylor]: Taking taylor expansion of 1.0 in n
21.018 * [backup-simplify]: Simplify 1.0 into 1.0
21.018 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.018 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.018 * [taylor]: Taking taylor expansion of -2.0 in n
21.018 * [backup-simplify]: Simplify -2.0 into -2.0
21.018 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.018 * [taylor]: Taking taylor expansion of PI in n
21.018 * [backup-simplify]: Simplify PI into PI
21.018 * [taylor]: Taking taylor expansion of n in n
21.018 * [backup-simplify]: Simplify 0 into 0
21.018 * [backup-simplify]: Simplify 1 into 1
21.018 * [backup-simplify]: Simplify (/ PI 1) into PI
21.019 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.024 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.024 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.025 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
21.026 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.027 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
21.028 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
21.028 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
21.028 * [taylor]: Taking taylor expansion of (/ -1 k) in n
21.028 * [taylor]: Taking taylor expansion of -1 in n
21.029 * [backup-simplify]: Simplify -1 into -1
21.029 * [taylor]: Taking taylor expansion of k in n
21.029 * [backup-simplify]: Simplify k into k
21.029 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
21.029 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
21.029 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
21.029 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
21.030 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (sqrt (/ -1 k)))
21.030 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
21.030 * [taylor]: Taking taylor expansion of 1.0 in k
21.030 * [backup-simplify]: Simplify 1.0 into 1.0
21.030 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
21.030 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
21.030 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
21.031 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
21.031 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
21.031 * [taylor]: Taking taylor expansion of 0.5 in k
21.031 * [backup-simplify]: Simplify 0.5 into 0.5
21.031 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
21.031 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.031 * [taylor]: Taking taylor expansion of k in k
21.031 * [backup-simplify]: Simplify 0 into 0
21.031 * [backup-simplify]: Simplify 1 into 1
21.031 * [backup-simplify]: Simplify (/ 1 1) into 1
21.031 * [taylor]: Taking taylor expansion of 1.0 in k
21.031 * [backup-simplify]: Simplify 1.0 into 1.0
21.031 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
21.031 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
21.031 * [taylor]: Taking taylor expansion of -2.0 in k
21.031 * [backup-simplify]: Simplify -2.0 into -2.0
21.032 * [taylor]: Taking taylor expansion of (/ PI n) in k
21.032 * [taylor]: Taking taylor expansion of PI in k
21.032 * [backup-simplify]: Simplify PI into PI
21.032 * [taylor]: Taking taylor expansion of n in k
21.032 * [backup-simplify]: Simplify n into n
21.032 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
21.032 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
21.032 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
21.032 * [backup-simplify]: Simplify (+ 1 0) into 1
21.033 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
21.033 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
21.033 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
21.033 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
21.033 * [taylor]: Taking taylor expansion of (/ -1 k) in k
21.033 * [taylor]: Taking taylor expansion of -1 in k
21.033 * [backup-simplify]: Simplify -1 into -1
21.033 * [taylor]: Taking taylor expansion of k in k
21.033 * [backup-simplify]: Simplify 0 into 0
21.033 * [backup-simplify]: Simplify 1 into 1
21.034 * [backup-simplify]: Simplify (/ -1 1) into -1
21.034 * [backup-simplify]: Simplify (sqrt 0) into 0
21.035 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
21.035 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))
21.035 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
21.036 * [taylor]: Taking taylor expansion of 1.0 in k
21.036 * [backup-simplify]: Simplify 1.0 into 1.0
21.036 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
21.036 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
21.036 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
21.036 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
21.036 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
21.036 * [taylor]: Taking taylor expansion of 0.5 in k
21.036 * [backup-simplify]: Simplify 0.5 into 0.5
21.036 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
21.036 * [taylor]: Taking taylor expansion of (/ 1 k) in k
21.036 * [taylor]: Taking taylor expansion of k in k
21.036 * [backup-simplify]: Simplify 0 into 0
21.036 * [backup-simplify]: Simplify 1 into 1
21.036 * [backup-simplify]: Simplify (/ 1 1) into 1
21.036 * [taylor]: Taking taylor expansion of 1.0 in k
21.036 * [backup-simplify]: Simplify 1.0 into 1.0
21.036 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
21.036 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
21.036 * [taylor]: Taking taylor expansion of -2.0 in k
21.036 * [backup-simplify]: Simplify -2.0 into -2.0
21.036 * [taylor]: Taking taylor expansion of (/ PI n) in k
21.036 * [taylor]: Taking taylor expansion of PI in k
21.036 * [backup-simplify]: Simplify PI into PI
21.036 * [taylor]: Taking taylor expansion of n in k
21.037 * [backup-simplify]: Simplify n into n
21.037 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
21.037 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
21.037 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
21.037 * [backup-simplify]: Simplify (+ 1 0) into 1
21.038 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
21.038 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
21.038 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
21.038 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
21.038 * [taylor]: Taking taylor expansion of (/ -1 k) in k
21.038 * [taylor]: Taking taylor expansion of -1 in k
21.038 * [backup-simplify]: Simplify -1 into -1
21.038 * [taylor]: Taking taylor expansion of k in k
21.038 * [backup-simplify]: Simplify 0 into 0
21.038 * [backup-simplify]: Simplify 1 into 1
21.038 * [backup-simplify]: Simplify (/ -1 1) into -1
21.039 * [backup-simplify]: Simplify (sqrt 0) into 0
21.040 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
21.040 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))
21.041 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))
21.041 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
21.041 * [taylor]: Taking taylor expansion of +nan.0 in n
21.041 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.041 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
21.041 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
21.041 * [taylor]: Taking taylor expansion of 0.5 in n
21.041 * [backup-simplify]: Simplify 0.5 into 0.5
21.041 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
21.041 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.041 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.041 * [taylor]: Taking taylor expansion of k in n
21.041 * [backup-simplify]: Simplify k into k
21.041 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.041 * [taylor]: Taking taylor expansion of 1.0 in n
21.041 * [backup-simplify]: Simplify 1.0 into 1.0
21.041 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.041 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.041 * [taylor]: Taking taylor expansion of -2.0 in n
21.041 * [backup-simplify]: Simplify -2.0 into -2.0
21.041 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.041 * [taylor]: Taking taylor expansion of PI in n
21.041 * [backup-simplify]: Simplify PI into PI
21.041 * [taylor]: Taking taylor expansion of n in n
21.041 * [backup-simplify]: Simplify 0 into 0
21.041 * [backup-simplify]: Simplify 1 into 1
21.042 * [backup-simplify]: Simplify (/ PI 1) into PI
21.042 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.043 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.043 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.045 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.046 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
21.047 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
21.048 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
21.049 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
21.050 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
21.051 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
21.054 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
21.055 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))
21.056 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))
21.056 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
21.056 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
21.056 * [taylor]: Taking taylor expansion of +nan.0 in n
21.056 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.056 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
21.056 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
21.056 * [taylor]: Taking taylor expansion of 0.5 in n
21.056 * [backup-simplify]: Simplify 0.5 into 0.5
21.056 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
21.056 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.056 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.056 * [taylor]: Taking taylor expansion of k in n
21.056 * [backup-simplify]: Simplify k into k
21.056 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.056 * [taylor]: Taking taylor expansion of 1.0 in n
21.056 * [backup-simplify]: Simplify 1.0 into 1.0
21.056 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.057 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.057 * [taylor]: Taking taylor expansion of -2.0 in n
21.057 * [backup-simplify]: Simplify -2.0 into -2.0
21.057 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.057 * [taylor]: Taking taylor expansion of PI in n
21.057 * [backup-simplify]: Simplify PI into PI
21.057 * [taylor]: Taking taylor expansion of n in n
21.057 * [backup-simplify]: Simplify 0 into 0
21.057 * [backup-simplify]: Simplify 1 into 1
21.057 * [backup-simplify]: Simplify (/ PI 1) into PI
21.058 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.059 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.059 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.060 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.062 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
21.063 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
21.064 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
21.065 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
21.066 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
21.068 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
21.068 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
21.069 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
21.071 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
21.071 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
21.071 * [backup-simplify]: Simplify (+ 0 0) into 0
21.073 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.074 * [backup-simplify]: Simplify (+ (* (+ (/ 1 k) 1.0) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
21.075 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into 0
21.077 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
21.079 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into 0
21.079 * [backup-simplify]: Simplify 0 into 0
21.080 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
21.083 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
21.085 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))
21.086 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))))
21.086 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))))) in n
21.086 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))) in n
21.086 * [taylor]: Taking taylor expansion of +nan.0 in n
21.086 * [backup-simplify]: Simplify +nan.0 into +nan.0
21.086 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))))) in n
21.086 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))) in n
21.086 * [taylor]: Taking taylor expansion of 0.5 in n
21.086 * [backup-simplify]: Simplify 0.5 into 0.5
21.086 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n)))) in n
21.086 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
21.086 * [taylor]: Taking taylor expansion of (/ 1 k) in n
21.086 * [taylor]: Taking taylor expansion of k in n
21.086 * [backup-simplify]: Simplify k into k
21.086 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
21.086 * [taylor]: Taking taylor expansion of 1.0 in n
21.086 * [backup-simplify]: Simplify 1.0 into 1.0
21.086 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
21.086 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
21.086 * [taylor]: Taking taylor expansion of -2.0 in n
21.086 * [backup-simplify]: Simplify -2.0 into -2.0
21.086 * [taylor]: Taking taylor expansion of (/ PI n) in n
21.086 * [taylor]: Taking taylor expansion of PI in n
21.086 * [backup-simplify]: Simplify PI into PI
21.086 * [taylor]: Taking taylor expansion of n in n
21.086 * [backup-simplify]: Simplify 0 into 0
21.086 * [backup-simplify]: Simplify 1 into 1
21.087 * [backup-simplify]: Simplify (/ PI 1) into PI
21.088 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
21.089 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
21.089 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
21.090 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
21.091 * [backup-simplify]: Simplify (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) into (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))
21.092 * [backup-simplify]: Simplify (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
21.093 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
21.094 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))
21.096 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
21.097 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))))
21.101 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))))))
21.101 * * * [progress]: simplifying candidates
21.114 * [simplify]: Simplifying:
  (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (pow (* (* 2.0 PI) n) (/ 1.0 2.0))
  (pow (* (* 2.0 PI) n) (/ k 2.0))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) 1)
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (- (log (sqrt k)) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (- (log (sqrt k)) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (- (log (sqrt k)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (- (log (sqrt k)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (- (log (sqrt k)) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (log (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (exp (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (* (sqrt k) (sqrt k)) (sqrt k)) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (* (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- (sqrt k))
