36.033 * [progress]: [Phase 1 of 3] Setting up.
0.001 * * * [progress]: [1/2] Preparing points
0.229 * * * [progress]: [2/2] Setting up program.
0.236 * [progress]: [Phase 2 of 3] Improving.
0.236 * * * * [progress]: [ 1 / 1 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
0.236 * [simplify]: Simplifying:
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.236 * * [simplify]: iteration 1: (13 enodes)
0.243 * * [simplify]: iteration 2: (29 enodes)
0.254 * * [simplify]: iteration 3: (60 enodes)
0.278 * * [simplify]: iteration 4: (123 enodes)
0.388 * * [simplify]: iteration 5: (322 enodes)
0.620 * * [simplify]: iteration 6: (817 enodes)
1.556 * * [simplify]: Extracting #0: cost 1 inf + 0
1.556 * * [simplify]: Extracting #1: cost 58 inf + 0
1.559 * * [simplify]: Extracting #2: cost 198 inf + 1
1.562 * * [simplify]: Extracting #3: cost 265 inf + 46
1.565 * * [simplify]: Extracting #4: cost 245 inf + 1713
1.574 * * [simplify]: Extracting #5: cost 180 inf + 14173
1.595 * * [simplify]: Extracting #6: cost 61 inf + 110645
1.644 * * [simplify]: Extracting #7: cost 0 inf + 167860
1.695 * * [simplify]: Extracting #8: cost 0 inf + 164570
1.742 * [simplify]: Simplified to:
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
1.751 * * [progress]: iteration 1 / 4
1.751 * * * [progress]: picking best candidate
1.762 * * * * [pick]: Picked  #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))>
1.762 * * * [progress]: localizing error
1.784 * * * [progress]: generating rewritten candidates
1.784 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1)
1.809 * * * * [progress]: [ 2 / 3 ] rewriting at (2 1 1)
1.822 * * * * [progress]: [ 3 / 3 ] rewriting at (2)
1.835 * * * [progress]: generating series expansions
1.835 * * * * [progress]: [ 1 / 3 ] generating series at (2 1)
1.836 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
1.836 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
1.836 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
1.836 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
1.836 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
1.836 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
1.836 * [taylor]: Taking taylor expansion of 1/2 in k
1.836 * [backup-simplify]: Simplify 1/2 into 1/2
1.836 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
1.836 * [taylor]: Taking taylor expansion of 1/2 in k
1.836 * [backup-simplify]: Simplify 1/2 into 1/2
1.836 * [taylor]: Taking taylor expansion of k in k
1.836 * [backup-simplify]: Simplify 0 into 0
1.836 * [backup-simplify]: Simplify 1 into 1
1.836 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
1.836 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
1.836 * [taylor]: Taking taylor expansion of 2 in k
1.836 * [backup-simplify]: Simplify 2 into 2
1.836 * [taylor]: Taking taylor expansion of (* n PI) in k
1.836 * [taylor]: Taking taylor expansion of n in k
1.836 * [backup-simplify]: Simplify n into n
1.836 * [taylor]: Taking taylor expansion of PI in k
1.836 * [backup-simplify]: Simplify PI into PI
1.836 * [backup-simplify]: Simplify (* n PI) into (* n PI)
1.836 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
1.837 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
1.837 * [backup-simplify]: Simplify (* 1/2 0) into 0
1.837 * [backup-simplify]: Simplify (- 0) into 0
1.837 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
1.837 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
1.838 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
1.838 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
1.838 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
1.838 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
1.838 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
1.838 * [taylor]: Taking taylor expansion of 1/2 in n
1.838 * [backup-simplify]: Simplify 1/2 into 1/2
1.838 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
1.838 * [taylor]: Taking taylor expansion of 1/2 in n
1.838 * [backup-simplify]: Simplify 1/2 into 1/2
1.838 * [taylor]: Taking taylor expansion of k in n
1.838 * [backup-simplify]: Simplify k into k
1.838 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.838 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.838 * [taylor]: Taking taylor expansion of 2 in n
1.838 * [backup-simplify]: Simplify 2 into 2
1.838 * [taylor]: Taking taylor expansion of (* n PI) in n
1.838 * [taylor]: Taking taylor expansion of n in n
1.838 * [backup-simplify]: Simplify 0 into 0
1.838 * [backup-simplify]: Simplify 1 into 1
1.838 * [taylor]: Taking taylor expansion of PI in n
1.838 * [backup-simplify]: Simplify PI into PI
1.838 * [backup-simplify]: Simplify (* 0 PI) into 0
1.839 * [backup-simplify]: Simplify (* 2 0) into 0
1.839 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.840 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.841 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.841 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
1.841 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
1.841 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
1.842 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.843 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
1.844 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
1.844 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
1.844 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
1.844 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
1.844 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
1.844 * [taylor]: Taking taylor expansion of 1/2 in n
1.844 * [backup-simplify]: Simplify 1/2 into 1/2
1.844 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
1.844 * [taylor]: Taking taylor expansion of 1/2 in n
1.844 * [backup-simplify]: Simplify 1/2 into 1/2
1.844 * [taylor]: Taking taylor expansion of k in n
1.844 * [backup-simplify]: Simplify k into k
1.844 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
1.844 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
1.844 * [taylor]: Taking taylor expansion of 2 in n
1.844 * [backup-simplify]: Simplify 2 into 2
1.844 * [taylor]: Taking taylor expansion of (* n PI) in n
1.844 * [taylor]: Taking taylor expansion of n in n
1.844 * [backup-simplify]: Simplify 0 into 0
1.844 * [backup-simplify]: Simplify 1 into 1
1.844 * [taylor]: Taking taylor expansion of PI in n
1.844 * [backup-simplify]: Simplify PI into PI
1.844 * [backup-simplify]: Simplify (* 0 PI) into 0
1.845 * [backup-simplify]: Simplify (* 2 0) into 0
1.846 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.846 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
1.847 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.847 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
1.847 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
1.847 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
1.848 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.849 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
1.849 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
1.850 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
1.850 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
1.850 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
1.850 * [taylor]: Taking taylor expansion of 1/2 in k
1.850 * [backup-simplify]: Simplify 1/2 into 1/2
1.850 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
1.850 * [taylor]: Taking taylor expansion of 1/2 in k
1.850 * [backup-simplify]: Simplify 1/2 into 1/2
1.850 * [taylor]: Taking taylor expansion of k in k
1.850 * [backup-simplify]: Simplify 0 into 0
1.850 * [backup-simplify]: Simplify 1 into 1
1.850 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
1.850 * [taylor]: Taking taylor expansion of (log n) in k
1.850 * [taylor]: Taking taylor expansion of n in k
1.850 * [backup-simplify]: Simplify n into n
1.850 * [backup-simplify]: Simplify (log n) into (log n)
1.850 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.850 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.850 * [taylor]: Taking taylor expansion of 2 in k
1.850 * [backup-simplify]: Simplify 2 into 2
1.850 * [taylor]: Taking taylor expansion of PI in k
1.850 * [backup-simplify]: Simplify PI into PI
1.850 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.851 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.851 * [backup-simplify]: Simplify (* 1/2 0) into 0
1.851 * [backup-simplify]: Simplify (- 0) into 0
1.852 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
1.852 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.853 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
1.854 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.855 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
1.856 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
1.856 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
1.858 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.858 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
1.858 * [backup-simplify]: Simplify (- 0) into 0
1.858 * [backup-simplify]: Simplify (+ 0 0) into 0
1.859 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.860 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
1.861 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
1.861 * [taylor]: Taking taylor expansion of 0 in k
1.861 * [backup-simplify]: Simplify 0 into 0
1.861 * [backup-simplify]: Simplify 0 into 0
1.862 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
1.862 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.863 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.864 * [backup-simplify]: Simplify (+ 0 0) into 0
1.864 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
1.864 * [backup-simplify]: Simplify (- 1/2) into -1/2
1.865 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
1.865 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
1.867 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
1.869 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
1.870 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
1.871 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
1.873 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
1.874 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
1.874 * [backup-simplify]: Simplify (- 0) into 0
1.874 * [backup-simplify]: Simplify (+ 0 0) into 0
1.880 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
1.881 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.884 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.884 * [taylor]: Taking taylor expansion of 0 in k
1.884 * [backup-simplify]: Simplify 0 into 0
1.884 * [backup-simplify]: Simplify 0 into 0
1.884 * [backup-simplify]: Simplify 0 into 0
1.885 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
1.886 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.890 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
1.890 * [backup-simplify]: Simplify (+ 0 0) into 0
1.892 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
1.892 * [backup-simplify]: Simplify (- 0) into 0
1.892 * [backup-simplify]: Simplify (+ 0 0) into 0
1.894 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
1.898 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
1.903 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
1.912 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
1.913 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
1.913 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
1.913 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
1.913 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
1.913 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
1.913 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
1.913 * [taylor]: Taking taylor expansion of 1/2 in k
1.913 * [backup-simplify]: Simplify 1/2 into 1/2
1.913 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
1.913 * [taylor]: Taking taylor expansion of 1/2 in k
1.913 * [backup-simplify]: Simplify 1/2 into 1/2
1.913 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.913 * [taylor]: Taking taylor expansion of k in k
1.913 * [backup-simplify]: Simplify 0 into 0
1.913 * [backup-simplify]: Simplify 1 into 1
1.913 * [backup-simplify]: Simplify (/ 1 1) into 1
1.913 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
1.913 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
1.913 * [taylor]: Taking taylor expansion of 2 in k
1.913 * [backup-simplify]: Simplify 2 into 2
1.913 * [taylor]: Taking taylor expansion of (/ PI n) in k
1.913 * [taylor]: Taking taylor expansion of PI in k
1.913 * [backup-simplify]: Simplify PI into PI
1.913 * [taylor]: Taking taylor expansion of n in k
1.913 * [backup-simplify]: Simplify n into n
1.913 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
1.914 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
1.914 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
1.914 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.914 * [backup-simplify]: Simplify (- 1/2) into -1/2
1.914 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
1.914 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
1.915 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
1.915 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
1.915 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
1.915 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
1.915 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
1.915 * [taylor]: Taking taylor expansion of 1/2 in n
1.915 * [backup-simplify]: Simplify 1/2 into 1/2
1.915 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
1.915 * [taylor]: Taking taylor expansion of 1/2 in n
1.915 * [backup-simplify]: Simplify 1/2 into 1/2
1.915 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.915 * [taylor]: Taking taylor expansion of k in n
1.915 * [backup-simplify]: Simplify k into k
1.915 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.915 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
1.915 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.915 * [taylor]: Taking taylor expansion of 2 in n
1.915 * [backup-simplify]: Simplify 2 into 2
1.915 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.915 * [taylor]: Taking taylor expansion of PI in n
1.915 * [backup-simplify]: Simplify PI into PI
1.915 * [taylor]: Taking taylor expansion of n in n
1.915 * [backup-simplify]: Simplify 0 into 0
1.915 * [backup-simplify]: Simplify 1 into 1
1.915 * [backup-simplify]: Simplify (/ PI 1) into PI
1.916 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.916 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.916 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
1.916 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
1.916 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
1.918 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.918 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
1.919 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
1.919 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
1.919 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
1.919 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
1.919 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
1.919 * [taylor]: Taking taylor expansion of 1/2 in n
1.919 * [backup-simplify]: Simplify 1/2 into 1/2
1.919 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
1.919 * [taylor]: Taking taylor expansion of 1/2 in n
1.919 * [backup-simplify]: Simplify 1/2 into 1/2
1.919 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.919 * [taylor]: Taking taylor expansion of k in n
1.919 * [backup-simplify]: Simplify k into k
1.919 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.919 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