  (- (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (cbrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (cbrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1)
  (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt (cbrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt (cbrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (* (cbrt k) (cbrt k))) 1)
  (/ (sqrt (cbrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
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  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) 1))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ (sqrt 1.0) (/ 1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ (sqrt k) (pow n (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ 1 (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ (sqrt 1.0) (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ 1 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ (sqrt k) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ 1 1))
  (/ (sqrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ 1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ (sqrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ (sqrt 1.0) 1)
  (/ (sqrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (/ 1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
  (/ (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (/ 1 (* (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (cbrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (cbrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1))
  (/ 1.0 (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (cbrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ (sqrt (cbrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) 1))
  (/ 1.0 (/ (sqrt (cbrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt (cbrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1 (/ (sqrt 1) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt k) (pow n (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt 1) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt 1) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt k) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt 1) 1))
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt 1) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ (sqrt (sqrt k)) 1))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1 (/ 1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt k) (pow n (/ (- 1.0 k) 2.0))))
  (/ 1 (/ 1 (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ 1 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt k) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (/ 1 1))
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ 1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1 1)
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (sqrt k))
  (/ 1.0 (/ 1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
  (/ 1.0 (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (/ 1 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1.0)
  (/ 1.0 (* (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) 1))
  (/ 1.0 (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (* (cbrt k) (cbrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ (sqrt (* (cbrt k) (cbrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (* (cbrt k) (cbrt k))) 1))
  (/ 1.0 (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (sqrt k)) 1))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt 1) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt 1) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ (sqrt 1) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt 1) 1))
  (/ 1.0 (/ (sqrt 1) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ (sqrt (sqrt k)) 1))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 (/ 1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ 1 (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (/ 1 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (/ 1 1))
  (/ 1.0 (/ 1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ 1.0 1)
  (/ 1.0 (sqrt k))
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
  (/ (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt 1.0))
  (/ (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt 1.0))
  (/ (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1.0)
  (/ 1.0 (sqrt k))
  (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
  (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (+ (* +nan.0 (* (pow k 2) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log (* 2.0 PI)) 2)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (pow k 3) (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log (* 2.0 PI)) 2)) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (log (* 2.0 PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* k (pow (/ 1 (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (/ 1 (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (log n)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 3) (pow (log n) 2)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (/ 1 (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0)))) 0.5))) (- (* +nan.0 (* (* (pow k 3) (* (log (* 2.0 PI)) (log n))) (pow (/ 1 (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0)))) 0.5))))))))))))))))))))))))
  (- (+ (* +nan.0 (/ 1 (* k (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))))) (- (+ (* +nan.0 (/ 1 (* (pow k 2) (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))))) (- (* +nan.0 (/ 1 (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))))))))))
  (- (+ (* +nan.0 (/ 1 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))))) (- (+ (* +nan.0 (/ 1 (* k (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))) (- (* +nan.0 (/ 1 (* (pow k 2) (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))))))))
  (- (+ (* +nan.0 (* (* (pow k 2) (pow (log (* 2.0 PI)) 2)) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log (* 2.0 PI))) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (* (log (* 2.0 PI)) (log n))) (pow (* (pow PI 1.0) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log (* 2.0 PI))) (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) (- (+ (* +nan.0 (* (* (pow k 2) (pow (log n) 2)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (* (* k (log n)) (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow k 2) (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) (- (* +nan.0 (* k (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k)))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))))))))
21.132 * * [simplify]: iteration 0: 602 enodes
21.580 * * [simplify]: iteration 1: 1682 enodes
22.726 * * [simplify]: iteration complete: 5001 enodes
22.727 * * [simplify]: Extracting #0: cost 275 inf + 0
22.730 * * [simplify]: Extracting #1: cost 942 inf + 43
22.738 * * [simplify]: Extracting #2: cost 1407 inf + 1672
22.755 * * [simplify]: Extracting #3: cost 1449 inf + 42922
22.824 * * [simplify]: Extracting #4: cost 974 inf + 272613
22.954 * * [simplify]: Extracting #5: cost 588 inf + 527279
23.118 * * [simplify]: Extracting #6: cost 510 inf + 631239
23.316 * * [simplify]: Extracting #7: cost 288 inf + 880024
23.566 * * [simplify]: Extracting #8: cost 102 inf + 1084866
23.866 * * [simplify]: Extracting #9: cost 10 inf + 1207747
24.182 * * [simplify]: Extracting #10: cost 2 inf + 1227051
24.515 * * [simplify]: Extracting #11: cost 0 inf + 1231747
24.877 * * [simplify]: Extracting #12: cost 0 inf + 1231267
25.222 * * [simplify]: Extracting #13: cost 0 inf + 1231187
25.584 * [simplify]: Simplified to:
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (pow (* (* 2.0 PI) n) (/ 1.0 2.0))
  (pow (* (* 2.0 PI) n) (/ k 2.0))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* (* 2.0 PI) n) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (sqrt (- 1.0 k)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (* (* 2.0 PI) n)
  (pow (* (* 2.0 PI) n) (/ (/ (+ (sqrt 1.0) (sqrt k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k)))
  (pow (* (* 2.0 PI) n) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* n n) n) (* (* 2.0 (* (* 2.0 PI) (* 2.0 PI))) PI))
  (* (* (* 2.0 PI) (* (* (* 2.0 PI) n) (* (* 2.0 PI) n))) n)
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* 2.0 PI) n) (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (sqrt n) (* 2.0 PI))
  (* 2.0 PI)
  (* n PI)
  (- (log (sqrt k)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (- (log (sqrt k)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (- (log (sqrt k)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (- (log (sqrt k)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (- (log (sqrt k)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (- (log (sqrt k)) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (exp (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (sqrt k) k) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- (sqrt k))
  (- (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (cbrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (cbrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (sqrt k)))
  (/ (cbrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (cbrt (sqrt k)) (cbrt (sqrt k)))
  (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (fabs (cbrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt (cbrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (/ (fabs (cbrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt (cbrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (fabs (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (fabs (cbrt k))
  (/ (sqrt (cbrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (fabs (cbrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt (cbrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (sqrt k))
  (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ 1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt k) (pow n (/ (- 1.0 k) 2.0)))
  (/ (/ 1 (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt k) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  1
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ 1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (sqrt k))
  (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ 1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt k) (pow n (/ (- 1.0 k) 2.0)))
  (/ (/ 1 (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt k) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  1
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ 1 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ 1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ (sqrt k) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt k) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt k) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt k)
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (* 1.0 (* 1.0 1.0)) (* (sqrt k) k)) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (* (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- 1.0)
  (/ (- (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ (cbrt 1.0) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ (cbrt 1.0) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (cbrt 1.0) (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt 1.0) (pow n (/ (- 1.0 k) 2.0))) (cbrt (sqrt k)))
  (* (* (/ (cbrt 1.0) (cbrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (cbrt 1.0) (cbrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (cbrt 1.0) (/ (cbrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k))))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (* (cbrt 1.0) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (cbrt (sqrt k)))
  (* (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (/ (* (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (fabs (cbrt k)))
  (* (/ (cbrt 1.0) (sqrt (cbrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (fabs (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ (cbrt 1.0) (sqrt (cbrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k)))
  (/ (* (cbrt 1.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (cbrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (fabs (cbrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (sqrt k)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (* (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (cbrt 1.0) (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (* (cbrt 1.0) (cbrt 1.0)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt 1.0) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt k))
  (* (cbrt 1.0) (cbrt 1.0))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (* (cbrt 1.0) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt k))
  (* (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (sqrt (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (/ (sqrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (sqrt k)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (* (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (cbrt 1.0) (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (* (cbrt 1.0) (cbrt 1.0)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (cbrt 1.0) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt k))
  (* (cbrt 1.0) (cbrt 1.0))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (* (cbrt 1.0) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt k))
  (* (cbrt 1.0) (cbrt 1.0))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (cbrt 1.0))
  (* (cbrt 1.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (* (* (cbrt 1.0) (cbrt 1.0)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (sqrt k))
  (/ (cbrt 1.0) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (/ (sqrt 1.0) (* (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ (sqrt 1.0) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (* (sqrt 1.0) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (/ (/ (sqrt 1.0) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (sqrt 1.0) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (sqrt k)))
  (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt 1.0) (/ (fabs (cbrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (/ (* (sqrt 1.0) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (fabs (cbrt k)))
  (* (/ (sqrt 1.0) (sqrt (cbrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (sqrt 1.0) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (fabs (cbrt k)))
  (/ (sqrt 1.0) (/ (sqrt (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (fabs (cbrt k)))
  (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (sqrt 1.0) (/ (fabs (cbrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (cbrt k)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (* (sqrt 1.0) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt k)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (* (sqrt 1.0) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (* (sqrt 1.0) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt 1.0) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (sqrt 1.0) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt k))
  (sqrt 1.0)
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (* (sqrt 1.0) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt k)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ (sqrt 1.0) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (* (sqrt 1.0) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (* (sqrt 1.0) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (sqrt 1.0) (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt 1.0) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* (sqrt 1.0) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt k))
  (sqrt 1.0)
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ (sqrt 1.0) (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (sqrt 1.0)
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (sqrt 1.0) (sqrt k))
  (* (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
  (/ (sqrt 1.0) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (/ 1 (* (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1.0 (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ (* 1 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (* (/ 1.0 (cbrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (/ 1 (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ (* 1.0 (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (sqrt k)))
  (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (cbrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (/ (cbrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ 1 (fabs (cbrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (cbrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (/ 1 (fabs (cbrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ 1.0 (sqrt (cbrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ 1 (fabs (cbrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (cbrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (/ 1 (fabs (cbrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (cbrt k)))
  (/ 1 (/ (fabs (cbrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (sqrt (cbrt k)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (/ 1 (sqrt (sqrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ 1.0 (sqrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* 1 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt k)))
  (* (/ 1.0 (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (sqrt (sqrt k)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (* (/ 1.0 (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  1
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
  (* (/ 1 (sqrt (sqrt k))) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ 1.0 (sqrt (sqrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* 1 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (sqrt k)))
  (* (/ 1.0 (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1 (sqrt (sqrt k)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (* (/ 1.0 (sqrt k)) (pow n (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt k) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  1
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  1
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ 1 (sqrt k))
  (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
  (/ 1.0 (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1.0)
  (/ 1.0 (* (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (sqrt (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ 1.0 (* (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (/ (cbrt (sqrt k)) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (/ 1.0 (* (/ (cbrt (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (sqrt k))))
  (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (fabs (cbrt k)))
  (* (* (/ 1.0 (fabs (cbrt k))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ 1.0 (fabs (cbrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (fabs (cbrt k)))
  (/ 1.0 (/ (fabs (cbrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (* 1.0 (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt k)))
  (* (/ 1.0 (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* 1.0 (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* 1.0 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  1.0
  (* 1.0 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (/ (* 1.0 (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt k)))
  (* (/ 1.0 (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))
  (* 1.0 (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* 1.0 (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* 1.0 (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  1.0
  (* 1.0 (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  1.0
  (/ 1.0 (sqrt k))
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
  (/ (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt 1.0))
  (/ (/ (sqrt k) (sqrt 1.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (/ (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1.0)
  (/ 1.0 (sqrt k))
  (+ (* (* 0.125 (* k k)) (+ (* (* (exp (* (log (* (* 2.0 PI) n)) 0.5)) (log (* 2.0 PI))) (log (* 2.0 PI))) (* (* (log n) (exp (* (log (* (* 2.0 PI) n)) 0.5))) (log n)))) (- (+ (exp (* (log (* (* 2.0 PI) n)) 0.5)) (* (* (* k k) (* (* (log n) (exp (* (log (* (* 2.0 PI) n)) 0.5))) (log (* 2.0 PI)))) 0.25)) (* 0.5 (* k (+ (* (exp (* (log (* (* 2.0 PI) n)) 0.5)) (log (* 2.0 PI))) (* (log n) (exp (* (log (* (* 2.0 PI) n)) 0.5))))))))
  (exp (* (* (log (* (* 2.0 PI) n)) (- 1.0 k)) 0.5))
  (exp (* (* 0.5 (- 1.0 k)) (- (log (* -2.0 PI)) (log (/ -1 n)))))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (* (- +nan.0) (* (* k k) (pow (/ (/ 1 (pow PI 1.0)) (* (pow 2.0 1.0) (pow n 1.0))) 0.5))) (+ (* (* +nan.0 (* (* (log (* 2.0 PI)) (log (* 2.0 PI))) (* k (* k k)))) (pow (/ (/ 1 (pow PI 1.0)) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)) (+ (* (- +nan.0) (* (pow (/ (/ 1 (pow PI 1.0)) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) (* k (* k k)))) (- (* (* +nan.0 (* (* (log (* 2.0 PI)) (log (* 2.0 PI))) (* k (* k k)))) (pow (/ (/ 1 (pow PI 1.0)) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)) (- (* (* (* (log (* 2.0 PI)) k) (* k k)) (* (pow (/ (/ 1 (pow PI 1.0)) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) +nan.0)) (- (* (* +nan.0 k) (pow (/ (/ 1 (pow PI 1.0)) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)) (- (* (* +nan.0 (* (log (* 2.0 PI)) (* k k))) (pow (/ (/ 1 (pow PI 1.0)) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)) (- (* (* (log n) (* k (* k k))) (* (pow (/ (/ 1 (pow PI 1.0)) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) +nan.0)) (- (* (pow (/ (/ 1 (pow PI 1.0)) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) (* (* (* (log n) (* k (* k k))) (log n)) +nan.0)) (* +nan.0 (- (* (* (* k k) (pow (/ (/ 1 (pow PI 1.0)) (* (pow 2.0 1.0) (pow n 1.0))) 0.5)) (log n)) (* (* (pow (/ (/ 1 (pow PI 1.0)) (* (pow 2.0 1.0) (pow n 1.0))) 0.5) (* k (* k k))) (* (log (* 2.0 PI)) (log n))))))))))))))
  (+ (/ (- +nan.0) (* k (exp (* (* (log (* (* 2.0 PI) n)) (- 1.0 k)) 0.5)))) (- (/ (/ +nan.0 (* k k)) (exp (* (* (log (* (* 2.0 PI) n)) (- 1.0 k)) 0.5))) (/ +nan.0 (exp (* (* (log (* (* 2.0 PI) n)) (- 1.0 k)) 0.5)))))
  (- (- (/ +nan.0 (exp (* (* 0.5 (- 1.0 k)) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (- (/ (/ +nan.0 (exp (* (* 0.5 (- 1.0 k)) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k) (/ (/ +nan.0 (exp (* (* 0.5 (- 1.0 k)) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (* k k)))))
  (- (- (* (* +nan.0 (* (* (log (* 2.0 PI)) (* k k)) (log (* 2.0 PI)))) (pow (* (* (pow 2.0 1.0) (pow n 1.0)) (pow PI 1.0)) 0.5)) (- (* (pow (* (* (pow 2.0 1.0) (pow n 1.0)) (pow PI 1.0)) 0.5) (* (* (log (* 2.0 PI)) (* k k)) +nan.0)) (- (* (pow (* (* (pow 2.0 1.0) (pow n 1.0)) (pow PI 1.0)) 0.5) (* (* (* (log (* 2.0 PI)) (* k k)) (log n)) +nan.0)) (- (* (* +nan.0 (* (log n) (* k k))) (pow (* (* (pow 2.0 1.0) (pow n 1.0)) (pow PI 1.0)) 0.5)) (+ (- (* (* (* (pow (* (* (pow 2.0 1.0) (pow n 1.0)) (pow PI 1.0)) 0.5) (log (* 2.0 PI))) k) +nan.0) (* (* +nan.0 (* (* (log n) (log n)) (* k k))) (pow (* (* (pow 2.0 1.0) (pow n 1.0)) (pow PI 1.0)) 0.5))) (+ (- (* (* +nan.0 (* k (log n))) (pow (* (* (pow 2.0 1.0) (pow n 1.0)) (pow PI 1.0)) 0.5)) (* +nan.0 (pow (* (* (pow 2.0 1.0) (pow n 1.0)) (pow PI 1.0)) 0.5))) (* +nan.0 (- (* (* k k) (pow (* (* (pow 2.0 1.0) (pow n 1.0)) (pow PI 1.0)) 0.5)) (* (pow (* (* (pow 2.0 1.0) (pow n 1.0)) (pow PI 1.0)) 0.5) k))))))))))
  (+ (/ (- (* +nan.0 (exp (* (* (log (* (* 2.0 PI) n)) (- 1.0 k)) 0.5)))) (* k (* k k))) (* +nan.0 (- (/ (exp (* (* (log (* (* 2.0 PI) n)) (- 1.0 k)) 0.5)) k) (/ (exp (* (* (log (* (* 2.0 PI) n)) (- 1.0 k)) 0.5)) (* k k)))))
  (- (- (/ (exp (* (* 0.5 (- 1.0 k)) (- (log (* -2.0 PI)) (log (/ -1 n))))) (/ k +nan.0)) (* +nan.0 (- (/ (exp (* (* 0.5 (- 1.0 k)) (- (log (* -2.0 PI)) (log (/ -1 n))))) (* k k)) (exp (* (* 0.5 (- 1.0 k)) (- (log (* -2.0 PI)) (log (/ -1 n)))))))))
25.641 * * * [progress]: adding candidates to table
27.940 * * [progress]: iteration 4 / 4
27.940 * * * [progress]: picking best candidate
28.040 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))>
28.040 * * * [progress]: localizing error
28.106 * * * [progress]: generating rewritten candidates
28.106 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2)
28.159 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1)
28.210 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 1)
28.245 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1)
28.338 * * * [progress]: generating series expansions
28.338 * * * * [progress]: [ 1 / 4 ] generating series at (2 2)
28.339 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
28.339 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
28.339 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
28.339 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
28.339 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
28.339 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
28.339 * [taylor]: Taking taylor expansion of 0.5 in k
28.339 * [backup-simplify]: Simplify 0.5 into 0.5
28.339 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
28.339 * [taylor]: Taking taylor expansion of 1.0 in k
28.339 * [backup-simplify]: Simplify 1.0 into 1.0
28.339 * [taylor]: Taking taylor expansion of k in k
28.339 * [backup-simplify]: Simplify 0 into 0
28.339 * [backup-simplify]: Simplify 1 into 1
28.340 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
28.340 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
28.340 * [taylor]: Taking taylor expansion of 2.0 in k
28.340 * [backup-simplify]: Simplify 2.0 into 2.0
28.340 * [taylor]: Taking taylor expansion of (* n PI) in k
28.340 * [taylor]: Taking taylor expansion of n in k
28.340 * [backup-simplify]: Simplify n into n
28.340 * [taylor]: Taking taylor expansion of PI in k
28.340 * [backup-simplify]: Simplify PI into PI
28.340 * [backup-simplify]: Simplify (* n PI) into (* n PI)
28.340 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
28.340 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
28.341 * [backup-simplify]: Simplify (- 0) into 0
28.342 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
28.342 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
28.342 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
28.342 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
28.342 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
28.342 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
28.343 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
28.343 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
28.343 * [taylor]: Taking taylor expansion of 0.5 in n
28.343 * [backup-simplify]: Simplify 0.5 into 0.5
28.343 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
28.343 * [taylor]: Taking taylor expansion of 1.0 in n
28.343 * [backup-simplify]: Simplify 1.0 into 1.0
28.343 * [taylor]: Taking taylor expansion of k in n
28.343 * [backup-simplify]: Simplify k into k
28.343 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
28.343 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
28.343 * [taylor]: Taking taylor expansion of 2.0 in n
28.343 * [backup-simplify]: Simplify 2.0 into 2.0
28.343 * [taylor]: Taking taylor expansion of (* n PI) in n
28.343 * [taylor]: Taking taylor expansion of n in n
28.343 * [backup-simplify]: Simplify 0 into 0
28.343 * [backup-simplify]: Simplify 1 into 1
28.343 * [taylor]: Taking taylor expansion of PI in n
28.343 * [backup-simplify]: Simplify PI into PI
28.344 * [backup-simplify]: Simplify (* 0 PI) into 0
28.344 * [backup-simplify]: Simplify (* 2.0 0) into 0
28.346 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
28.348 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
28.349 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
28.350 * [backup-simplify]: Simplify (- k) into (- k)
28.350 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
28.350 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
28.351 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
28.353 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
28.354 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
28.354 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
28.354 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
28.354 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
28.354 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
28.354 * [taylor]: Taking taylor expansion of 0.5 in n
28.354 * [backup-simplify]: Simplify 0.5 into 0.5
28.354 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
28.354 * [taylor]: Taking taylor expansion of 1.0 in n
28.354 * [backup-simplify]: Simplify 1.0 into 1.0
28.354 * [taylor]: Taking taylor expansion of k in n
28.354 * [backup-simplify]: Simplify k into k
28.354 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
28.354 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
28.354 * [taylor]: Taking taylor expansion of 2.0 in n
28.354 * [backup-simplify]: Simplify 2.0 into 2.0
28.355 * [taylor]: Taking taylor expansion of (* n PI) in n
28.355 * [taylor]: Taking taylor expansion of n in n
28.355 * [backup-simplify]: Simplify 0 into 0
28.355 * [backup-simplify]: Simplify 1 into 1
28.355 * [taylor]: Taking taylor expansion of PI in n
28.355 * [backup-simplify]: Simplify PI into PI
28.355 * [backup-simplify]: Simplify (* 0 PI) into 0
28.356 * [backup-simplify]: Simplify (* 2.0 0) into 0
28.357 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
28.359 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
28.360 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
28.360 * [backup-simplify]: Simplify (- k) into (- k)
28.360 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
28.361 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
28.362 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
28.363 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
28.365 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
28.365 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
28.365 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
28.365 * [taylor]: Taking taylor expansion of 0.5 in k
28.365 * [backup-simplify]: Simplify 0.5 into 0.5
28.365 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
28.366 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
28.366 * [taylor]: Taking taylor expansion of 1.0 in k
28.366 * [backup-simplify]: Simplify 1.0 into 1.0
28.366 * [taylor]: Taking taylor expansion of k in k
28.366 * [backup-simplify]: Simplify 0 into 0
28.366 * [backup-simplify]: Simplify 1 into 1