1.919 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
1.919 * [taylor]: Taking taylor expansion of 2 in n
1.919 * [backup-simplify]: Simplify 2 into 2
1.919 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.919 * [taylor]: Taking taylor expansion of PI in n
1.919 * [backup-simplify]: Simplify PI into PI
1.919 * [taylor]: Taking taylor expansion of n in n
1.919 * [backup-simplify]: Simplify 0 into 0
1.919 * [backup-simplify]: Simplify 1 into 1
1.920 * [backup-simplify]: Simplify (/ PI 1) into PI
1.920 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.921 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.921 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
1.921 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
1.921 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
1.922 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.922 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
1.923 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
1.923 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
1.923 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
1.923 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
1.923 * [taylor]: Taking taylor expansion of 1/2 in k
1.923 * [backup-simplify]: Simplify 1/2 into 1/2
1.923 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
1.923 * [taylor]: Taking taylor expansion of 1/2 in k
1.923 * [backup-simplify]: Simplify 1/2 into 1/2
1.923 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.923 * [taylor]: Taking taylor expansion of k in k
1.923 * [backup-simplify]: Simplify 0 into 0
1.923 * [backup-simplify]: Simplify 1 into 1
1.924 * [backup-simplify]: Simplify (/ 1 1) into 1
1.924 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
1.924 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
1.924 * [taylor]: Taking taylor expansion of (* 2 PI) in k
1.924 * [taylor]: Taking taylor expansion of 2 in k
1.924 * [backup-simplify]: Simplify 2 into 2
1.924 * [taylor]: Taking taylor expansion of PI in k
1.924 * [backup-simplify]: Simplify PI into PI
1.924 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
1.925 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
1.925 * [taylor]: Taking taylor expansion of (log n) in k
1.925 * [taylor]: Taking taylor expansion of n in k
1.925 * [backup-simplify]: Simplify n into n
1.925 * [backup-simplify]: Simplify (log n) into (log n)
1.925 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.925 * [backup-simplify]: Simplify (- 1/2) into -1/2
1.926 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
1.926 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
1.926 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
1.927 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
1.928 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
1.928 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
1.929 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.929 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
1.930 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
1.930 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.931 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
1.931 * [backup-simplify]: Simplify (- 0) into 0
1.931 * [backup-simplify]: Simplify (+ 0 0) into 0
1.932 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.933 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
1.934 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
1.934 * [taylor]: Taking taylor expansion of 0 in k
1.934 * [backup-simplify]: Simplify 0 into 0
1.934 * [backup-simplify]: Simplify 0 into 0
1.934 * [backup-simplify]: Simplify 0 into 0
1.935 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.936 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
1.937 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
1.937 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.938 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
1.938 * [backup-simplify]: Simplify (- 0) into 0
1.938 * [backup-simplify]: Simplify (+ 0 0) into 0
1.940 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.941 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
1.944 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.944 * [taylor]: Taking taylor expansion of 0 in k
1.944 * [backup-simplify]: Simplify 0 into 0
1.944 * [backup-simplify]: Simplify 0 into 0
1.944 * [backup-simplify]: Simplify 0 into 0
1.944 * [backup-simplify]: Simplify 0 into 0
1.945 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.946 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.952 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
1.953 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.954 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
1.954 * [backup-simplify]: Simplify (- 0) into 0
1.955 * [backup-simplify]: Simplify (+ 0 0) into 0
1.956 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
1.957 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
1.958 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
1.958 * [taylor]: Taking taylor expansion of 0 in k
1.958 * [backup-simplify]: Simplify 0 into 0
1.958 * [backup-simplify]: Simplify 0 into 0
1.959 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
1.960 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
1.960 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
1.960 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
1.960 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
1.960 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
1.960 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
1.960 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
1.960 * [taylor]: Taking taylor expansion of 1/2 in k
1.960 * [backup-simplify]: Simplify 1/2 into 1/2
1.960 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.960 * [taylor]: Taking taylor expansion of k in k
1.960 * [backup-simplify]: Simplify 0 into 0
1.960 * [backup-simplify]: Simplify 1 into 1
1.960 * [backup-simplify]: Simplify (/ 1 1) into 1
1.960 * [taylor]: Taking taylor expansion of 1/2 in k
1.960 * [backup-simplify]: Simplify 1/2 into 1/2
1.960 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
1.960 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
1.960 * [taylor]: Taking taylor expansion of -2 in k
1.960 * [backup-simplify]: Simplify -2 into -2
1.960 * [taylor]: Taking taylor expansion of (/ PI n) in k
1.960 * [taylor]: Taking taylor expansion of PI in k
1.960 * [backup-simplify]: Simplify PI into PI
1.960 * [taylor]: Taking taylor expansion of n in k
1.960 * [backup-simplify]: Simplify n into n
1.960 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
1.960 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
1.960 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
1.961 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.961 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
1.961 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
1.961 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
1.961 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
1.961 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
1.961 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
1.961 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
1.961 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
1.961 * [taylor]: Taking taylor expansion of 1/2 in n
1.961 * [backup-simplify]: Simplify 1/2 into 1/2
1.961 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.961 * [taylor]: Taking taylor expansion of k in n
1.961 * [backup-simplify]: Simplify k into k
1.961 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.961 * [taylor]: Taking taylor expansion of 1/2 in n
1.961 * [backup-simplify]: Simplify 1/2 into 1/2
1.961 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
1.961 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.961 * [taylor]: Taking taylor expansion of -2 in n
1.961 * [backup-simplify]: Simplify -2 into -2
1.961 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.961 * [taylor]: Taking taylor expansion of PI in n
1.961 * [backup-simplify]: Simplify PI into PI
1.961 * [taylor]: Taking taylor expansion of n in n
1.961 * [backup-simplify]: Simplify 0 into 0
1.961 * [backup-simplify]: Simplify 1 into 1
1.962 * [backup-simplify]: Simplify (/ PI 1) into PI
1.962 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.963 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.963 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
1.963 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
1.964 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.964 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
1.965 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
1.965 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
1.965 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
1.965 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
1.965 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
1.965 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
1.965 * [taylor]: Taking taylor expansion of 1/2 in n
1.965 * [backup-simplify]: Simplify 1/2 into 1/2
1.965 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.965 * [taylor]: Taking taylor expansion of k in n
1.965 * [backup-simplify]: Simplify k into k
1.965 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.965 * [taylor]: Taking taylor expansion of 1/2 in n
1.965 * [backup-simplify]: Simplify 1/2 into 1/2
1.965 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
1.965 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
1.965 * [taylor]: Taking taylor expansion of -2 in n
1.965 * [backup-simplify]: Simplify -2 into -2
1.965 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.965 * [taylor]: Taking taylor expansion of PI in n
1.965 * [backup-simplify]: Simplify PI into PI
1.965 * [taylor]: Taking taylor expansion of n in n
1.965 * [backup-simplify]: Simplify 0 into 0
1.965 * [backup-simplify]: Simplify 1 into 1
1.966 * [backup-simplify]: Simplify (/ PI 1) into PI
1.966 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.967 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.967 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
1.967 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
1.968 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.968 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
1.969 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
1.969 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
1.969 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
1.969 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
1.969 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
1.969 * [taylor]: Taking taylor expansion of 1/2 in k
1.969 * [backup-simplify]: Simplify 1/2 into 1/2
1.969 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.969 * [taylor]: Taking taylor expansion of k in k
1.969 * [backup-simplify]: Simplify 0 into 0
1.969 * [backup-simplify]: Simplify 1 into 1
1.970 * [backup-simplify]: Simplify (/ 1 1) into 1
1.970 * [taylor]: Taking taylor expansion of 1/2 in k
1.970 * [backup-simplify]: Simplify 1/2 into 1/2
1.970 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
1.970 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
1.970 * [taylor]: Taking taylor expansion of (* -2 PI) in k
1.970 * [taylor]: Taking taylor expansion of -2 in k
1.970 * [backup-simplify]: Simplify -2 into -2
1.970 * [taylor]: Taking taylor expansion of PI in k
1.970 * [backup-simplify]: Simplify PI into PI
1.970 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
1.971 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
1.971 * [taylor]: Taking taylor expansion of (log n) in k
1.971 * [taylor]: Taking taylor expansion of n in k
1.971 * [backup-simplify]: Simplify n into n
1.971 * [backup-simplify]: Simplify (log n) into (log n)
1.971 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
1.971 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
1.971 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
1.972 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
1.973 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
1.973 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
1.974 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
1.975 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.975 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
1.976 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
1.976 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.976 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
1.977 * [backup-simplify]: Simplify (+ 0 0) into 0
1.978 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.978 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
1.979 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
1.979 * [taylor]: Taking taylor expansion of 0 in k
1.979 * [backup-simplify]: Simplify 0 into 0
1.979 * [backup-simplify]: Simplify 0 into 0
1.979 * [backup-simplify]: Simplify 0 into 0
1.980 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.981 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
1.985 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
1.986 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
1.987 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
1.987 * [backup-simplify]: Simplify (+ 0 0) into 0
1.989 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
1.990 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
1.993 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
1.993 * [taylor]: Taking taylor expansion of 0 in k
1.993 * [backup-simplify]: Simplify 0 into 0
1.993 * [backup-simplify]: Simplify 0 into 0
1.993 * [backup-simplify]: Simplify 0 into 0
1.993 * [backup-simplify]: Simplify 0 into 0
1.994 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.995 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.002 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
2.003 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.004 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
2.004 * [backup-simplify]: Simplify (+ 0 0) into 0
2.006 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.008 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
2.011 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.011 * [taylor]: Taking taylor expansion of 0 in k
2.011 * [backup-simplify]: Simplify 0 into 0
2.011 * [backup-simplify]: Simplify 0 into 0
2.012 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
2.013 * * * * [progress]: [ 2 / 3 ] generating series at (2 1 1)
2.013 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
2.013 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
2.013 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.013 * [taylor]: Taking taylor expansion of 2 in n
2.013 * [backup-simplify]: Simplify 2 into 2
2.013 * [taylor]: Taking taylor expansion of (* n PI) in n
2.013 * [taylor]: Taking taylor expansion of n in n
2.013 * [backup-simplify]: Simplify 0 into 0
2.013 * [backup-simplify]: Simplify 1 into 1
2.013 * [taylor]: Taking taylor expansion of PI in n
2.013 * [backup-simplify]: Simplify PI into PI
2.013 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.013 * [taylor]: Taking taylor expansion of 2 in n
2.014 * [backup-simplify]: Simplify 2 into 2
2.014 * [taylor]: Taking taylor expansion of (* n PI) in n
2.014 * [taylor]: Taking taylor expansion of n in n
2.014 * [backup-simplify]: Simplify 0 into 0
2.014 * [backup-simplify]: Simplify 1 into 1
2.014 * [taylor]: Taking taylor expansion of PI in n
2.014 * [backup-simplify]: Simplify PI into PI
2.014 * [backup-simplify]: Simplify (* 0 PI) into 0
2.015 * [backup-simplify]: Simplify (* 2 0) into 0
2.015 * [backup-simplify]: Simplify 0 into 0
2.017 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.018 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.019 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.020 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
2.021 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
2.021 * [backup-simplify]: Simplify 0 into 0
2.022 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
2.023 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
2.023 * [backup-simplify]: Simplify 0 into 0
2.025 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.026 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
2.026 * [backup-simplify]: Simplify 0 into 0
2.028 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.029 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
2.029 * [backup-simplify]: Simplify 0 into 0
2.031 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.033 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
2.033 * [backup-simplify]: Simplify 0 into 0
2.035 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
2.037 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
2.037 * [backup-simplify]: Simplify 0 into 0
2.037 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
2.038 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
2.038 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
2.038 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.038 * [taylor]: Taking taylor expansion of 2 in n
2.038 * [backup-simplify]: Simplify 2 into 2
2.038 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.038 * [taylor]: Taking taylor expansion of PI in n
2.038 * [backup-simplify]: Simplify PI into PI
2.038 * [taylor]: Taking taylor expansion of n in n
2.038 * [backup-simplify]: Simplify 0 into 0
2.038 * [backup-simplify]: Simplify 1 into 1
2.038 * [backup-simplify]: Simplify (/ PI 1) into PI
2.038 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.038 * [taylor]: Taking taylor expansion of 2 in n
2.038 * [backup-simplify]: Simplify 2 into 2
2.038 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.039 * [taylor]: Taking taylor expansion of PI in n
2.039 * [backup-simplify]: Simplify PI into PI
2.039 * [taylor]: Taking taylor expansion of n in n
2.039 * [backup-simplify]: Simplify 0 into 0
2.039 * [backup-simplify]: Simplify 1 into 1
2.039 * [backup-simplify]: Simplify (/ PI 1) into PI
2.040 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.040 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.041 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.042 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.042 * [backup-simplify]: Simplify 0 into 0
2.043 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.043 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.043 * [backup-simplify]: Simplify 0 into 0
2.044 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.045 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.045 * [backup-simplify]: Simplify 0 into 0
2.045 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.046 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.046 * [backup-simplify]: Simplify 0 into 0
2.047 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.048 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.048 * [backup-simplify]: Simplify 0 into 0
2.048 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.049 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.049 * [backup-simplify]: Simplify 0 into 0
2.050 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
2.050 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
2.050 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
2.050 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.050 * [taylor]: Taking taylor expansion of -2 in n
2.050 * [backup-simplify]: Simplify -2 into -2
2.050 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.050 * [taylor]: Taking taylor expansion of PI in n
2.050 * [backup-simplify]: Simplify PI into PI
2.050 * [taylor]: Taking taylor expansion of n in n
2.050 * [backup-simplify]: Simplify 0 into 0
2.050 * [backup-simplify]: Simplify 1 into 1
2.050 * [backup-simplify]: Simplify (/ PI 1) into PI
2.051 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.051 * [taylor]: Taking taylor expansion of -2 in n
2.051 * [backup-simplify]: Simplify -2 into -2
2.051 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.051 * [taylor]: Taking taylor expansion of PI in n
2.051 * [backup-simplify]: Simplify PI into PI
2.051 * [taylor]: Taking taylor expansion of n in n
2.051 * [backup-simplify]: Simplify 0 into 0
2.051 * [backup-simplify]: Simplify 1 into 1
2.051 * [backup-simplify]: Simplify (/ PI 1) into PI
2.051 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.052 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.052 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.053 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.053 * [backup-simplify]: Simplify 0 into 0
2.053 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.054 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.054 * [backup-simplify]: Simplify 0 into 0
2.054 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.055 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.055 * [backup-simplify]: Simplify 0 into 0
2.056 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.057 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.057 * [backup-simplify]: Simplify 0 into 0
2.057 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.058 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
2.058 * [backup-simplify]: Simplify 0 into 0
2.059 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.060 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
2.060 * [backup-simplify]: Simplify 0 into 0
2.060 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
2.060 * * * * [progress]: [ 3 / 3 ] generating series at (2)
2.061 * [backup-simplify]: Simplify (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) into (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))))
2.061 * [approximate]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in (n k) around 0
2.061 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in k
2.061 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
2.061 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.061 * [taylor]: Taking taylor expansion of k in k
2.061 * [backup-simplify]: Simplify 0 into 0
2.061 * [backup-simplify]: Simplify 1 into 1
2.061 * [backup-simplify]: Simplify (/ 1 1) into 1
2.061 * [backup-simplify]: Simplify (sqrt 0) into 0
2.062 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.062 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
2.062 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
2.062 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
2.062 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
2.062 * [taylor]: Taking taylor expansion of 1/2 in k
2.062 * [backup-simplify]: Simplify 1/2 into 1/2
2.062 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
2.062 * [taylor]: Taking taylor expansion of 1/2 in k
2.062 * [backup-simplify]: Simplify 1/2 into 1/2
2.062 * [taylor]: Taking taylor expansion of k in k
2.062 * [backup-simplify]: Simplify 0 into 0
2.062 * [backup-simplify]: Simplify 1 into 1
2.062 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
2.062 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
2.062 * [taylor]: Taking taylor expansion of 2 in k
2.062 * [backup-simplify]: Simplify 2 into 2
2.062 * [taylor]: Taking taylor expansion of (* n PI) in k
2.062 * [taylor]: Taking taylor expansion of n in k
2.062 * [backup-simplify]: Simplify n into n
2.062 * [taylor]: Taking taylor expansion of PI in k
2.062 * [backup-simplify]: Simplify PI into PI
2.063 * [backup-simplify]: Simplify (* n PI) into (* n PI)
2.063 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
2.063 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
2.063 * [backup-simplify]: Simplify (* 1/2 0) into 0
2.063 * [backup-simplify]: Simplify (- 0) into 0
2.063 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.063 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
2.064 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
2.064 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
2.064 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
2.064 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.064 * [taylor]: Taking taylor expansion of k in n
2.064 * [backup-simplify]: Simplify k into k
2.064 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.064 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
2.064 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.064 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
2.064 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
2.064 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
2.064 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
2.064 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
2.064 * [taylor]: Taking taylor expansion of 1/2 in n
2.064 * [backup-simplify]: Simplify 1/2 into 1/2
2.064 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
2.064 * [taylor]: Taking taylor expansion of 1/2 in n
2.064 * [backup-simplify]: Simplify 1/2 into 1/2
2.064 * [taylor]: Taking taylor expansion of k in n
2.064 * [backup-simplify]: Simplify k into k
2.064 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
2.064 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.064 * [taylor]: Taking taylor expansion of 2 in n
2.064 * [backup-simplify]: Simplify 2 into 2
2.064 * [taylor]: Taking taylor expansion of (* n PI) in n
2.064 * [taylor]: Taking taylor expansion of n in n
2.064 * [backup-simplify]: Simplify 0 into 0
2.064 * [backup-simplify]: Simplify 1 into 1
2.064 * [taylor]: Taking taylor expansion of PI in n
2.064 * [backup-simplify]: Simplify PI into PI
2.064 * [backup-simplify]: Simplify (* 0 PI) into 0
2.065 * [backup-simplify]: Simplify (* 2 0) into 0
2.066 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.066 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.067 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.067 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
2.067 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
2.067 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
2.068 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.069 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
2.070 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
2.070 * [taylor]: Taking taylor expansion of (* (sqrt (/ 1 k)) (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))) in n
2.070 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
2.070 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.070 * [taylor]: Taking taylor expansion of k in n
2.070 * [backup-simplify]: Simplify k into k
2.070 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.070 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
2.070 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.070 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
2.070 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
2.070 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
2.070 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
2.070 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
2.070 * [taylor]: Taking taylor expansion of 1/2 in n
2.070 * [backup-simplify]: Simplify 1/2 into 1/2
2.070 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
2.070 * [taylor]: Taking taylor expansion of 1/2 in n
2.070 * [backup-simplify]: Simplify 1/2 into 1/2
2.070 * [taylor]: Taking taylor expansion of k in n
2.070 * [backup-simplify]: Simplify k into k
2.070 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
2.070 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
2.070 * [taylor]: Taking taylor expansion of 2 in n
2.070 * [backup-simplify]: Simplify 2 into 2
2.070 * [taylor]: Taking taylor expansion of (* n PI) in n
2.070 * [taylor]: Taking taylor expansion of n in n
2.070 * [backup-simplify]: Simplify 0 into 0
2.070 * [backup-simplify]: Simplify 1 into 1
2.070 * [taylor]: Taking taylor expansion of PI in n
2.070 * [backup-simplify]: Simplify PI into PI
2.070 * [backup-simplify]: Simplify (* 0 PI) into 0
2.071 * [backup-simplify]: Simplify (* 2 0) into 0
2.072 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.073 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
2.073 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.073 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
2.073 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
2.074 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
2.074 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.075 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
2.076 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
2.077 * [backup-simplify]: Simplify (* (sqrt (/ 1 k)) (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))) into (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k)))
2.077 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (sqrt (/ 1 k))) in k
2.077 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
2.077 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
2.077 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
2.077 * [taylor]: Taking taylor expansion of 1/2 in k
2.077 * [backup-simplify]: Simplify 1/2 into 1/2
2.077 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
2.077 * [taylor]: Taking taylor expansion of 1/2 in k
2.077 * [backup-simplify]: Simplify 1/2 into 1/2
2.077 * [taylor]: Taking taylor expansion of k in k
2.077 * [backup-simplify]: Simplify 0 into 0
2.077 * [backup-simplify]: Simplify 1 into 1
2.077 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
2.077 * [taylor]: Taking taylor expansion of (log n) in k
2.077 * [taylor]: Taking taylor expansion of n in k
2.077 * [backup-simplify]: Simplify n into n
2.077 * [backup-simplify]: Simplify (log n) into (log n)
2.077 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.077 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.077 * [taylor]: Taking taylor expansion of 2 in k
2.077 * [backup-simplify]: Simplify 2 into 2
2.077 * [taylor]: Taking taylor expansion of PI in k
2.077 * [backup-simplify]: Simplify PI into PI
2.077 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.078 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.078 * [backup-simplify]: Simplify (* 1/2 0) into 0
2.078 * [backup-simplify]: Simplify (- 0) into 0
2.079 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.080 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.081 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
2.082 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
2.082 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
2.082 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.082 * [taylor]: Taking taylor expansion of k in k
2.082 * [backup-simplify]: Simplify 0 into 0
2.082 * [backup-simplify]: Simplify 1 into 1
2.083 * [backup-simplify]: Simplify (/ 1 1) into 1
2.083 * [backup-simplify]: Simplify (sqrt 0) into 0
2.085 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.086 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) 0) into 0
2.086 * [backup-simplify]: Simplify 0 into 0
2.087 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
2.088 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
2.090 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.090 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
2.091 * [backup-simplify]: Simplify (- 0) into 0
2.091 * [backup-simplify]: Simplify (+ 0 0) into 0