28.366 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
28.366 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
28.366 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
28.366 * [taylor]: Taking taylor expansion of 2.0 in k
28.366 * [backup-simplify]: Simplify 2.0 into 2.0
28.366 * [taylor]: Taking taylor expansion of PI in k
28.366 * [backup-simplify]: Simplify PI into PI
28.367 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
28.368 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
28.368 * [taylor]: Taking taylor expansion of (log n) in k
28.368 * [taylor]: Taking taylor expansion of n in k
28.368 * [backup-simplify]: Simplify n into n
28.368 * [backup-simplify]: Simplify (log n) into (log n)
28.368 * [backup-simplify]: Simplify (- 0) into 0
28.369 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
28.370 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
28.371 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
28.372 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
28.374 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
28.375 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
28.376 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
28.377 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
28.379 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
28.380 * [backup-simplify]: Simplify (- 0) into 0
28.380 * [backup-simplify]: Simplify (+ 0 0) into 0
28.381 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
28.382 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
28.384 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
28.387 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
28.387 * [taylor]: Taking taylor expansion of 0 in k
28.387 * [backup-simplify]: Simplify 0 into 0
28.387 * [backup-simplify]: Simplify 0 into 0
28.388 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
28.390 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
28.391 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
28.392 * [backup-simplify]: Simplify (+ 0 0) into 0
28.392 * [backup-simplify]: Simplify (- 1) into -1
28.393 * [backup-simplify]: Simplify (+ 0 -1) into -1
28.394 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
28.408 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
28.411 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
28.414 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
28.416 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
28.417 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
28.426 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
28.427 * [backup-simplify]: Simplify (- 0) into 0
28.427 * [backup-simplify]: Simplify (+ 0 0) into 0
28.428 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
28.430 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
28.431 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
28.434 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
28.434 * [taylor]: Taking taylor expansion of 0 in k
28.434 * [backup-simplify]: Simplify 0 into 0
28.434 * [backup-simplify]: Simplify 0 into 0
28.434 * [backup-simplify]: Simplify 0 into 0
28.435 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
28.439 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
28.441 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
28.442 * [backup-simplify]: Simplify (+ 0 0) into 0
28.442 * [backup-simplify]: Simplify (- 0) into 0
28.442 * [backup-simplify]: Simplify (+ 0 0) into 0
28.444 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
28.447 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
28.451 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
28.457 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
28.468 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (+ (* 0.125 (pow (log n) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
28.470 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))
28.470 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
28.470 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
28.470 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
28.470 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
28.470 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
28.470 * [taylor]: Taking taylor expansion of 0.5 in k
28.470 * [backup-simplify]: Simplify 0.5 into 0.5
28.470 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
28.470 * [taylor]: Taking taylor expansion of 1.0 in k
28.470 * [backup-simplify]: Simplify 1.0 into 1.0
28.470 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.470 * [taylor]: Taking taylor expansion of k in k
28.470 * [backup-simplify]: Simplify 0 into 0
28.470 * [backup-simplify]: Simplify 1 into 1
28.470 * [backup-simplify]: Simplify (/ 1 1) into 1
28.470 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
28.470 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
28.471 * [taylor]: Taking taylor expansion of 2.0 in k
28.471 * [backup-simplify]: Simplify 2.0 into 2.0
28.471 * [taylor]: Taking taylor expansion of (/ PI n) in k
28.471 * [taylor]: Taking taylor expansion of PI in k
28.471 * [backup-simplify]: Simplify PI into PI
28.471 * [taylor]: Taking taylor expansion of n in k
28.471 * [backup-simplify]: Simplify n into n
28.471 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
28.471 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
28.471 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
28.471 * [backup-simplify]: Simplify (- 1) into -1
28.472 * [backup-simplify]: Simplify (+ 0 -1) into -1
28.472 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
28.472 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
28.473 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* 2.0 (/ PI n))) (- 1.0 (/ 1 k)))))
28.473 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
28.473 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
28.473 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
28.473 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
28.473 * [taylor]: Taking taylor expansion of 0.5 in n
28.473 * [backup-simplify]: Simplify 0.5 into 0.5
28.473 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
28.473 * [taylor]: Taking taylor expansion of 1.0 in n
28.473 * [backup-simplify]: Simplify 1.0 into 1.0
28.473 * [taylor]: Taking taylor expansion of (/ 1 k) in n
28.473 * [taylor]: Taking taylor expansion of k in n
28.473 * [backup-simplify]: Simplify k into k
28.473 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
28.473 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
28.473 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
28.473 * [taylor]: Taking taylor expansion of 2.0 in n
28.473 * [backup-simplify]: Simplify 2.0 into 2.0
28.473 * [taylor]: Taking taylor expansion of (/ PI n) in n
28.473 * [taylor]: Taking taylor expansion of PI in n
28.473 * [backup-simplify]: Simplify PI into PI
28.474 * [taylor]: Taking taylor expansion of n in n
28.474 * [backup-simplify]: Simplify 0 into 0
28.474 * [backup-simplify]: Simplify 1 into 1
28.474 * [backup-simplify]: Simplify (/ PI 1) into PI
28.475 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
28.476 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
28.476 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
28.476 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
28.476 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
28.478 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
28.479 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
28.481 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
28.481 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
28.481 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
28.481 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
28.481 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
28.481 * [taylor]: Taking taylor expansion of 0.5 in n
28.481 * [backup-simplify]: Simplify 0.5 into 0.5
28.481 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
28.481 * [taylor]: Taking taylor expansion of 1.0 in n
28.481 * [backup-simplify]: Simplify 1.0 into 1.0
28.481 * [taylor]: Taking taylor expansion of (/ 1 k) in n
28.481 * [taylor]: Taking taylor expansion of k in n
28.481 * [backup-simplify]: Simplify k into k
28.481 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
28.481 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
28.481 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
28.481 * [taylor]: Taking taylor expansion of 2.0 in n
28.481 * [backup-simplify]: Simplify 2.0 into 2.0
28.481 * [taylor]: Taking taylor expansion of (/ PI n) in n
28.481 * [taylor]: Taking taylor expansion of PI in n
28.481 * [backup-simplify]: Simplify PI into PI
28.481 * [taylor]: Taking taylor expansion of n in n
28.481 * [backup-simplify]: Simplify 0 into 0
28.481 * [backup-simplify]: Simplify 1 into 1
28.482 * [backup-simplify]: Simplify (/ PI 1) into PI
28.483 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
28.484 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
28.484 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
28.484 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
28.484 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
28.486 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
28.487 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))
28.489 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
28.489 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) in k
28.489 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))) in k
28.489 * [taylor]: Taking taylor expansion of 0.5 in k
28.489 * [backup-simplify]: Simplify 0.5 into 0.5
28.489 * [taylor]: Taking taylor expansion of (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))) in k
28.489 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
28.489 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
28.489 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
28.489 * [taylor]: Taking taylor expansion of 2.0 in k
28.489 * [backup-simplify]: Simplify 2.0 into 2.0
28.489 * [taylor]: Taking taylor expansion of PI in k
28.489 * [backup-simplify]: Simplify PI into PI
28.490 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
28.491 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
28.491 * [taylor]: Taking taylor expansion of (log n) in k
28.491 * [taylor]: Taking taylor expansion of n in k
28.491 * [backup-simplify]: Simplify n into n
28.491 * [backup-simplify]: Simplify (log n) into (log n)
28.491 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
28.491 * [taylor]: Taking taylor expansion of 1.0 in k
28.491 * [backup-simplify]: Simplify 1.0 into 1.0
28.491 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.491 * [taylor]: Taking taylor expansion of k in k
28.491 * [backup-simplify]: Simplify 0 into 0
28.491 * [backup-simplify]: Simplify 1 into 1
28.492 * [backup-simplify]: Simplify (/ 1 1) into 1
28.492 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
28.493 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
28.493 * [backup-simplify]: Simplify (- 1) into -1
28.494 * [backup-simplify]: Simplify (+ 0 -1) into -1
28.495 * [backup-simplify]: Simplify (* (- (log (* 2.0 PI)) (log n)) -1) into (* -1 (- (log (* 2.0 PI)) (log n)))
28.496 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
28.497 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
28.499 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k)))))
28.500 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
28.501 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
28.503 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
28.503 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
28.503 * [backup-simplify]: Simplify (- 0) into 0
28.504 * [backup-simplify]: Simplify (+ 0 0) into 0
28.504 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
28.506 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
28.507 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
28.509 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 1) 1)))) into 0
28.509 * [taylor]: Taking taylor expansion of 0 in k
28.509 * [backup-simplify]: Simplify 0 into 0
28.509 * [backup-simplify]: Simplify 0 into 0
28.509 * [backup-simplify]: Simplify 0 into 0
28.511 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.512 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
28.516 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
28.516 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
28.516 * [backup-simplify]: Simplify (- 0) into 0
28.517 * [backup-simplify]: Simplify (+ 0 0) into 0
28.518 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
28.519 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
28.520 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
28.522 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
28.522 * [taylor]: Taking taylor expansion of 0 in k
28.522 * [backup-simplify]: Simplify 0 into 0
28.522 * [backup-simplify]: Simplify 0 into 0
28.523 * [backup-simplify]: Simplify 0 into 0
28.523 * [backup-simplify]: Simplify 0 into 0
28.524 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.525 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
28.531 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
28.531 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
28.532 * [backup-simplify]: Simplify (- 0) into 0
28.532 * [backup-simplify]: Simplify (+ 0 0) into 0
28.533 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
28.535 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
28.536 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
28.539 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* 2.0 PI)) (log n)) (- 1.0 (/ 1 k))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
28.539 * [taylor]: Taking taylor expansion of 0 in k
28.539 * [backup-simplify]: Simplify 0 into 0
28.539 * [backup-simplify]: Simplify 0 into 0
28.540 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 (/ 1 (/ 1 k)))))) into (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
28.541 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))
28.541 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
28.541 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
28.541 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
28.541 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
28.541 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
28.541 * [taylor]: Taking taylor expansion of 0.5 in k
28.541 * [backup-simplify]: Simplify 0.5 into 0.5
28.541 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
28.541 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.541 * [taylor]: Taking taylor expansion of k in k
28.541 * [backup-simplify]: Simplify 0 into 0
28.541 * [backup-simplify]: Simplify 1 into 1
28.542 * [backup-simplify]: Simplify (/ 1 1) into 1
28.542 * [taylor]: Taking taylor expansion of 1.0 in k
28.542 * [backup-simplify]: Simplify 1.0 into 1.0
28.542 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
28.542 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
28.542 * [taylor]: Taking taylor expansion of -2.0 in k
28.542 * [backup-simplify]: Simplify -2.0 into -2.0
28.542 * [taylor]: Taking taylor expansion of (/ PI n) in k
28.542 * [taylor]: Taking taylor expansion of PI in k
28.542 * [backup-simplify]: Simplify PI into PI
28.542 * [taylor]: Taking taylor expansion of n in k