2.093 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.094 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
2.096 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.097 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))) into 0
2.097 * [taylor]: Taking taylor expansion of 0 in k
2.097 * [backup-simplify]: Simplify 0 into 0
2.098 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
2.099 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.100 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.101 * [backup-simplify]: Simplify (+ 0 0) into 0
2.102 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
2.102 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.102 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.104 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
2.110 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.114 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.115 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.116 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
2.117 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
2.118 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
2.119 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
2.119 * [backup-simplify]: Simplify (- 0) into 0
2.119 * [backup-simplify]: Simplify (+ 0 0) into 0
2.120 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.121 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.123 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.123 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.123 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
2.124 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))))) into 0
2.124 * [taylor]: Taking taylor expansion of 0 in k
2.124 * [backup-simplify]: Simplify 0 into 0
2.124 * [backup-simplify]: Simplify 0 into 0
2.125 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
2.127 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.128 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
2.128 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.130 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
2.130 * [backup-simplify]: Simplify (+ 0 0) into 0
2.131 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
2.131 * [backup-simplify]: Simplify (- 0) into 0
2.131 * [backup-simplify]: Simplify (+ 0 0) into 0
2.132 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
2.135 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
2.141 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) 0))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
2.146 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))
2.147 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
2.149 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
2.154 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
2.156 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 k)))) into 0
2.156 * [backup-simplify]: Simplify (- 0) into 0
2.156 * [backup-simplify]: Simplify (+ 0 0) into 0
2.158 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
2.160 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.163 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.163 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.164 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
2.166 * [backup-simplify]: Simplify (+ (* (sqrt (/ 1 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))))))) into 0
2.166 * [taylor]: Taking taylor expansion of 0 in k
2.166 * [backup-simplify]: Simplify 0 into 0
2.166 * [backup-simplify]: Simplify 0 into 0
2.166 * [backup-simplify]: Simplify 0 into 0
2.167 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.171 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.174 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
2.175 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.178 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
2.179 * [backup-simplify]: Simplify (+ 0 0) into 0
2.179 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 1) (* 0 0)))) into 0
2.180 * [backup-simplify]: Simplify (- 0) into 0
2.180 * [backup-simplify]: Simplify (+ 0 0) into 0
2.181 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI))))))) into 0
2.185 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
2.195 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) +nan.0) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) +nan.0) (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) +nan.0) (* (* -1 (* (+ (* 1/48 (pow (log n) 3)) (+ (* 1/16 (* (pow (log n) 2) (log (* 2 PI)))) (+ (* 1/16 (* (log n) (pow (log (* 2 PI)) 2))) (* 1/48 (pow (log (* 2 PI)) 3))))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) 0)))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
2.202 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) into (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n))))))))))))))
2.227 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log (* 2 PI)) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow (log n) 2))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (log (* 2 PI))))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log (* 2 PI)))) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (log n)))))))) (* k 1)) (- (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI))))))))) into (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
2.228 * [backup-simplify]: Simplify (/ (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) (sqrt (/ 1 k))) into (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))))
2.228 * [approximate]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in (n k) around 0
2.228 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in k
2.228 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.228 * [taylor]: Taking taylor expansion of k in k
2.228 * [backup-simplify]: Simplify 0 into 0
2.228 * [backup-simplify]: Simplify 1 into 1
2.228 * [backup-simplify]: Simplify (sqrt 0) into 0
2.230 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.230 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
2.230 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
2.230 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
2.230 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
2.230 * [taylor]: Taking taylor expansion of 1/2 in k
2.230 * [backup-simplify]: Simplify 1/2 into 1/2
2.230 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.230 * [taylor]: Taking taylor expansion of 1/2 in k
2.230 * [backup-simplify]: Simplify 1/2 into 1/2
2.230 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.230 * [taylor]: Taking taylor expansion of k in k
2.230 * [backup-simplify]: Simplify 0 into 0
2.230 * [backup-simplify]: Simplify 1 into 1
2.231 * [backup-simplify]: Simplify (/ 1 1) into 1
2.231 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
2.231 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
2.231 * [taylor]: Taking taylor expansion of 2 in k
2.231 * [backup-simplify]: Simplify 2 into 2
2.231 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.231 * [taylor]: Taking taylor expansion of PI in k
2.231 * [backup-simplify]: Simplify PI into PI
2.231 * [taylor]: Taking taylor expansion of n in k
2.231 * [backup-simplify]: Simplify n into n
2.231 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.231 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
2.231 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
2.231 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.231 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.232 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.232 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
2.232 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
2.232 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
2.232 * [taylor]: Taking taylor expansion of (sqrt k) in n
2.232 * [taylor]: Taking taylor expansion of k in n
2.232 * [backup-simplify]: Simplify k into k
2.232 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
2.232 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
2.232 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
2.232 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.232 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.232 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
2.232 * [taylor]: Taking taylor expansion of 1/2 in n
2.232 * [backup-simplify]: Simplify 1/2 into 1/2
2.232 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.232 * [taylor]: Taking taylor expansion of 1/2 in n
2.232 * [backup-simplify]: Simplify 1/2 into 1/2
2.232 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.232 * [taylor]: Taking taylor expansion of k in n
2.232 * [backup-simplify]: Simplify k into k
2.232 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.232 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.232 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.232 * [taylor]: Taking taylor expansion of 2 in n
2.232 * [backup-simplify]: Simplify 2 into 2
2.232 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.232 * [taylor]: Taking taylor expansion of PI in n
2.232 * [backup-simplify]: Simplify PI into PI
2.232 * [taylor]: Taking taylor expansion of n in n
2.232 * [backup-simplify]: Simplify 0 into 0
2.232 * [backup-simplify]: Simplify 1 into 1
2.233 * [backup-simplify]: Simplify (/ PI 1) into PI
2.233 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.234 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.234 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.234 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
2.234 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
2.235 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.236 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
2.236 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
2.236 * [taylor]: Taking taylor expansion of (* (sqrt k) (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))) in n
2.236 * [taylor]: Taking taylor expansion of (sqrt k) in n
2.236 * [taylor]: Taking taylor expansion of k in n
2.236 * [backup-simplify]: Simplify k into k
2.236 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
2.237 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
2.237 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
2.237 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
2.237 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
2.237 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
2.237 * [taylor]: Taking taylor expansion of 1/2 in n
2.237 * [backup-simplify]: Simplify 1/2 into 1/2
2.237 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.237 * [taylor]: Taking taylor expansion of 1/2 in n
2.237 * [backup-simplify]: Simplify 1/2 into 1/2
2.237 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.237 * [taylor]: Taking taylor expansion of k in n
2.237 * [backup-simplify]: Simplify k into k
2.237 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.237 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
2.237 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
2.237 * [taylor]: Taking taylor expansion of 2 in n
2.237 * [backup-simplify]: Simplify 2 into 2
2.237 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.237 * [taylor]: Taking taylor expansion of PI in n
2.237 * [backup-simplify]: Simplify PI into PI
2.237 * [taylor]: Taking taylor expansion of n in n
2.237 * [backup-simplify]: Simplify 0 into 0
2.237 * [backup-simplify]: Simplify 1 into 1
2.237 * [backup-simplify]: Simplify (/ PI 1) into PI
2.237 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.238 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.238 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.238 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
2.238 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
2.239 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.240 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
2.241 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
2.241 * [backup-simplify]: Simplify (* (sqrt k) (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))) into (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k))
2.241 * [taylor]: Taking taylor expansion of (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (sqrt k)) in k
2.241 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
2.241 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
2.242 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
2.242 * [taylor]: Taking taylor expansion of 1/2 in k
2.242 * [backup-simplify]: Simplify 1/2 into 1/2
2.242 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.242 * [taylor]: Taking taylor expansion of 1/2 in k
2.242 * [backup-simplify]: Simplify 1/2 into 1/2
2.242 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.242 * [taylor]: Taking taylor expansion of k in k
2.242 * [backup-simplify]: Simplify 0 into 0
2.242 * [backup-simplify]: Simplify 1 into 1
2.242 * [backup-simplify]: Simplify (/ 1 1) into 1
2.242 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
2.242 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
2.242 * [taylor]: Taking taylor expansion of (* 2 PI) in k
2.242 * [taylor]: Taking taylor expansion of 2 in k
2.242 * [backup-simplify]: Simplify 2 into 2
2.242 * [taylor]: Taking taylor expansion of PI in k
2.242 * [backup-simplify]: Simplify PI into PI
2.242 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
2.243 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
2.243 * [taylor]: Taking taylor expansion of (log n) in k
2.243 * [taylor]: Taking taylor expansion of n in k
2.243 * [backup-simplify]: Simplify n into n
2.243 * [backup-simplify]: Simplify (log n) into (log n)
2.243 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.244 * [backup-simplify]: Simplify (- 1/2) into -1/2
2.244 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
2.244 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.245 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
2.245 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
2.246 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
2.246 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.246 * [taylor]: Taking taylor expansion of k in k
2.246 * [backup-simplify]: Simplify 0 into 0
2.246 * [backup-simplify]: Simplify 1 into 1
2.246 * [backup-simplify]: Simplify (sqrt 0) into 0
2.247 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.248 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) 0) into 0
2.248 * [backup-simplify]: Simplify 0 into 0
2.248 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.249 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
2.250 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
2.250 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.250 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
2.251 * [backup-simplify]: Simplify (- 0) into 0
2.251 * [backup-simplify]: Simplify (+ 0 0) into 0
2.252 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.252 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
2.253 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.254 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into 0
2.254 * [taylor]: Taking taylor expansion of 0 in k
2.254 * [backup-simplify]: Simplify 0 into 0
2.254 * [backup-simplify]: Simplify 0 into 0
2.255 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
2.256 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
2.257 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.257 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
2.259 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
2.259 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.260 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