28.542 * [backup-simplify]: Simplify n into n
28.542 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
28.542 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
28.542 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
28.543 * [backup-simplify]: Simplify (+ 1 0) into 1
28.543 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
28.543 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
28.543 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (log (* -2.0 (/ PI n))))))
28.543 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
28.543 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
28.543 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
28.544 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
28.544 * [taylor]: Taking taylor expansion of 0.5 in n
28.544 * [backup-simplify]: Simplify 0.5 into 0.5
28.544 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
28.544 * [taylor]: Taking taylor expansion of (/ 1 k) in n
28.544 * [taylor]: Taking taylor expansion of k in n
28.544 * [backup-simplify]: Simplify k into k
28.544 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
28.544 * [taylor]: Taking taylor expansion of 1.0 in n
28.544 * [backup-simplify]: Simplify 1.0 into 1.0
28.544 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
28.544 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
28.544 * [taylor]: Taking taylor expansion of -2.0 in n
28.544 * [backup-simplify]: Simplify -2.0 into -2.0
28.544 * [taylor]: Taking taylor expansion of (/ PI n) in n
28.544 * [taylor]: Taking taylor expansion of PI in n
28.544 * [backup-simplify]: Simplify PI into PI
28.544 * [taylor]: Taking taylor expansion of n in n
28.544 * [backup-simplify]: Simplify 0 into 0
28.544 * [backup-simplify]: Simplify 1 into 1
28.544 * [backup-simplify]: Simplify (/ PI 1) into PI
28.545 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
28.546 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
28.546 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
28.546 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
28.548 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
28.549 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
28.550 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
28.550 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
28.550 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
28.550 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
28.550 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
28.550 * [taylor]: Taking taylor expansion of 0.5 in n
28.550 * [backup-simplify]: Simplify 0.5 into 0.5
28.550 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
28.550 * [taylor]: Taking taylor expansion of (/ 1 k) in n
28.550 * [taylor]: Taking taylor expansion of k in n
28.550 * [backup-simplify]: Simplify k into k
28.550 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
28.550 * [taylor]: Taking taylor expansion of 1.0 in n
28.550 * [backup-simplify]: Simplify 1.0 into 1.0
28.550 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
28.550 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
28.550 * [taylor]: Taking taylor expansion of -2.0 in n
28.550 * [backup-simplify]: Simplify -2.0 into -2.0
28.550 * [taylor]: Taking taylor expansion of (/ PI n) in n
28.550 * [taylor]: Taking taylor expansion of PI in n
28.550 * [backup-simplify]: Simplify PI into PI
28.550 * [taylor]: Taking taylor expansion of n in n
28.550 * [backup-simplify]: Simplify 0 into 0
28.550 * [backup-simplify]: Simplify 1 into 1
28.551 * [backup-simplify]: Simplify (/ PI 1) into PI
28.551 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
28.552 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
28.552 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
28.552 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
28.554 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
28.555 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))
28.556 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
28.557 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) in k
28.557 * [taylor]: Taking taylor expansion of (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))) in k
28.557 * [taylor]: Taking taylor expansion of 0.5 in k
28.557 * [backup-simplify]: Simplify 0.5 into 0.5
28.557 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))) in k
28.557 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
28.557 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.557 * [taylor]: Taking taylor expansion of k in k
28.557 * [backup-simplify]: Simplify 0 into 0
28.557 * [backup-simplify]: Simplify 1 into 1
28.557 * [backup-simplify]: Simplify (/ 1 1) into 1
28.557 * [taylor]: Taking taylor expansion of 1.0 in k
28.557 * [backup-simplify]: Simplify 1.0 into 1.0
28.557 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
28.557 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
28.557 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
28.557 * [taylor]: Taking taylor expansion of -2.0 in k
28.557 * [backup-simplify]: Simplify -2.0 into -2.0
28.557 * [taylor]: Taking taylor expansion of PI in k
28.557 * [backup-simplify]: Simplify PI into PI
28.558 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
28.559 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
28.559 * [taylor]: Taking taylor expansion of (log n) in k
28.559 * [taylor]: Taking taylor expansion of n in k
28.559 * [backup-simplify]: Simplify n into n
28.559 * [backup-simplify]: Simplify (log n) into (log n)
28.559 * [backup-simplify]: Simplify (+ 1 0) into 1
28.559 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
28.561 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
28.562 * [backup-simplify]: Simplify (* 1 (- (log (* -2.0 PI)) (log n))) into (- (log (* -2.0 PI)) (log n))
28.563 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
28.569 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
28.571 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) into (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n)))))
28.572 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
28.572 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
28.574 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
28.574 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
28.575 * [backup-simplify]: Simplify (+ 0 0) into 0
28.575 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
28.577 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
28.578 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
28.580 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
28.580 * [taylor]: Taking taylor expansion of 0 in k
28.580 * [backup-simplify]: Simplify 0 into 0
28.580 * [backup-simplify]: Simplify 0 into 0
28.580 * [backup-simplify]: Simplify 0 into 0
28.581 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.582 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
28.586 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
28.586 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
28.587 * [backup-simplify]: Simplify (+ 0 0) into 0
28.588 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
28.589 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
28.591 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
28.593 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
28.593 * [taylor]: Taking taylor expansion of 0 in k
28.593 * [backup-simplify]: Simplify 0 into 0
28.593 * [backup-simplify]: Simplify 0 into 0
28.593 * [backup-simplify]: Simplify 0 into 0
28.593 * [backup-simplify]: Simplify 0 into 0
28.595 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.596 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
28.602 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0
28.602 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
28.603 * [backup-simplify]: Simplify (+ 0 0) into 0
28.604 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
28.605 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
28.607 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
28.610 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (+ (/ 1 k) 1.0) (- (log (* -2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
28.610 * [taylor]: Taking taylor expansion of 0 in k
28.610 * [backup-simplify]: Simplify 0 into 0
28.610 * [backup-simplify]: Simplify 0 into 0
28.612 * [backup-simplify]: Simplify (exp (* 0.5 (* (+ (/ 1 (/ 1 (- k))) 1.0) (- (log (* -2.0 PI)) (log (/ 1 (- n))))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
28.612 * * * * [progress]: [ 2 / 4 ] generating series at (2 1)
28.612 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) into (* 1.0 (sqrt (/ 1 k)))
28.612 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0
28.612 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
28.612 * [taylor]: Taking taylor expansion of 1.0 in k
28.612 * [backup-simplify]: Simplify 1.0 into 1.0
28.612 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
28.612 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.612 * [taylor]: Taking taylor expansion of k in k
28.612 * [backup-simplify]: Simplify 0 into 0
28.612 * [backup-simplify]: Simplify 1 into 1
28.613 * [backup-simplify]: Simplify (/ 1 1) into 1
28.613 * [backup-simplify]: Simplify (sqrt 0) into 0
28.614 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
28.614 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
28.614 * [taylor]: Taking taylor expansion of 1.0 in k
28.614 * [backup-simplify]: Simplify 1.0 into 1.0
28.614 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
28.614 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.614 * [taylor]: Taking taylor expansion of k in k
28.614 * [backup-simplify]: Simplify 0 into 0
28.615 * [backup-simplify]: Simplify 1 into 1
28.615 * [backup-simplify]: Simplify (/ 1 1) into 1
28.615 * [backup-simplify]: Simplify (sqrt 0) into 0
28.617 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
28.617 * [backup-simplify]: Simplify (* 1.0 0) into 0
28.617 * [backup-simplify]: Simplify 0 into 0
28.618 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
28.619 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
28.620 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
28.623 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
28.625 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
28.625 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
28.626 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.630 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
28.632 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
28.633 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
28.634 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0)))))
28.634 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))) into (* 1.0 (sqrt k))
28.634 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0
28.634 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
28.635 * [taylor]: Taking taylor expansion of 1.0 in k
28.635 * [backup-simplify]: Simplify 1.0 into 1.0
28.635 * [taylor]: Taking taylor expansion of (sqrt k) in k
28.635 * [taylor]: Taking taylor expansion of k in k
28.635 * [backup-simplify]: Simplify 0 into 0
28.635 * [backup-simplify]: Simplify 1 into 1
28.635 * [backup-simplify]: Simplify (sqrt 0) into 0
28.636 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
28.636 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
28.636 * [taylor]: Taking taylor expansion of 1.0 in k
28.636 * [backup-simplify]: Simplify 1.0 into 1.0
28.636 * [taylor]: Taking taylor expansion of (sqrt k) in k
28.636 * [taylor]: Taking taylor expansion of k in k
28.636 * [backup-simplify]: Simplify 0 into 0
28.637 * [backup-simplify]: Simplify 1 into 1
28.637 * [backup-simplify]: Simplify (sqrt 0) into 0
28.638 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
28.639 * [backup-simplify]: Simplify (* 1.0 0) into 0
28.639 * [backup-simplify]: Simplify 0 into 0
28.640 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
28.641 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
28.644 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
28.646 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
28.647 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
28.651 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
28.653 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
28.654 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
28.655 * [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))))))))
28.656 * [backup-simplify]: Simplify (/ (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))) into (/ 1.0 (sqrt (/ -1 k)))
28.656 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0
28.656 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
28.656 * [taylor]: Taking taylor expansion of 1.0 in k
28.656 * [backup-simplify]: Simplify 1.0 into 1.0
28.656 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
28.656 * [taylor]: Taking taylor expansion of (/ -1 k) in k
28.656 * [taylor]: Taking taylor expansion of -1 in k
28.656 * [backup-simplify]: Simplify -1 into -1
28.656 * [taylor]: Taking taylor expansion of k in k
28.656 * [backup-simplify]: Simplify 0 into 0
28.656 * [backup-simplify]: Simplify 1 into 1
28.657 * [backup-simplify]: Simplify (/ -1 1) into -1
28.657 * [backup-simplify]: Simplify (sqrt 0) into 0
28.658 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
28.659 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
28.659 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
28.659 * [taylor]: Taking taylor expansion of 1.0 in k
28.659 * [backup-simplify]: Simplify 1.0 into 1.0
28.659 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
28.659 * [taylor]: Taking taylor expansion of (/ -1 k) in k
28.659 * [taylor]: Taking taylor expansion of -1 in k
28.659 * [backup-simplify]: Simplify -1 into -1
28.659 * [taylor]: Taking taylor expansion of k in k
28.659 * [backup-simplify]: Simplify 0 into 0
28.659 * [backup-simplify]: Simplify 1 into 1
28.659 * [backup-simplify]: Simplify (/ -1 1) into -1
28.660 * [backup-simplify]: Simplify (sqrt 0) into 0
28.661 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
28.662 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
28.662 * [backup-simplify]: Simplify +nan.0 into +nan.0
28.663 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
28.665 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
28.668 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
28.669 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
28.670 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.674 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
28.678 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
28.678 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
28.679 * [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)))))
28.679 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 1)
28.680 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
28.680 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
28.680 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
28.680 * [taylor]: Taking taylor expansion of 2.0 in n
28.680 * [backup-simplify]: Simplify 2.0 into 2.0
28.680 * [taylor]: Taking taylor expansion of (* n PI) in n
28.680 * [taylor]: Taking taylor expansion of n in n
28.680 * [backup-simplify]: Simplify 0 into 0