2.260 * [backup-simplify]: Simplify (- 0) into 0
2.260 * [backup-simplify]: Simplify (+ 0 0) into 0
2.261 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.262 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
2.263 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.264 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
2.265 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))) into 0
2.265 * [taylor]: Taking taylor expansion of 0 in k
2.265 * [backup-simplify]: Simplify 0 into 0
2.265 * [backup-simplify]: Simplify 0 into 0
2.265 * [backup-simplify]: Simplify 0 into 0
2.267 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.268 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
2.269 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
2.270 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.270 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.273 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
2.274 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.274 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
2.275 * [backup-simplify]: Simplify (- 0) into 0
2.275 * [backup-simplify]: Simplify (+ 0 0) into 0
2.276 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
2.277 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
2.278 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.279 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
2.280 * [backup-simplify]: Simplify (+ (* (sqrt k) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))))) into 0
2.280 * [taylor]: Taking taylor expansion of 0 in k
2.280 * [backup-simplify]: Simplify 0 into 0
2.280 * [backup-simplify]: Simplify 0 into 0
2.280 * [backup-simplify]: Simplify 0 into 0
2.280 * [backup-simplify]: Simplify 0 into 0
2.282 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.284 * [backup-simplify]: Simplify (+ (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
2.285 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))))
2.288 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
2.288 * [backup-simplify]: Simplify (/ (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) (sqrt (/ 1 (- k)))) into (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k)))
2.288 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in (n k) around 0
2.288 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in k
2.289 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
2.289 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
2.289 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
2.289 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
2.289 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.289 * [taylor]: Taking taylor expansion of 1/2 in k
2.289 * [backup-simplify]: Simplify 1/2 into 1/2
2.289 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.289 * [taylor]: Taking taylor expansion of k in k
2.289 * [backup-simplify]: Simplify 0 into 0
2.289 * [backup-simplify]: Simplify 1 into 1
2.289 * [backup-simplify]: Simplify (/ 1 1) into 1
2.289 * [taylor]: Taking taylor expansion of 1/2 in k
2.289 * [backup-simplify]: Simplify 1/2 into 1/2
2.289 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
2.289 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
2.289 * [taylor]: Taking taylor expansion of -2 in k
2.289 * [backup-simplify]: Simplify -2 into -2
2.289 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.290 * [taylor]: Taking taylor expansion of PI in k
2.290 * [backup-simplify]: Simplify PI into PI
2.290 * [taylor]: Taking taylor expansion of n in k
2.290 * [backup-simplify]: Simplify n into n
2.290 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.290 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
2.290 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
2.290 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.291 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.291 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
2.291 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
2.291 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.291 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.291 * [taylor]: Taking taylor expansion of -1 in k
2.291 * [backup-simplify]: Simplify -1 into -1
2.291 * [taylor]: Taking taylor expansion of k in k
2.291 * [backup-simplify]: Simplify 0 into 0
2.291 * [backup-simplify]: Simplify 1 into 1
2.292 * [backup-simplify]: Simplify (/ -1 1) into -1
2.292 * [backup-simplify]: Simplify (sqrt 0) into 0
2.294 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.294 * [backup-simplify]: Simplify (/ (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))) +nan.0) into (* +nan.0 (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2))))
2.294 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
2.294 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
2.294 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
2.294 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
2.294 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
2.294 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.294 * [taylor]: Taking taylor expansion of 1/2 in n
2.294 * [backup-simplify]: Simplify 1/2 into 1/2
2.294 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.294 * [taylor]: Taking taylor expansion of k in n
2.294 * [backup-simplify]: Simplify k into k
2.294 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.294 * [taylor]: Taking taylor expansion of 1/2 in n
2.294 * [backup-simplify]: Simplify 1/2 into 1/2
2.294 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.294 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.294 * [taylor]: Taking taylor expansion of -2 in n
2.294 * [backup-simplify]: Simplify -2 into -2
2.294 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.294 * [taylor]: Taking taylor expansion of PI in n
2.295 * [backup-simplify]: Simplify PI into PI
2.295 * [taylor]: Taking taylor expansion of n in n
2.295 * [backup-simplify]: Simplify 0 into 0
2.295 * [backup-simplify]: Simplify 1 into 1
2.295 * [backup-simplify]: Simplify (/ PI 1) into PI
2.296 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.297 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.297 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.297 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
2.298 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.299 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
2.301 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
2.301 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.301 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.301 * [taylor]: Taking taylor expansion of -1 in n
2.301 * [backup-simplify]: Simplify -1 into -1
2.301 * [taylor]: Taking taylor expansion of k in n
2.301 * [backup-simplify]: Simplify k into k
2.301 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.301 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.301 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.301 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.302 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
2.302 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) (sqrt (/ -1 k))) in n
2.302 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
2.303 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
2.303 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
2.303 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
2.303 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
2.303 * [taylor]: Taking taylor expansion of 1/2 in n
2.303 * [backup-simplify]: Simplify 1/2 into 1/2
2.303 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.303 * [taylor]: Taking taylor expansion of k in n
2.303 * [backup-simplify]: Simplify k into k
2.303 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.303 * [taylor]: Taking taylor expansion of 1/2 in n
2.303 * [backup-simplify]: Simplify 1/2 into 1/2
2.303 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
2.303 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
2.303 * [taylor]: Taking taylor expansion of -2 in n
2.303 * [backup-simplify]: Simplify -2 into -2
2.303 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.303 * [taylor]: Taking taylor expansion of PI in n
2.303 * [backup-simplify]: Simplify PI into PI
2.303 * [taylor]: Taking taylor expansion of n in n
2.303 * [backup-simplify]: Simplify 0 into 0
2.303 * [backup-simplify]: Simplify 1 into 1
2.304 * [backup-simplify]: Simplify (/ PI 1) into PI
2.304 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.305 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.305 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
2.305 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
2.307 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.308 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
2.309 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
2.309 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.309 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.309 * [taylor]: Taking taylor expansion of -1 in n
2.309 * [backup-simplify]: Simplify -1 into -1
2.309 * [taylor]: Taking taylor expansion of k in n
2.309 * [backup-simplify]: Simplify k into k
2.309 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.310 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.310 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.310 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.311 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) into (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k)))
2.311 * [taylor]: Taking taylor expansion of (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) in k
2.311 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
2.311 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
2.311 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
2.311 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
2.311 * [taylor]: Taking taylor expansion of 1/2 in k
2.311 * [backup-simplify]: Simplify 1/2 into 1/2
2.311 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.311 * [taylor]: Taking taylor expansion of k in k
2.311 * [backup-simplify]: Simplify 0 into 0
2.311 * [backup-simplify]: Simplify 1 into 1
2.312 * [backup-simplify]: Simplify (/ 1 1) into 1
2.312 * [taylor]: Taking taylor expansion of 1/2 in k
2.312 * [backup-simplify]: Simplify 1/2 into 1/2
2.312 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
2.312 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
2.312 * [taylor]: Taking taylor expansion of (* -2 PI) in k
2.312 * [taylor]: Taking taylor expansion of -2 in k
2.312 * [backup-simplify]: Simplify -2 into -2
2.312 * [taylor]: Taking taylor expansion of PI in k
2.312 * [backup-simplify]: Simplify PI into PI
2.312 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
2.314 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
2.314 * [taylor]: Taking taylor expansion of (log n) in k
2.314 * [taylor]: Taking taylor expansion of n in k
2.314 * [backup-simplify]: Simplify n into n
2.314 * [backup-simplify]: Simplify (log n) into (log n)
2.314 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
2.315 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
2.315 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.318 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
2.318 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
2.319 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
2.319 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.319 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.319 * [taylor]: Taking taylor expansion of -1 in k
2.319 * [backup-simplify]: Simplify -1 into -1
2.319 * [taylor]: Taking taylor expansion of k in k
2.319 * [backup-simplify]: Simplify 0 into 0
2.319 * [backup-simplify]: Simplify 1 into 1
2.320 * [backup-simplify]: Simplify (/ -1 1) into -1
2.320 * [backup-simplify]: Simplify (sqrt 0) into 0
2.321 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.321 * [backup-simplify]: Simplify (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) +nan.0) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
2.322 * [backup-simplify]: Simplify (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) into (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))
2.323 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.323 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
2.324 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
2.324 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.325 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
2.325 * [backup-simplify]: Simplify (+ 0 0) into 0
2.326 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.327 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
2.328 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.329 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
2.329 * [taylor]: Taking taylor expansion of 0 in k
2.329 * [backup-simplify]: Simplify 0 into 0
2.329 * [backup-simplify]: Simplify 0 into 0
2.329 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
2.331 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.332 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
2.333 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
2.334 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.335 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
2.336 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
2.337 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.337 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
2.337 * [backup-simplify]: Simplify (+ 0 0) into 0
2.338 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
2.339 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
2.341 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.341 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.341 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
2.342 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
2.342 * [taylor]: Taking taylor expansion of 0 in k
2.342 * [backup-simplify]: Simplify 0 into 0
2.342 * [backup-simplify]: Simplify 0 into 0
2.342 * [backup-simplify]: Simplify 0 into 0
2.343 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.345 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.347 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
2.348 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))))) into (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))))
2.351 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) into (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
2.351 * * * [progress]: simplifying candidates
2.351 * * * * [progress]: [ 1 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
2.351 * * * * [progress]: [ 2 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
2.351 * * * * [progress]: [ 3 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
2.351 * * * * [progress]: [ 4 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))) (sqrt k)))>
2.351 * * * * [progress]: [ 5 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
2.351 * * * * [progress]: [ 6 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
2.351 * * * * [progress]: [ 7 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2)))) (sqrt k)))>
2.351 * * * * [progress]: [ 8 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2))) (sqrt k)))>
2.351 * * * * [progress]: [ 9 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (sqrt k)))>
2.351 * * * * [progress]: [ 10 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (sqrt k)))>