28.680 * [backup-simplify]: Simplify 1 into 1
28.680 * [taylor]: Taking taylor expansion of PI in n
28.680 * [backup-simplify]: Simplify PI into PI
28.680 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
28.680 * [taylor]: Taking taylor expansion of 2.0 in n
28.680 * [backup-simplify]: Simplify 2.0 into 2.0
28.680 * [taylor]: Taking taylor expansion of (* n PI) in n
28.680 * [taylor]: Taking taylor expansion of n in n
28.680 * [backup-simplify]: Simplify 0 into 0
28.681 * [backup-simplify]: Simplify 1 into 1
28.681 * [taylor]: Taking taylor expansion of PI in n
28.681 * [backup-simplify]: Simplify PI into PI
28.681 * [backup-simplify]: Simplify (* 0 PI) into 0
28.682 * [backup-simplify]: Simplify (* 2.0 0) into 0
28.682 * [backup-simplify]: Simplify 0 into 0
28.684 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
28.685 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
28.686 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
28.687 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
28.688 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
28.688 * [backup-simplify]: Simplify 0 into 0
28.689 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
28.690 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
28.691 * [backup-simplify]: Simplify 0 into 0
28.692 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
28.694 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
28.694 * [backup-simplify]: Simplify 0 into 0
28.695 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
28.697 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
28.697 * [backup-simplify]: Simplify 0 into 0
28.699 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
28.701 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
28.701 * [backup-simplify]: Simplify 0 into 0
28.704 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
28.707 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
28.707 * [backup-simplify]: Simplify 0 into 0
28.708 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
28.709 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
28.709 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
28.709 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
28.709 * [taylor]: Taking taylor expansion of 2.0 in n
28.709 * [backup-simplify]: Simplify 2.0 into 2.0
28.709 * [taylor]: Taking taylor expansion of (/ PI n) in n
28.709 * [taylor]: Taking taylor expansion of PI in n
28.709 * [backup-simplify]: Simplify PI into PI
28.709 * [taylor]: Taking taylor expansion of n in n
28.709 * [backup-simplify]: Simplify 0 into 0
28.709 * [backup-simplify]: Simplify 1 into 1
28.709 * [backup-simplify]: Simplify (/ PI 1) into PI
28.709 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
28.710 * [taylor]: Taking taylor expansion of 2.0 in n
28.710 * [backup-simplify]: Simplify 2.0 into 2.0
28.710 * [taylor]: Taking taylor expansion of (/ PI n) in n
28.710 * [taylor]: Taking taylor expansion of PI in n
28.710 * [backup-simplify]: Simplify PI into PI
28.710 * [taylor]: Taking taylor expansion of n in n
28.710 * [backup-simplify]: Simplify 0 into 0
28.710 * [backup-simplify]: Simplify 1 into 1
28.710 * [backup-simplify]: Simplify (/ PI 1) into PI
28.711 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
28.712 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
28.713 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
28.714 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
28.714 * [backup-simplify]: Simplify 0 into 0
28.715 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.716 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
28.716 * [backup-simplify]: Simplify 0 into 0
28.717 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.723 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
28.723 * [backup-simplify]: Simplify 0 into 0
28.724 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.726 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
28.726 * [backup-simplify]: Simplify 0 into 0
28.727 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.729 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
28.729 * [backup-simplify]: Simplify 0 into 0
28.730 * [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
28.731 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
28.732 * [backup-simplify]: Simplify 0 into 0
28.732 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
28.733 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
28.733 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
28.733 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
28.733 * [taylor]: Taking taylor expansion of -2.0 in n
28.733 * [backup-simplify]: Simplify -2.0 into -2.0
28.733 * [taylor]: Taking taylor expansion of (/ PI n) in n
28.733 * [taylor]: Taking taylor expansion of PI in n
28.733 * [backup-simplify]: Simplify PI into PI
28.733 * [taylor]: Taking taylor expansion of n in n
28.733 * [backup-simplify]: Simplify 0 into 0
28.733 * [backup-simplify]: Simplify 1 into 1
28.733 * [backup-simplify]: Simplify (/ PI 1) into PI
28.733 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
28.734 * [taylor]: Taking taylor expansion of -2.0 in n
28.734 * [backup-simplify]: Simplify -2.0 into -2.0
28.734 * [taylor]: Taking taylor expansion of (/ PI n) in n
28.734 * [taylor]: Taking taylor expansion of PI in n
28.734 * [backup-simplify]: Simplify PI into PI
28.734 * [taylor]: Taking taylor expansion of n in n
28.734 * [backup-simplify]: Simplify 0 into 0
28.734 * [backup-simplify]: Simplify 1 into 1
28.734 * [backup-simplify]: Simplify (/ PI 1) into PI
28.735 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
28.735 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
28.736 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
28.737 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
28.737 * [backup-simplify]: Simplify 0 into 0
28.738 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.739 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
28.739 * [backup-simplify]: Simplify 0 into 0
28.740 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.741 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
28.741 * [backup-simplify]: Simplify 0 into 0
28.742 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.743 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
28.743 * [backup-simplify]: Simplify 0 into 0
28.744 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.746 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
28.746 * [backup-simplify]: Simplify 0 into 0
28.747 * [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
28.749 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
28.749 * [backup-simplify]: Simplify 0 into 0
28.750 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
28.750 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1)
28.750 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt k))) into (* 1.0 (pow (/ 1 k) 1/4))
28.750 * [approximate]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in (k) around 0
28.750 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k
28.750 * [taylor]: Taking taylor expansion of 1.0 in k
28.750 * [backup-simplify]: Simplify 1.0 into 1.0
28.750 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
28.750 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
28.750 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
28.750 * [taylor]: Taking taylor expansion of 1/4 in k
28.750 * [backup-simplify]: Simplify 1/4 into 1/4
28.750 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
28.750 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.750 * [taylor]: Taking taylor expansion of k in k
28.750 * [backup-simplify]: Simplify 0 into 0
28.750 * [backup-simplify]: Simplify 1 into 1
28.751 * [backup-simplify]: Simplify (/ 1 1) into 1
28.751 * [backup-simplify]: Simplify (log 1) into 0
28.752 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
28.752 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
28.752 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
28.752 * [taylor]: Taking taylor expansion of (* 1.0 (pow (/ 1 k) 1/4)) in k
28.752 * [taylor]: Taking taylor expansion of 1.0 in k
28.752 * [backup-simplify]: Simplify 1.0 into 1.0
28.752 * [taylor]: Taking taylor expansion of (pow (/ 1 k) 1/4) in k
28.752 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log (/ 1 k)))) in k
28.752 * [taylor]: Taking taylor expansion of (* 1/4 (log (/ 1 k))) in k
28.752 * [taylor]: Taking taylor expansion of 1/4 in k
28.752 * [backup-simplify]: Simplify 1/4 into 1/4
28.752 * [taylor]: Taking taylor expansion of (log (/ 1 k)) in k
28.752 * [taylor]: Taking taylor expansion of (/ 1 k) in k
28.752 * [taylor]: Taking taylor expansion of k in k
28.752 * [backup-simplify]: Simplify 0 into 0
28.752 * [backup-simplify]: Simplify 1 into 1
28.753 * [backup-simplify]: Simplify (/ 1 1) into 1
28.753 * [backup-simplify]: Simplify (log 1) into 0
28.753 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
28.753 * [backup-simplify]: Simplify (* 1/4 (- (log k))) into (* -1/4 (log k))
28.753 * [backup-simplify]: Simplify (exp (* -1/4 (log k))) into (pow k -1/4)
28.754 * [backup-simplify]: Simplify (* 1.0 (pow k -1/4)) into (* 1.0 (pow (/ 1 k) 1/4))
28.754 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4))
28.755 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
28.756 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
28.756 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
28.757 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (- (log k)))) into 0
28.758 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
28.758 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k -1/4))) into 0
28.758 * [backup-simplify]: Simplify 0 into 0
28.759 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.762 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
28.762 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
28.763 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (- (log k))))) into 0
28.764 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
28.765 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k -1/4)))) into 0
28.765 * [backup-simplify]: Simplify 0 into 0
28.766 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.771 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
28.771 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
28.772 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))) into 0
28.774 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
28.775 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))) into 0
28.775 * [backup-simplify]: Simplify 0 into 0
28.776 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.787 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0
28.788 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
28.789 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))) into 0
28.792 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
28.794 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))) into 0
28.794 * [backup-simplify]: Simplify 0 into 0
28.796 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.813 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0
28.814 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
28.816 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k)))))))) into 0
28.820 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
28.821 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4))))))) into 0
28.821 * [backup-simplify]: Simplify 0 into 0
28.823 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
28.851 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0
28.852 * [backup-simplify]: Simplify (+ (* (- 1) (log k)) 0) into (- (log k))
28.854 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log k))))))))) into 0
28.861 * [backup-simplify]: Simplify (* (exp (* -1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
28.864 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k -1/4)))))))) into 0
28.864 * [backup-simplify]: Simplify 0 into 0
28.864 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4))
28.865 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 k)))) into (* 1.0 (pow k 1/4))
28.865 * [approximate]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in (k) around 0
28.865 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k
28.865 * [taylor]: Taking taylor expansion of 1.0 in k
28.865 * [backup-simplify]: Simplify 1.0 into 1.0
28.865 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
28.865 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
28.865 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
28.865 * [taylor]: Taking taylor expansion of 1/4 in k
28.865 * [backup-simplify]: Simplify 1/4 into 1/4
28.865 * [taylor]: Taking taylor expansion of (log k) in k
28.865 * [taylor]: Taking taylor expansion of k in k
28.865 * [backup-simplify]: Simplify 0 into 0
28.865 * [backup-simplify]: Simplify 1 into 1
28.866 * [backup-simplify]: Simplify (log 1) into 0
28.866 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
28.866 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
28.866 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
28.866 * [taylor]: Taking taylor expansion of (* 1.0 (pow k 1/4)) in k
28.866 * [taylor]: Taking taylor expansion of 1.0 in k
28.866 * [backup-simplify]: Simplify 1.0 into 1.0
28.866 * [taylor]: Taking taylor expansion of (pow k 1/4) in k
28.866 * [taylor]: Taking taylor expansion of (exp (* 1/4 (log k))) in k
28.866 * [taylor]: Taking taylor expansion of (* 1/4 (log k)) in k
28.866 * [taylor]: Taking taylor expansion of 1/4 in k
28.867 * [backup-simplify]: Simplify 1/4 into 1/4
28.867 * [taylor]: Taking taylor expansion of (log k) in k
28.867 * [taylor]: Taking taylor expansion of k in k
28.867 * [backup-simplify]: Simplify 0 into 0
28.867 * [backup-simplify]: Simplify 1 into 1
28.867 * [backup-simplify]: Simplify (log 1) into 0
28.868 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
28.868 * [backup-simplify]: Simplify (* 1/4 (log k)) into (* 1/4 (log k))
28.868 * [backup-simplify]: Simplify (exp (* 1/4 (log k))) into (pow k 1/4)
28.868 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4))
28.868 * [backup-simplify]: Simplify (* 1.0 (pow k 1/4)) into (* 1.0 (pow k 1/4))
28.878 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
28.879 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
28.879 * [backup-simplify]: Simplify (+ (* 1/4 0) (* 0 (log k))) into 0
28.880 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 1) 1)))) into 0
28.881 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (pow k 1/4))) into 0
28.881 * [backup-simplify]: Simplify 0 into 0
28.884 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
28.884 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
28.885 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (* 0 (log k)))) into 0
28.887 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
28.888 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (pow k 1/4)))) into 0
28.888 * [backup-simplify]: Simplify 0 into 0
28.893 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow 1 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow 1 1)))) 6) into 0
28.894 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
28.895 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))) into 0