2.351 * * * * [progress]: [ 11 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.351 * * * * [progress]: [ 12 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (sqrt k)))>
2.351 * * * * [progress]: [ 13 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (sqrt k)))>
2.351 * * * * [progress]: [ 14 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.351 * * * * [progress]: [ 15 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))) (sqrt k)))>
2.351 * * * * [progress]: [ 16 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2)))) (sqrt k)))>
2.351 * * * * [progress]: [ 17 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2)))) (sqrt k)))>
2.352 * * * * [progress]: [ 18 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
2.352 * * * * [progress]: [ 19 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.352 * * * * [progress]: [ 20 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (log (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.352 * * * * [progress]: [ 21 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.352 * * * * [progress]: [ 22 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (cbrt (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.352 * * * * [progress]: [ 23 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.352 * * * * [progress]: [ 24 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k)))>
2.352 * * * * [progress]: [ 25 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))) (sqrt k)))>
2.352 * * * * [progress]: [ 26 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (posit16->real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt k)))>
2.352 * * * * [progress]: [ 27 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.352 * * * * [progress]: [ 28 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.352 * * * * [progress]: [ 29 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2))) (sqrt k)))>
2.352 * * * * [progress]: [ 30 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (+ (log 2) (log PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.352 * * * * [progress]: [ 31 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (+ (log n) (log (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.352 * * * * [progress]: [ 32 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (exp (log (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.352 * * * * [progress]: [ 33 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (log (exp (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.352 * * * * [progress]: [ 34 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.352 * * * * [progress]: [ 35 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.352 * * * * [progress]: [ 36 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.352 * * * * [progress]: [ 37 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.352 * * * * [progress]: [ 38 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.352 * * * * [progress]: [ 39 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.352 * * * * [progress]: [ 40 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* n 2) PI) (- 1/2 (/ k 2))) (sqrt k)))>
2.352 * * * * [progress]: [ 41 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.352 * * * * [progress]: [ 42 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.352 * * * * [progress]: [ 43 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2))) (sqrt k)))>
2.352 * * * * [progress]: [ 44 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2))) (sqrt k)))>
2.353 * * * * [progress]: [ 45 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* (* 2 PI) n) (- 1/2 (/ k 2))) (sqrt k)))>
2.353 * * * * [progress]: [ 46 / 127 ] simplifiying candidate #<alt (λ (k n) (pow (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) 1))>
2.353 * * * * [progress]: [ 47 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.353 * * * * [progress]: [ 48 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.353 * * * * [progress]: [ 49 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.353 * * * * [progress]: [ 50 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))))>
2.353 * * * * [progress]: [ 51 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (- (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))))>
2.353 * * * * [progress]: [ 52 / 127 ] simplifiying candidate #<alt (λ (k n) (exp (log (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.353 * * * * [progress]: [ 53 / 127 ] simplifiying candidate #<alt (λ (k n) (log (exp (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.353 * * * * [progress]: [ 54 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (/ (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))))>
2.353 * * * * [progress]: [ 55 / 127 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.353 * * * * [progress]: [ 56 / 127 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.353 * * * * [progress]: [ 57 / 127 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.353 * * * * [progress]: [ 58 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (- (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (- (sqrt k))))>
2.353 * * * * [progress]: [ 59 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k)))))>
2.353 * * * * [progress]: [ 60 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (cbrt k)))))>
2.353 * * * * [progress]: [ 61 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
2.353 * * * * [progress]: [ 62 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt 1)) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
2.353 * * * * [progress]: [ 63 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
2.353 * * * * [progress]: [ 64 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) 1) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
2.353 * * * * [progress]: [ 65 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k)))))>
2.353 * * * * [progress]: [ 66 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (cbrt k)))))>
2.353 * * * * [progress]: [ 67 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
2.353 * * * * [progress]: [ 68 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt 1)) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
2.353 * * * * [progress]: [ 69 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))))>
2.354 * * * * [progress]: [ 70 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) 1/2) 1) (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))))>
2.354 * * * * [progress]: [ 71 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
2.354 * * * * [progress]: [ 72 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
2.354 * * * * [progress]: [ 73 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.354 * * * * [progress]: [ 74 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt 1)) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))))>
2.354 * * * * [progress]: [ 75 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.354 * * * * [progress]: [ 76 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) 1) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))))>
2.354 * * * * [progress]: [ 77 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
2.354 * * * * [progress]: [ 78 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
2.354 * * * * [progress]: [ 79 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.354 * * * * [progress]: [ 80 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt 1)) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
2.354 * * * * [progress]: [ 81 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k))) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.354 * * * * [progress]: [ 82 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) 1) (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
2.354 * * * * [progress]: [ 83 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))))>
2.354 * * * * [progress]: [ 84 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))))>
2.354 * * * * [progress]: [ 85 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.354 * * * * [progress]: [ 86 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt 1)) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
2.354 * * * * [progress]: [ 87 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k))) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))))>
2.354 * * * * [progress]: [ 88 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))))>
2.354 * * * * [progress]: [ 89 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))))>
2.354 * * * * [progress]: [ 90 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))>
2.354 * * * * [progress]: [ 91 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.354 * * * * [progress]: [ 92 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))>
2.355 * * * * [progress]: [ 93 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>
2.355 * * * * [progress]: [ 94 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))>
2.355 * * * * [progress]: [ 95 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))))>
2.355 * * * * [progress]: [ 96 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k)))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))))>
2.355 * * * * [progress]: [ 97 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
2.355 * * * * [progress]: [ 98 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1)) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
2.355 * * * * [progress]: [ 99 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k))) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))))>
2.355 * * * * [progress]: [ 100 / 127 ] simplifiying candidate #<alt (λ (k n) (* (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))))>
2.355 * * * * [progress]: [ 101 / 127 ] simplifiying candidate #<alt (λ (k n) (* 1 (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))>
2.355 * * * * [progress]: [ 102 / 127 ] simplifiying candidate #<alt (λ (k n) (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (/ 1 (sqrt k))))>
2.355 * * * * [progress]: [ 103 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
2.355 * * * * [progress]: [ 104 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))))>
2.355 * * * * [progress]: [ 105 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))))>
2.355 * * * * [progress]: [ 106 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.355 * * * * [progress]: [ 107 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt 1)) (sqrt k)))>
2.355 * * * * [progress]: [ 108 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k))) (sqrt (sqrt k))))>
2.355 * * * * [progress]: [ 109 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1) (sqrt k)))>
2.355 * * * * [progress]: [ 110 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
2.356 * * * * [progress]: [ 111 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))))>
2.356 * * * * [progress]: [ 112 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow n (- 1/2 (/ k 2))) (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))))>
2.356 * * * * [progress]: [ 113 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
2.356 * * * * [progress]: [ 114 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
2.356 * * * * [progress]: [ 115 / 127 ] simplifiying candidate #<alt (λ (k n) (/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))>
2.356 * * * * [progress]: [ 116 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))>
2.356 * * * * [progress]: [ 117 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* n (* 2 PI)) 1/2) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))>
2.356 * * * * [progress]: [ 118 / 127 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))))>
2.356 * * * * [progress]: [ 119 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))))) (sqrt k)))>
2.356 * * * * [progress]: [ 120 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (sqrt k)))>
2.356 * * * * [progress]: [ 121 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (sqrt k)))>
2.356 * * * * [progress]: [ 122 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.356 * * * * [progress]: [ 123 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.356 * * * * [progress]: [ 124 / 127 ] simplifiying candidate #<alt (λ (k n) (/ (pow (* 2 (* n PI)) (- 1/2 (/ k 2))) (sqrt k)))>
2.356 * * * * [progress]: [ 125 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k)))))))))))))))))))))))>
2.356 * * * * [progress]: [ 126 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2)))))))))>
2.356 * * * * [progress]: [ 127 / 127 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))))))))))>
2.358 * [simplify]: Simplifying:
  (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))
  (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* 2 PI) (- 1/2 (/ k 2)))
  (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (- (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))) (log (sqrt k)))
  (- (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (log (sqrt k)))
  (log (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (exp (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (/ (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (* (* (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (- (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (- (sqrt k))
  (/ (pow (* n (* 2 PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) 1)
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))
  (/ (pow (* n (* 2 PI)) 1/2) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))
  (/ (pow (* n (* 2 PI)) 1/2) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) 1/2) 1)
  (/ (pow (* n (* 2 PI)) (- (/ k 2))) (sqrt k))
  (/ (pow n (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt 1))
  (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow n (- 1/2 (/ k 2))) 1)
  (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt k))
  (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt 1))
  (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) 1)
  (/ (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt 1))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) 1)
  (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ 1 1)
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) 1)
  (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt 1))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1)
  (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt k) (pow (* n (* 2 PI)) (- (/ k 2))))
  (/ (sqrt k) (pow (* 2 PI) (- 1/2 (/ k 2))))
  (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
  (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))
  (real->posit16 (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k)))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)) (- (+ (* +nan.0 (exp (* 1/2 (+ (log n) (log (* 2 PI)))))) (- (+ (* +nan.0 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k))) (- (* +nan.0 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 3))) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) k)) (- (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n))))) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) k)) (- (+ (* +nan.0 (/ (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n))))) (pow k 2))) (- (* +nan.0 (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))))
2.360 * * [simplify]: iteration 1: (267 enodes)
2.442 * * [simplify]: iteration 2: (644 enodes)
2.958 * * [simplify]: Extracting #0: cost 97 inf + 0
2.959 * * [simplify]: Extracting #1: cost 372 inf + 1
2.965 * * [simplify]: Extracting #2: cost 513 inf + 18891
2.983 * * [simplify]: Extracting #3: cost 411 inf + 87524
3.001 * * [simplify]: Extracting #4: cost 283 inf + 135704
3.048 * * [simplify]: Extracting #5: cost 156 inf + 192203
3.087 * * [simplify]: Extracting #6: cost 96 inf + 227990