28.897 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
28.899 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))) into 0
28.899 * [backup-simplify]: Simplify 0 into 0
28.910 * [backup-simplify]: Simplify (/ (+ (* -6 (/ (* (pow (* 1 0) 4)) (pow 1 4))) (* 12 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 1)) (pow 1 3))) (* -3 (/ (* 1 (pow (* 2 0) 2)) (pow 1 2))) (* -4 (/ (* (pow (* 1 0) 1) 1 (pow (* 6 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 (pow (* 24 0) 1)) (pow 1 1)))) 24) into 0
28.911 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
28.912 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))) into 0
28.915 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 4) 24)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
28.917 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))) into 0
28.917 * [backup-simplify]: Simplify 0 into 0
28.935 * [backup-simplify]: Simplify (/ (+ (* 24 (/ (* (pow (* 1 0) 5)) (pow 1 5))) (* -60 (/ (* (pow (* 1 0) 3) (pow (* 2 0) 1)) (pow 1 4))) (* 30 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 2)) (pow 1 3))) (* 20 (/ (* (pow (* 1 0) 2) 1 (pow (* 6 0) 1)) (pow 1 3))) (* -10 (/ (* 1 (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 2))) (* -5 (/ (* (pow (* 1 0) 1) 1 1 (pow (* 24 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 (pow (* 120 0) 1)) (pow 1 1)))) 120) into 0
28.936 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
28.938 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k))))))) into 0
28.942 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 5) 120)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
28.944 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4))))))) into 0
28.944 * [backup-simplify]: Simplify 0 into 0
28.977 * [backup-simplify]: Simplify (/ (+ (* -120 (/ (* (pow (* 1 0) 6)) (pow 1 6))) (* 360 (/ (* (pow (* 1 0) 4) (pow (* 2 0) 1)) (pow 1 5))) (* -270 (/ (* (pow (* 1 0) 2) (pow (* 2 0) 2)) (pow 1 4))) (* -120 (/ (* (pow (* 1 0) 3) 1 (pow (* 6 0) 1)) (pow 1 4))) (* 30 (/ (* 1 (pow (* 2 0) 3)) (pow 1 3))) (* 120 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1) (pow (* 6 0) 1)) (pow 1 3))) (* 30 (/ (* (pow (* 1 0) 2) 1 1 (pow (* 24 0) 1)) (pow 1 3))) (* -10 (/ (* 1 1 (pow (* 6 0) 2)) (pow 1 2))) (* -15 (/ (* 1 (pow (* 2 0) 1) 1 (pow (* 24 0) 1)) (pow 1 2))) (* -6 (/ (* (pow (* 1 0) 1) 1 1 1 (pow (* 120 0) 1)) (pow 1 2))) (* 1 (/ (* 1 1 1 1 1 (pow (* 720 0) 1)) (pow 1 1)))) 720) into 0
28.977 * [backup-simplify]: Simplify (+ (* (- -1) (log k)) 0) into (log k)
28.980 * [backup-simplify]: Simplify (+ (* 1/4 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (log k)))))))) into 0
28.986 * [backup-simplify]: Simplify (* (exp (* 1/4 (log k))) (+ (* (/ (pow 0 6) 720)) (* (/ (pow 0 4) 24) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2) (/ (pow 0 2) 2)) (* (/ (pow 0 2) 2) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
28.988 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow k 1/4)))))))) into 0
28.989 * [backup-simplify]: Simplify 0 into 0
28.989 * [backup-simplify]: Simplify (* 1.0 (pow (/ 1 k) 1/4)) into (* 1.0 (pow (/ 1 k) 1/4))
28.989 * [backup-simplify]: Simplify (/ 1.0 (sqrt (sqrt (/ 1 (- k))))) into (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k)))))
28.989 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in (k) around 0
28.989 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k
28.989 * [taylor]: Taking taylor expansion of 1.0 in k
28.989 * [backup-simplify]: Simplify 1.0 into 1.0
28.989 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k
28.989 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
28.989 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
28.989 * [taylor]: Taking taylor expansion of (/ -1 k) in k
28.989 * [taylor]: Taking taylor expansion of -1 in k
28.989 * [backup-simplify]: Simplify -1 into -1
28.989 * [taylor]: Taking taylor expansion of k in k
28.989 * [backup-simplify]: Simplify 0 into 0
28.989 * [backup-simplify]: Simplify 1 into 1
28.990 * [backup-simplify]: Simplify (/ -1 1) into -1
28.990 * [backup-simplify]: Simplify (sqrt 0) into 0
28.992 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
28.992 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
28.993 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
28.993 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
28.996 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
28.998 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
28.999 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
28.999 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 (sqrt (/ -1 k))))) in k
28.999 * [taylor]: Taking taylor expansion of 1.0 in k
29.000 * [backup-simplify]: Simplify 1.0 into 1.0
29.000 * [taylor]: Taking taylor expansion of (sqrt (/ 1 (sqrt (/ -1 k)))) in k
29.000 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
29.000 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
29.000 * [taylor]: Taking taylor expansion of (/ -1 k) in k
29.000 * [taylor]: Taking taylor expansion of -1 in k
29.000 * [backup-simplify]: Simplify -1 into -1
29.000 * [taylor]: Taking taylor expansion of k in k
29.000 * [backup-simplify]: Simplify 0 into 0
29.000 * [backup-simplify]: Simplify 1 into 1
29.000 * [backup-simplify]: Simplify (/ -1 1) into -1
29.000 * [backup-simplify]: Simplify (sqrt 0) into 0
29.002 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
29.002 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
29.002 * [backup-simplify]: Simplify (sqrt +nan.0) into (sqrt +nan.0)
29.003 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
29.006 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
29.007 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
29.009 * [backup-simplify]: Simplify (/ (- +nan.0) (* 2 (sqrt +nan.0))) into (/ +nan.0 (sqrt +nan.0))
29.010 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0))
29.011 * [backup-simplify]: Simplify (* 1.0 (sqrt +nan.0)) into (* 1.0 (sqrt +nan.0))
29.013 * [backup-simplify]: Simplify (+ (* 1.0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0))) into (- (* +nan.0 (/ 1 (sqrt +nan.0))))
29.016 * [backup-simplify]: Simplify (- (* +nan.0 (/ 1 (sqrt +nan.0)))) into (- (* +nan.0 (/ 1 (sqrt +nan.0))))
29.017 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
29.021 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
29.030 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
29.036 * [backup-simplify]: Simplify (/ (- (- +nan.0) (pow (/ +nan.0 (sqrt +nan.0)) 2) (+)) (* 2 (sqrt +nan.0))) into (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))
29.050 * [backup-simplify]: Simplify (+ (* 1.0 (* -1/2 (/ (+ (* +nan.0 (/ 1 (pow (sqrt +nan.0) 2))) (- +nan.0)) (sqrt +nan.0)))) (+ (* 0 (/ +nan.0 (sqrt +nan.0))) (* 0 (sqrt +nan.0)))) into (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))))
29.059 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) into (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3))))))
29.070 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (/ 1 (sqrt +nan.0))) (- (* +nan.0 (/ 1 (pow (sqrt +nan.0) 3)))))) (pow (/ 1 (- k)) 2)) (+ (* (- (* +nan.0 (/ 1 (sqrt +nan.0)))) (/ 1 (- k))) (* 1.0 (sqrt +nan.0)))) into (- (* 1.0 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))))))))
29.071 * * * [progress]: simplifying candidates
29.087 * [simplify]: Simplifying:
  (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (pow (* (* 2.0 PI) n) (/ 1.0 2.0))
  (pow (* (* 2.0 PI) n) (/ k 2.0))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) 1)
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
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  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ (/ 1 1) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (/ 1 1) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 1) (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 1) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 1) (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ (/ 1 1) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 1) 1)
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1 1)
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt 1)))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt 1))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1.0 1)
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt 1)))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt 1))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) 1)
  (/ (sqrt (sqrt k)) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1.0 (cbrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (cbrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (cbrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (sqrt k)) (/ 1 (sqrt (sqrt k))))
  (* (sqrt (sqrt k)) (sqrt (sqrt k)))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (- (log 1.0) (log (sqrt (sqrt k))))
  (log (/ 1.0 (sqrt (sqrt k))))
  (exp (/ 1.0 (sqrt (sqrt k))))
  (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt (sqrt k)) (sqrt (sqrt k))) (sqrt (sqrt k))))
  (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (cbrt (/ 1.0 (sqrt (sqrt k))))
  (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (- 1.0)
  (- (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (cbrt 1.0) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (cbrt 1.0) (sqrt (cbrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (cbrt 1.0) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt 1)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) 1)
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt 1.0) (cbrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ (sqrt 1.0) (sqrt (cbrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ (sqrt 1.0) (sqrt (sqrt (cbrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt 1)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt 1))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) 1)
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1.0 (cbrt (sqrt (sqrt k))))
  (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1.0 (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1.0 (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt 1)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt 1))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1 1)
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (sqrt (sqrt k)) 1.0)
  (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))
  (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k)))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt 1)))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt 1))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ 1.0 1)
  (/ (sqrt (sqrt k)) (cbrt 1.0))
  (/ (sqrt (sqrt k)) (sqrt 1.0))
  (/ (sqrt (sqrt k)) 1.0)
  (- (+ (* 0.125 (* (pow k 2) (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.125 (* (pow k 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))) (+ (* 0.25 (* (pow k 2) (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0.5 (* k (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.5 (* k (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))))
  (exp (* 0.5 (* (- (log (* 2.0 PI)) (log (/ 1 n))) (- 1.0 k))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
  (- (+ (* +nan.0 k) (- (+ (* +nan.0 (pow k 2)) (- +nan.0)))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 1.0 (pow (/ 1 k) 1/4))
  (* 1.0 (pow (/ 1 k) 1/4))
  (- (* 1.0 (sqrt +nan.0)) (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) (pow k 2)))) (- (+ (* +nan.0 (/ 1 (* (sqrt +nan.0) k))) (- (* +nan.0 (/ 1 (* (pow (sqrt +nan.0) 3) (pow k 2)))))))))
29.114 * * [simplify]: iteration 0: 558 enodes
29.546 * * [simplify]: iteration 1: 1376 enodes
30.473 * * [simplify]: iteration 2: 3464 enodes
32.072 * * [simplify]: iteration complete: 5010 enodes
32.073 * * [simplify]: Extracting #0: cost 245 inf + 0
32.078 * * [simplify]: Extracting #1: cost 1359 inf + 2
32.090 * * [simplify]: Extracting #2: cost 1958 inf + 6844
32.124 * * [simplify]: Extracting #3: cost 1759 inf + 65374
32.191 * * [simplify]: Extracting #4: cost 882 inf + 277990
32.335 * * [simplify]: Extracting #5: cost 174 inf + 520265
32.485 * * [simplify]: Extracting #6: cost 30 inf + 578537
32.648 * * [simplify]: Extracting #7: cost 5 inf + 586103
32.809 * * [simplify]: Extracting #8: cost 1 inf + 586991
32.977 * * [simplify]: Extracting #9: cost 0 inf + 587286
33.147 * [simplify]: Simplified to:
  (* (log (* (* n 2.0) PI)) (/ (- 1.0 k) 2.0))
  (* (log (* (* n 2.0) PI)) (/ (- 1.0 k) 2.0))
  (* (log (* (* n 2.0) PI)) (/ (- 1.0 k) 2.0))
  (* (log (* (* n 2.0) PI)) (/ (- 1.0 k) 2.0))
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (pow (* (* n 2.0) PI) (/ 1.0 2.0))
  (pow (* (* n 2.0) PI) (/ k 2.0))
  (pow (* (* n 2.0) PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* n 2.0) PI) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* n 2.0) PI) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0))))
  (pow (* (* n 2.0) PI) (* (/ (cbrt (- 1.0 k)) (sqrt 2.0)) (cbrt (- 1.0 k))))
  (pow (* (* n 2.0) PI) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* (* n 2.0) PI) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* (* n 2.0) PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* n 2.0) PI) (sqrt (- 1.0 k)))
  (pow (* (* n 2.0) PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* n 2.0) PI) (/ 1 (sqrt 2.0)))
  (* (* n 2.0) PI)
  (pow (* (* n 2.0) PI) (/ (/ (+ (sqrt 1.0) (sqrt k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* (* n 2.0) PI) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* n 2.0) PI) (+ (sqrt 1.0) (sqrt k)))
  (pow (* (* n 2.0) PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* n 2.0) PI) (/ 1 (sqrt 2.0)))
  (* (* n 2.0) PI)
  (* (* n 2.0) PI)
  (pow (* (* n 2.0) PI) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (* (log (* (* n 2.0) PI)) (/ (- 1.0 k) 2.0))
  (exp (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))
  (pow (* (* n 2.0) PI) (/ (- 1.0 k) (* 2 2.0)))
  (pow (* (* n 2.0) PI) (/ (- 1.0 k) (* 2 2.0)))
  (log (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (/ 1.0 (* (/ (sqrt (sqrt k)) (/ 1.0 (sqrt k))) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt k)))))
  (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (* (/ 1.0 (sqrt k)) (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (- (/ 1.0 (sqrt (sqrt k))))
  (- (sqrt (sqrt k)))
  (* (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (* (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (fabs (cbrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (/ (sqrt (fabs (cbrt k))) (cbrt (/ 1.0 (sqrt (sqrt k))))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (cbrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (fabs (cbrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (fabs (cbrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (/ (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (sqrt k)))
  (* (/ (cbrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (/ (cbrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))))
  (/ (cbrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (fabs (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k))))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (* (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k))))) (sqrt (fabs (cbrt k))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (* (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (* (cbrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))))