3.166 * * [simplify]: Extracting #7: cost 25 inf + 269385
3.236 * * [simplify]: Extracting #8: cost 0 inf + 290477
3.339 * * [simplify]: Extracting #9: cost 0 inf + 287997
3.414 * * [simplify]: Extracting #10: cost 0 inf + 287757
3.494 * [simplify]: Simplified to:
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (/ k 2))
  (pow (* (* PI 2) n) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* PI 2) n) (sqrt (- 1/2 (/ k 2))))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* PI 2) n) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* (* PI 2) n)
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (- (/ k 2)))
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* PI 2) (- 1/2 (/ k 2)))
  (* (- 1/2 (/ k 2)) (log (* (* PI 2) n)))
  (exp (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (* (exp (* PI n)) (exp (* PI n)))
  (* n (* (* n n) (* PI (* (* PI PI) 8))))
  (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n)))
  (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n)))
  (cbrt (* (* PI 2) n))
  (* (* (* PI 2) n) (* (* (* PI 2) n) (* (* PI 2) n)))
  (sqrt (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (* n 2)
  (* (cbrt n) (* PI 2))
  (* (sqrt n) (* PI 2))
  (* (* PI 2) n)
  (real->posit16 (* (* PI 2) n))
  (- (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (log (sqrt k)))
  (- (* (- 1/2 (/ k 2)) (log (* (* PI 2) n))) (log (sqrt k)))
  (exp (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)))
  (/ (* (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (/ k (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))))
  (* (cbrt (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))) (cbrt (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))))
  (cbrt (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)))
  (* (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)) (* (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)) (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))))
  (sqrt (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)))
  (sqrt (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)))
  (- (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (- (sqrt k))
  (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (sqrt (* (* PI 2) n)) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* PI 2) n))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt k))
  (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* PI 2) n))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt k))
  (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))
  (/ (sqrt (* (* PI 2) n)) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (cbrt k)))
  (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* PI 2) n))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt k))
  (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))
  (sqrt (* (* PI 2) n))
  (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt k))
  (/ (/ (pow n (- 1/2 (/ k 2))) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (fabs (cbrt k)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow n (- 1/2 (/ k 2)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow n (- 1/2 (/ k 2)))
  (/ (pow (* PI 2) (- 1/2 (/ k 2))) (sqrt k))
  (* (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k))) (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k))))
  (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (fabs (cbrt k)))
  (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))) (sqrt (sqrt k)))
  (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (fabs (cbrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (cbrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt (sqrt k)))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  1
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  1
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (cbrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (cbrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt k))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (/ (pow (* (* PI 2) n) (- 1/4 (/ k 4))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (fabs (cbrt k)))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (- 1/2 (/ k 2)))
  (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt (sqrt k)))
  (pow (* (* PI 2) n) (- 1/2 (/ k 2)))
  (/ (sqrt k) (pow (* (* PI 2) n) (- (/ k 2))))
  (/ (sqrt k) (pow (* (* PI 2) n) (- (/ k 2))))
  (/ (sqrt k) (pow (* PI 2) (- 1/2 (/ k 2))))
  (/ (sqrt k) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (/ (sqrt k) (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (/ (sqrt k) (pow (* (* PI 2) n) (- 1/4 (/ k 4))))
  (* (sqrt k) (pow (* (* PI 2) n) (/ k 2)))
  (real->posit16 (/ (pow (* (* PI 2) n) (- 1/2 (/ k 2))) (sqrt k)))
  (+ (* -1/2 (* k (+ (* (sqrt (* (* PI 2) n)) (log n)) (* (sqrt (* (* PI 2) n)) (log (* PI 2)))))) (+ (* (* (* (log n) k) (* (log n) k)) (* (sqrt (* (* PI 2) n)) 1/8)) (+ (+ (* (* (log (* PI 2)) (* (* (sqrt (* (* PI 2) n)) (* k k)) (log (* PI 2)))) 1/8) (sqrt (* (* PI 2) n))) (* (* (sqrt (* (* PI 2) n)) (log (* PI 2))) (* (* (* (log n) k) k) 1/4)))))
  (exp (* (log (* (* PI 2) n)) (- 1/2 (* k 1/2))))
  (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (* (* PI 2) n)
  (- (+ (* (* (* (sqrt (* (* PI 2) n)) (* k k)) (log n)) (* (log (* PI 2)) +nan.0)) (- (* (- +nan.0) (* (* (sqrt (* (* PI 2) n)) (* k k)) (log (* PI 2)))) (+ (+ (- (* (* k (sqrt (* (* PI 2) n))) +nan.0) (* (sqrt (* (* PI 2) n)) +nan.0)) (+ (+ (* (* (log (* PI 2)) (* (* (sqrt (* (* PI 2) n)) (* k k)) (log (* PI 2)))) +nan.0) (* (* (* (sqrt (* (* PI 2) n)) (* k k)) (log n)) (- +nan.0))) (+ (- (* (* k k) (* (sqrt (* (* PI 2) n)) +nan.0)) (* (* (* (log (* PI 2)) +nan.0) (sqrt (* (* PI 2) n))) k)) (* (* (log n) k) (* (sqrt (* (* PI 2) n)) +nan.0))))) (* (* (* (* (log n) k) (* (log n) k)) (sqrt (* (* PI 2) n))) (- +nan.0))))))
  (- (+ (- (* (/ +nan.0 (* k k)) (/ (exp (* (log (* (* PI 2) n)) (- 1/2 (* k 1/2)))) k)) (/ (* (exp (* (log (* (* PI 2) n)) (- 1/2 (* k 1/2)))) +nan.0) k)) (/ (/ (* (exp (* (log (* (* PI 2) n)) (- 1/2 (* k 1/2)))) +nan.0) k) k)))
  (- (- (/ +nan.0 (/ k (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2)))))) (* +nan.0 (- (/ (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2)))) (* k k)) (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))))))
3.510 * * * [progress]: adding candidates to table
4.865 * * [progress]: iteration 2 / 4
4.865 * * * [progress]: picking best candidate
4.926 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
4.926 * * * [progress]: localizing error
4.975 * * * [progress]: generating rewritten candidates
4.975 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2)
5.012 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1)
5.027 * * * * [progress]: [ 3 / 4 ] rewriting at (2 1)
5.032 * * * * [progress]: [ 4 / 4 ] rewriting at (2)
5.064 * * * [progress]: generating series expansions
5.064 * * * * [progress]: [ 1 / 4 ] generating series at (2 2)
5.065 * [backup-simplify]: Simplify (pow (* (* 2 PI) n) (/ (- 1 k) 2)) into (pow (* 2 (* n PI)) (* 1/2 (- 1 k)))
5.065 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in (n k) around 0
5.065 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
5.065 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
5.065 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
5.065 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
5.065 * [taylor]: Taking taylor expansion of 1/2 in k
5.065 * [backup-simplify]: Simplify 1/2 into 1/2
5.065 * [taylor]: Taking taylor expansion of (- 1 k) in k
5.065 * [taylor]: Taking taylor expansion of 1 in k
5.065 * [backup-simplify]: Simplify 1 into 1
5.065 * [taylor]: Taking taylor expansion of k in k
5.065 * [backup-simplify]: Simplify 0 into 0
5.065 * [backup-simplify]: Simplify 1 into 1
5.065 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
5.065 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
5.065 * [taylor]: Taking taylor expansion of 2 in k
5.065 * [backup-simplify]: Simplify 2 into 2
5.065 * [taylor]: Taking taylor expansion of (* n PI) in k
5.065 * [taylor]: Taking taylor expansion of n in k
5.065 * [backup-simplify]: Simplify n into n
5.065 * [taylor]: Taking taylor expansion of PI in k
5.065 * [backup-simplify]: Simplify PI into PI
5.065 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.065 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
5.065 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
5.065 * [backup-simplify]: Simplify (- 0) into 0
5.066 * [backup-simplify]: Simplify (+ 1 0) into 1
5.066 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.066 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
5.066 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
5.066 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
5.066 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
5.066 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
5.066 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
5.066 * [taylor]: Taking taylor expansion of 1/2 in n
5.066 * [backup-simplify]: Simplify 1/2 into 1/2
5.066 * [taylor]: Taking taylor expansion of (- 1 k) in n
5.066 * [taylor]: Taking taylor expansion of 1 in n
5.066 * [backup-simplify]: Simplify 1 into 1
5.066 * [taylor]: Taking taylor expansion of k in n
5.066 * [backup-simplify]: Simplify k into k
5.066 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.066 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.066 * [taylor]: Taking taylor expansion of 2 in n
5.066 * [backup-simplify]: Simplify 2 into 2
5.066 * [taylor]: Taking taylor expansion of (* n PI) in n
5.066 * [taylor]: Taking taylor expansion of n in n
5.066 * [backup-simplify]: Simplify 0 into 0
5.066 * [backup-simplify]: Simplify 1 into 1
5.066 * [taylor]: Taking taylor expansion of PI in n
5.066 * [backup-simplify]: Simplify PI into PI
5.069 * [backup-simplify]: Simplify (* 0 PI) into 0
5.070 * [backup-simplify]: Simplify (* 2 0) into 0
5.071 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.072 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.072 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.072 * [backup-simplify]: Simplify (- k) into (- k)
5.072 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
5.072 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
5.073 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.074 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
5.075 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
5.075 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
5.075 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
5.075 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
5.075 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
5.075 * [taylor]: Taking taylor expansion of 1/2 in n
5.075 * [backup-simplify]: Simplify 1/2 into 1/2
5.075 * [taylor]: Taking taylor expansion of (- 1 k) in n
5.075 * [taylor]: Taking taylor expansion of 1 in n
5.075 * [backup-simplify]: Simplify 1 into 1
5.075 * [taylor]: Taking taylor expansion of k in n
5.075 * [backup-simplify]: Simplify k into k
5.075 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.075 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.075 * [taylor]: Taking taylor expansion of 2 in n
5.075 * [backup-simplify]: Simplify 2 into 2
5.075 * [taylor]: Taking taylor expansion of (* n PI) in n
5.075 * [taylor]: Taking taylor expansion of n in n
5.075 * [backup-simplify]: Simplify 0 into 0
5.075 * [backup-simplify]: Simplify 1 into 1
5.075 * [taylor]: Taking taylor expansion of PI in n
5.075 * [backup-simplify]: Simplify PI into PI
5.075 * [backup-simplify]: Simplify (* 0 PI) into 0
5.076 * [backup-simplify]: Simplify (* 2 0) into 0
5.076 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.077 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.078 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.078 * [backup-simplify]: Simplify (- k) into (- k)
5.078 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
5.078 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
5.080 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.081 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
5.082 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
5.082 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) in k
5.082 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))) in k
5.082 * [taylor]: Taking taylor expansion of 1/2 in k
5.082 * [backup-simplify]: Simplify 1/2 into 1/2
5.082 * [taylor]: Taking taylor expansion of (* (- 1 k) (+ (log n) (log (* 2 PI)))) in k
5.082 * [taylor]: Taking taylor expansion of (- 1 k) in k
5.082 * [taylor]: Taking taylor expansion of 1 in k
5.082 * [backup-simplify]: Simplify 1 into 1
5.082 * [taylor]: Taking taylor expansion of k in k
5.082 * [backup-simplify]: Simplify 0 into 0
5.082 * [backup-simplify]: Simplify 1 into 1
5.082 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
5.082 * [taylor]: Taking taylor expansion of (log n) in k
5.082 * [taylor]: Taking taylor expansion of n in k
5.082 * [backup-simplify]: Simplify n into n
5.082 * [backup-simplify]: Simplify (log n) into (log n)
5.082 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
5.082 * [taylor]: Taking taylor expansion of (* 2 PI) in k
5.082 * [taylor]: Taking taylor expansion of 2 in k
5.083 * [backup-simplify]: Simplify 2 into 2
5.083 * [taylor]: Taking taylor expansion of PI in k
5.083 * [backup-simplify]: Simplify PI into PI
5.083 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.084 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.085 * [backup-simplify]: Simplify (- 0) into 0
5.085 * [backup-simplify]: Simplify (+ 1 0) into 1
5.086 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.087 * [backup-simplify]: Simplify (* 1 (+ (log n) (log (* 2 PI)))) into (+ (log n) (log (* 2 PI)))
5.088 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
5.090 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
5.091 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
5.092 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.093 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.094 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.095 * [backup-simplify]: Simplify (- 0) into 0
5.095 * [backup-simplify]: Simplify (+ 0 0) into 0
5.096 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 k))) into 0
5.097 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.098 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
5.100 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.100 * [taylor]: Taking taylor expansion of 0 in k
5.100 * [backup-simplify]: Simplify 0 into 0
5.100 * [backup-simplify]: Simplify 0 into 0
5.101 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
5.101 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.103 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.103 * [backup-simplify]: Simplify (+ 0 0) into 0
5.104 * [backup-simplify]: Simplify (- 1) into -1
5.104 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.106 * [backup-simplify]: Simplify (+ (* 1 0) (* -1 (+ (log n) (log (* 2 PI))))) into (- (+ (log (* 2 PI)) (log n)))
5.108 * [backup-simplify]: Simplify (+ (* 1/2 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))))
5.111 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
5.114 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
5.115 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.116 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.120 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
5.120 * [backup-simplify]: Simplify (- 0) into 0
5.121 * [backup-simplify]: Simplify (+ 0 0) into 0
5.121 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 k)))) into 0