  (* (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (* (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (* (cbrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))))
  (* (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (* (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))
  (/ (cbrt 1.0) (* (cbrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))))
  (* (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (fabs (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k))))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (* (/ (cbrt 1.0) (fabs (cbrt (sqrt k)))) (/ (cbrt 1.0) (fabs (cbrt (sqrt k)))))
  (/ (cbrt 1.0) (cbrt (sqrt k)))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt (sqrt k)))) (sqrt (fabs (cbrt k))))
  (/ (/ (cbrt 1.0) (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt (sqrt k)))) (fabs (cbrt (sqrt k))))
  (/ (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
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  (/ 1 (* (sqrt (sqrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))))
  (/ 1.0 (* (cbrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))))
  (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ 1.0 (* (sqrt (sqrt k)) (cbrt (sqrt (sqrt k)))))
  (/ 1 (* (sqrt (sqrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))))
  (/ 1.0 (* (cbrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))))
  (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ 1.0 (* (sqrt (sqrt k)) (cbrt (sqrt (sqrt k)))))
  (/ 1 (* (sqrt (sqrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))))
  (/ 1.0 (* (cbrt (sqrt (sqrt k))) (sqrt (sqrt (sqrt k)))))
  (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ 1.0 (* (sqrt (sqrt k)) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (fabs (cbrt (sqrt k))))
  (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (sqrt (cbrt (sqrt k))))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (cbrt (sqrt k)))
  (/ 1 (* (fabs (cbrt (sqrt k))) (sqrt (fabs (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k))))
  (/ 1 (* (fabs (cbrt (sqrt k))) (sqrt (sqrt (sqrt k)))))
  (/ 1.0 (* (sqrt (cbrt (sqrt k))) (sqrt (sqrt (sqrt k)))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ 1.0 (* (sqrt (sqrt k)) (sqrt (cbrt (sqrt k)))))
  (/ 1 (* (fabs (cbrt (sqrt k))) (sqrt (sqrt (sqrt k)))))
  (/ 1.0 (* (sqrt (cbrt (sqrt k))) (sqrt (sqrt (sqrt k)))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ 1.0 (* (sqrt (sqrt k)) (sqrt (cbrt (sqrt k)))))
  (/ 1 (* (fabs (cbrt (sqrt k))) (sqrt (sqrt (sqrt k)))))
  (/ 1.0 (* (sqrt (cbrt (sqrt k))) (sqrt (sqrt (sqrt k)))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ 1.0 (* (sqrt (sqrt k)) (sqrt (cbrt (sqrt k)))))
  (/ (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (fabs (cbrt k))))
  (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ (/ 1 (fabs (cbrt (sqrt k)))) (sqrt (fabs (cbrt k))))
  (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k))))
  (/ 1 (fabs (cbrt k)))
  (/ 1.0 (sqrt (cbrt k)))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (fabs (cbrt k))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (fabs (cbrt k))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (sqrt (fabs (cbrt k))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (fabs (cbrt (sqrt k))))
  (/ (/ 1.0 (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ 1 (* (sqrt (sqrt (sqrt k))) (sqrt (fabs (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ (/ 1.0 (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k)))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  1
  (/ 1.0 (sqrt k))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (fabs (cbrt (sqrt k))))
  (/ (/ 1.0 (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ 1 (* (sqrt (sqrt (sqrt k))) (sqrt (fabs (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ (/ 1.0 (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k)))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  1
  (/ 1.0 (sqrt k))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt (sqrt k)))) (fabs (cbrt (sqrt k))))
  (/ (/ 1.0 (sqrt (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))
  (/ 1 (* (sqrt (sqrt (sqrt k))) (sqrt (fabs (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ (/ 1.0 (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k)))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  1
  (/ 1.0 (sqrt k))
  (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ (/ 1.0 (sqrt (cbrt (sqrt k)))) (sqrt (sqrt k)))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ (/ 1.0 (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  1
  (/ 1.0 (sqrt k))
  (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (/ 1 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))
  (/ 1.0 (fabs (cbrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (cbrt (sqrt k))))
  (/ 1.0 (sqrt (fabs (cbrt k))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (cbrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  1.0
  (/ 1 (sqrt k))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  1.0
  (/ 1 (sqrt k))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  1.0
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (* (sqrt (sqrt k)) (sqrt (sqrt k))) 1.0)
  (/ (/ (/ 1.0 (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ 1.0 (* (sqrt (sqrt k)) (fabs (cbrt (sqrt k)))))
  (/ 1.0 (* (sqrt (sqrt k)) (sqrt (fabs (cbrt k)))))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (sqrt (sqrt k)) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))))
  (* (/ (sqrt (sqrt k)) (cbrt 1.0)) (sqrt (cbrt (sqrt k))))
  (* (sqrt (sqrt (cbrt k))) (/ (sqrt (sqrt k)) (cbrt 1.0)))
  (* (sqrt (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (cbrt 1.0)))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k))))
  (* (sqrt (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (cbrt 1.0)))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k))))
  (* (sqrt (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (cbrt 1.0)))
  (/ (sqrt (sqrt k)) (/ (cbrt 1.0) (sqrt (sqrt k))))
  (* (cbrt (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (sqrt 1.0)))
  (/ (sqrt (sqrt k)) (/ (sqrt 1.0) (sqrt (cbrt (sqrt k)))))
  (* (/ (sqrt (sqrt k)) (sqrt 1.0)) (sqrt (sqrt (cbrt k))))
  (/ (* (sqrt (sqrt k)) (sqrt (sqrt (sqrt k)))) (sqrt 1.0))
  (* (/ (sqrt (sqrt k)) (sqrt 1.0)) (sqrt (sqrt k)))
  (/ (* (sqrt (sqrt k)) (sqrt (sqrt (sqrt k)))) (sqrt 1.0))
  (* (/ (sqrt (sqrt k)) (sqrt 1.0)) (sqrt (sqrt k)))
  (/ (* (sqrt (sqrt k)) (sqrt (sqrt (sqrt k)))) (sqrt 1.0))
  (* (/ (sqrt (sqrt k)) (sqrt 1.0)) (sqrt (sqrt k)))
  (* (cbrt (sqrt (sqrt k))) (/ (sqrt (sqrt k)) 1.0))
  (/ (* (sqrt (sqrt k)) (sqrt (cbrt (sqrt k)))) 1.0)
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (cbrt k)))))
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))))
  (/ (* (sqrt (sqrt k)) (sqrt (sqrt k))) 1.0)
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))))
  (/ (* (sqrt (sqrt k)) (sqrt (sqrt k))) 1.0)
  (/ (sqrt (sqrt k)) (/ 1.0 (sqrt (sqrt (sqrt k)))))
  (/ (* (sqrt (sqrt k)) (sqrt (sqrt k))) 1.0)
  (/ (* (sqrt (sqrt k)) (sqrt (sqrt k))) 1.0)
  (sqrt k)
  (sqrt k)
  (* (* n 2.0) PI)
  (* (* n 2.0) PI)
  (log (* (* n 2.0) PI))
  (log (* (* n 2.0) PI))
  (log (* (* n 2.0) PI))
  (exp (* (* n 2.0) PI))
  (* (* (* (* n 2.0) PI) (* (* n 2.0) PI)) (* (* n 2.0) PI))
  (* (* (* (* n 2.0) PI) (* (* n 2.0) PI)) (* (* n 2.0) PI))
  (* (cbrt (* (* n 2.0) PI)) (cbrt (* (* n 2.0) PI)))
  (cbrt (* (* n 2.0) PI))
  (* (* (* (* n 2.0) PI) (* (* n 2.0) PI)) (* (* n 2.0) PI))
  (sqrt (* (* n 2.0) PI))
  (sqrt (* (* n 2.0) PI))
  (* (* 2.0 (* PI (cbrt n))) (cbrt n))
  (* (* 2.0 PI) (sqrt n))
  (* 2.0 PI)
  (* n PI)
  (log (/ 1.0 (sqrt (sqrt k))))
  (log (/ 1.0 (sqrt (sqrt k))))
  (exp (/ 1.0 (sqrt (sqrt k))))
  (/ (* 1.0 1.0) (/ (sqrt (sqrt k)) (/ 1.0 (sqrt k))))
  (* (cbrt (/ 1.0 (sqrt (sqrt k)))) (cbrt (/ 1.0 (sqrt (sqrt k)))))
  (cbrt (/ 1.0 (sqrt (sqrt k))))
  (* (* (/ 1.0 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k)))) (/ 1.0 (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (sqrt (/ 1.0 (sqrt (sqrt k))))
  (- 1.0)
  (- (sqrt (sqrt k)))
  (* (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))) (/ (cbrt 1.0) (cbrt (sqrt (sqrt k)))))
  (/ (cbrt 1.0) (cbrt (sqrt (sqrt k))))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt (sqrt k))))
  (/ (cbrt 1.0) (sqrt (cbrt (sqrt k))))
  (/ (cbrt 1.0) (/ (sqrt (fabs (cbrt k))) (cbrt 1.0)))
  (/ (cbrt 1.0) (sqrt (sqrt (cbrt k))))
  (* (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (/ (cbrt 1.0) (sqrt (sqrt (sqrt k)))) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt (sqrt (sqrt k))))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ (sqrt 1.0) (cbrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (fabs (cbrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (cbrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (fabs (cbrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (cbrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (/ (sqrt 1.0) (sqrt (sqrt (sqrt k))))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))
  (/ 1.0 (cbrt (sqrt (sqrt k))))
  (/ 1 (fabs (cbrt (sqrt k))))
  (/ 1.0 (sqrt (cbrt (sqrt k))))
  (/ 1 (sqrt (fabs (cbrt k))))
  (/ 1.0 (sqrt (sqrt (cbrt k))))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  1
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  1
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt (sqrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  1
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (sqrt (sqrt k)) 1.0)
  (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))
  (/ 1.0 (fabs (cbrt (sqrt k))))
  (/ 1.0 (sqrt (fabs (cbrt k))))
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  1.0
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  1.0
  (/ 1.0 (sqrt (sqrt (sqrt k))))
  1.0
  (/ (sqrt (sqrt k)) (cbrt 1.0))
  (/ (sqrt (sqrt k)) (sqrt 1.0))
  (/ (sqrt (sqrt k)) 1.0)
  (+ (* (* (* k k) 0.125) (+ (* (* (log (* 2.0 PI)) (log (* 2.0 PI))) (exp (* 0.5 (log (* (* n 2.0) PI))))) (* (* (log n) (log n)) (exp (* 0.5 (log (* (* n 2.0) PI))))))) (- (+ (exp (* 0.5 (log (* (* n 2.0) PI)))) (* (* (* k k) 0.25) (* (* (log (* 2.0 PI)) (log n)) (exp (* 0.5 (log (* (* n 2.0) PI))))))) (* (* 0.5 k) (+ (* (log n) (exp (* 0.5 (log (* (* n 2.0) PI))))) (* (exp (* 0.5 (log (* (* n 2.0) PI)))) (log (* 2.0 PI)))))))
  (exp (* (* 0.5 (log (* (* n 2.0) PI))) (- 1.0 k)))
  (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5)))
  (- (- (* k +nan.0) (- (* (* k k) +nan.0) +nan.0)))
  (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ +nan.0 (* k (* k k)))))
  (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) +nan.0))
  (* (* n 2.0) PI)
  (* (* n 2.0) PI)
  (* (* n 2.0) PI)
  (* 1.0 (pow (/ 1 k) 1/4))
  (* 1.0 (pow (/ 1 k) 1/4))
  (- (* 1.0 (sqrt +nan.0)) (+ (- (/ +nan.0 (* (* k k) (sqrt +nan.0))) (/ (/ +nan.0 (sqrt +nan.0)) k)) (/ +nan.0 (* (* (* k k) +nan.0) (sqrt +nan.0)))))
33.265 * * * [progress]: adding candidates to table
36.265 * [progress]: [Phase 3 of 3] Extracting.
36.265 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (/ 1.0 (/ (sqrt (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ 1.0 (* (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))> #<alt (λ (k n) (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* 1.0 (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt k)))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)))))> #<alt (λ (k n) (* (* (/ (sqrt 1.0) (* (fabs (cbrt (sqrt k))) (sqrt (fabs (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k))))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))> #<alt (λ (k n) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))>)
36.273 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k)
36.273 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (#<alt (λ (k n) (/ 1.0 (/ (sqrt (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ 1.0 (* (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))> #<alt (λ (k n) (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* 1.0 (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt k)))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)))))> #<alt (λ (k n) (* (* (/ (sqrt 1.0) (* (fabs (cbrt (sqrt k))) (sqrt (fabs (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k))))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))> #<alt (λ (k n) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))>)
36.433 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (/ 1.0 (/ (sqrt (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ 1.0 (* (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))> #<alt (λ (k n) (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* 1.0 (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt k)))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)))))> #<alt (λ (k n) (* (* (/ (sqrt 1.0) (* (fabs (cbrt (sqrt k))) (sqrt (fabs (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k))))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))> #<alt (λ (k n) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))>)
36.597 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (/ 1.0 (/ (sqrt (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ 1.0 (* (/ (sqrt (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (/ (sqrt (sqrt k)) (pow n (/ (- 1.0 k) 2.0))))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n))) (cbrt (* (* 2.0 PI) n))) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (* (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))> #<alt (λ (k n) (* (/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* 1.0 (* (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt k)))> #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)))))> #<alt (λ (k n) (* (* (/ (sqrt 1.0) (* (fabs (cbrt (sqrt k))) (sqrt (fabs (cbrt k))))) (/ (/ (sqrt 1.0) (sqrt (sqrt (cbrt k)))) (sqrt (cbrt (sqrt k))))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))> #<alt (λ (k n) (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))>)
36.762 * * * [regime]: Found split indices: #<option (#s(si 10 255))>
36.763 * [simplify]: Simplifying:
  (/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
36.763 * * [simplify]: iteration 0: 13 enodes
36.765 * * [simplify]: iteration 1: 15 enodes
36.767 * * [simplify]: iteration complete: 15 enodes
36.767 * * [simplify]: Extracting #0: cost 1 inf + 0
36.767 * * [simplify]: Extracting #1: cost 3 inf + 0
36.767 * * [simplify]: Extracting #2: cost 4 inf + 1
36.767 * * [simplify]: Extracting #3: cost 7 inf + 1
36.768 * * [simplify]: Extracting #4: cost 9 inf + 43
36.768 * * [simplify]: Extracting #5: cost 6 inf + 170
36.768 * * [simplify]: Extracting #6: cost 3 inf + 296
36.768 * * [simplify]: Extracting #7: cost 1 inf + 1126
36.768 * * [simplify]: Extracting #8: cost 0 inf + 1621
36.769 * [simplify]: Simplified to:
  (/ 1.0 (/ (sqrt k) (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0))))
46.933 * [regime-testing]: Baseline error score: 0.36206858809282094
46.950 * [regime-testing]: Oracle error score: 0.036797080885471255
46.985 * [regime-testing]: End program error score: 0.36206858809282094