5.123 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.124 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.127 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.127 * [taylor]: Taking taylor expansion of 0 in k
5.127 * [backup-simplify]: Simplify 0 into 0
5.127 * [backup-simplify]: Simplify 0 into 0
5.127 * [backup-simplify]: Simplify 0 into 0
5.129 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
5.130 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.133 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
5.134 * [backup-simplify]: Simplify (+ 0 0) into 0
5.134 * [backup-simplify]: Simplify (- 0) into 0
5.135 * [backup-simplify]: Simplify (+ 0 0) into 0
5.137 * [backup-simplify]: Simplify (+ (* 1 0) (+ (* -1 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.139 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 (- (+ (log (* 2 PI)) (log n)))) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
5.143 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
5.148 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
5.154 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
5.154 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2)) into (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k))))
5.154 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in (n k) around 0
5.155 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
5.155 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
5.155 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
5.155 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
5.155 * [taylor]: Taking taylor expansion of 1/2 in k
5.155 * [backup-simplify]: Simplify 1/2 into 1/2
5.155 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
5.155 * [taylor]: Taking taylor expansion of 1 in k
5.155 * [backup-simplify]: Simplify 1 into 1
5.155 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.155 * [taylor]: Taking taylor expansion of k in k
5.155 * [backup-simplify]: Simplify 0 into 0
5.155 * [backup-simplify]: Simplify 1 into 1
5.155 * [backup-simplify]: Simplify (/ 1 1) into 1
5.155 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
5.155 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
5.155 * [taylor]: Taking taylor expansion of 2 in k
5.155 * [backup-simplify]: Simplify 2 into 2
5.155 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.155 * [taylor]: Taking taylor expansion of PI in k
5.155 * [backup-simplify]: Simplify PI into PI
5.155 * [taylor]: Taking taylor expansion of n in k
5.155 * [backup-simplify]: Simplify n into n
5.155 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.155 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
5.155 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
5.155 * [backup-simplify]: Simplify (- 1) into -1
5.156 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.156 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
5.156 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
5.156 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
5.156 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
5.156 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.156 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.156 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
5.156 * [taylor]: Taking taylor expansion of 1/2 in n
5.156 * [backup-simplify]: Simplify 1/2 into 1/2
5.156 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.156 * [taylor]: Taking taylor expansion of 1 in n
5.156 * [backup-simplify]: Simplify 1 into 1
5.156 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.156 * [taylor]: Taking taylor expansion of k in n
5.156 * [backup-simplify]: Simplify k into k
5.156 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.156 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.156 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.156 * [taylor]: Taking taylor expansion of 2 in n
5.157 * [backup-simplify]: Simplify 2 into 2
5.157 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.157 * [taylor]: Taking taylor expansion of PI in n
5.157 * [backup-simplify]: Simplify PI into PI
5.157 * [taylor]: Taking taylor expansion of n in n
5.157 * [backup-simplify]: Simplify 0 into 0
5.157 * [backup-simplify]: Simplify 1 into 1
5.157 * [backup-simplify]: Simplify (/ PI 1) into PI
5.157 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.158 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.158 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.158 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.158 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
5.159 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.160 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.160 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.160 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
5.161 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.161 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.161 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
5.161 * [taylor]: Taking taylor expansion of 1/2 in n
5.161 * [backup-simplify]: Simplify 1/2 into 1/2
5.161 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.161 * [taylor]: Taking taylor expansion of 1 in n
5.161 * [backup-simplify]: Simplify 1 into 1
5.161 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.161 * [taylor]: Taking taylor expansion of k in n
5.161 * [backup-simplify]: Simplify k into k
5.161 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.161 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.161 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.161 * [taylor]: Taking taylor expansion of 2 in n
5.161 * [backup-simplify]: Simplify 2 into 2
5.161 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.161 * [taylor]: Taking taylor expansion of PI in n
5.161 * [backup-simplify]: Simplify PI into PI
5.161 * [taylor]: Taking taylor expansion of n in n
5.161 * [backup-simplify]: Simplify 0 into 0
5.161 * [backup-simplify]: Simplify 1 into 1
5.161 * [backup-simplify]: Simplify (/ PI 1) into PI
5.161 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.162 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.162 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.162 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.162 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
5.163 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.164 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.165 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.165 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) in k
5.165 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) in k
5.165 * [taylor]: Taking taylor expansion of 1/2 in k
5.165 * [backup-simplify]: Simplify 1/2 into 1/2
5.165 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) in k
5.165 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
5.165 * [taylor]: Taking taylor expansion of 1 in k
5.165 * [backup-simplify]: Simplify 1 into 1
5.165 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.165 * [taylor]: Taking taylor expansion of k in k
5.165 * [backup-simplify]: Simplify 0 into 0
5.165 * [backup-simplify]: Simplify 1 into 1
5.165 * [backup-simplify]: Simplify (/ 1 1) into 1
5.165 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
5.165 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
5.165 * [taylor]: Taking taylor expansion of (* 2 PI) in k
5.165 * [taylor]: Taking taylor expansion of 2 in k
5.165 * [backup-simplify]: Simplify 2 into 2
5.165 * [taylor]: Taking taylor expansion of PI in k
5.165 * [backup-simplify]: Simplify PI into PI
5.166 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.166 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.166 * [taylor]: Taking taylor expansion of (log n) in k
5.166 * [taylor]: Taking taylor expansion of n in k
5.166 * [backup-simplify]: Simplify n into n
5.166 * [backup-simplify]: Simplify (log n) into (log n)
5.167 * [backup-simplify]: Simplify (- 1) into -1
5.167 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.167 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.168 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
5.168 * [backup-simplify]: Simplify (* -1 (- (log (* 2 PI)) (log n))) into (* -1 (- (log (* 2 PI)) (log n)))
5.169 * [backup-simplify]: Simplify (* 1/2 (* -1 (- (log (* 2 PI)) (log n)))) into (* -1/2 (- (log (* 2 PI)) (log n)))
5.170 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.170 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.171 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.172 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.173 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.173 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.173 * [backup-simplify]: Simplify (- 0) into 0
5.173 * [backup-simplify]: Simplify (+ 0 0) into 0
5.173 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (- 1 (/ 1 k)))) into 0
5.174 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.175 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
5.176 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.176 * [taylor]: Taking taylor expansion of 0 in k
5.176 * [backup-simplify]: Simplify 0 into 0
5.176 * [backup-simplify]: Simplify 0 into 0
5.176 * [backup-simplify]: Simplify 0 into 0
5.177 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.178 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.179 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
5.180 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.180 * [backup-simplify]: Simplify (- 0) into 0
5.180 * [backup-simplify]: Simplify (+ 0 0) into 0
5.181 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k))))) into 0
5.185 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.187 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
5.189 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.189 * [taylor]: Taking taylor expansion of 0 in k
5.189 * [backup-simplify]: Simplify 0 into 0
5.189 * [backup-simplify]: Simplify 0 into 0
5.189 * [backup-simplify]: Simplify 0 into 0
5.189 * [backup-simplify]: Simplify 0 into 0
5.191 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.192 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.198 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
5.198 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.199 * [backup-simplify]: Simplify (- 0) into 0
5.199 * [backup-simplify]: Simplify (+ 0 0) into 0
5.200 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1 (/ 1 k)))))) into 0
5.202 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.204 * [backup-simplify]: Simplify (+ (* (* 1/2 (- 1 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
5.207 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
5.207 * [taylor]: Taking taylor expansion of 0 in k
5.207 * [backup-simplify]: Simplify 0 into 0
5.207 * [backup-simplify]: Simplify 0 into 0
5.209 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))) into (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
5.209 * [backup-simplify]: Simplify (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2)) into (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1)))
5.209 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in (n k) around 0
5.209 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
5.209 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
5.210 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
5.210 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
5.210 * [taylor]: Taking taylor expansion of 1/2 in k
5.210 * [backup-simplify]: Simplify 1/2 into 1/2
5.210 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.210 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.210 * [taylor]: Taking taylor expansion of k in k
5.210 * [backup-simplify]: Simplify 0 into 0
5.210 * [backup-simplify]: Simplify 1 into 1
5.210 * [backup-simplify]: Simplify (/ 1 1) into 1
5.210 * [taylor]: Taking taylor expansion of 1 in k
5.210 * [backup-simplify]: Simplify 1 into 1
5.210 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
5.210 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
5.210 * [taylor]: Taking taylor expansion of -2 in k
5.210 * [backup-simplify]: Simplify -2 into -2
5.210 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.210 * [taylor]: Taking taylor expansion of PI in k
5.210 * [backup-simplify]: Simplify PI into PI
5.210 * [taylor]: Taking taylor expansion of n in k
5.210 * [backup-simplify]: Simplify n into n
5.211 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.211 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
5.211 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
5.211 * [backup-simplify]: Simplify (+ 1 0) into 1
5.211 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.211 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
5.211 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
5.211 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
5.212 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
5.212 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
5.212 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
5.212 * [taylor]: Taking taylor expansion of 1/2 in n
5.212 * [backup-simplify]: Simplify 1/2 into 1/2
5.212 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.212 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.212 * [taylor]: Taking taylor expansion of k in n
5.212 * [backup-simplify]: Simplify k into k
5.212 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.212 * [taylor]: Taking taylor expansion of 1 in n
5.212 * [backup-simplify]: Simplify 1 into 1
5.212 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.212 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.212 * [taylor]: Taking taylor expansion of -2 in n
5.212 * [backup-simplify]: Simplify -2 into -2
5.212 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.212 * [taylor]: Taking taylor expansion of PI in n
5.212 * [backup-simplify]: Simplify PI into PI
5.212 * [taylor]: Taking taylor expansion of n in n
5.212 * [backup-simplify]: Simplify 0 into 0
5.212 * [backup-simplify]: Simplify 1 into 1
5.212 * [backup-simplify]: Simplify (/ PI 1) into PI
5.212 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.213 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.213 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.213 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
5.214 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.215 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.216 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.216 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
5.216 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
5.216 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
5.216 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
5.216 * [taylor]: Taking taylor expansion of 1/2 in n
5.216 * [backup-simplify]: Simplify 1/2 into 1/2
5.216 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.216 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.216 * [taylor]: Taking taylor expansion of k in n
5.216 * [backup-simplify]: Simplify k into k
5.216 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.216 * [taylor]: Taking taylor expansion of 1 in n
5.216 * [backup-simplify]: Simplify 1 into 1
5.216 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.216 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.216 * [taylor]: Taking taylor expansion of -2 in n
5.216 * [backup-simplify]: Simplify -2 into -2
5.216 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.216 * [taylor]: Taking taylor expansion of PI in n
5.216 * [backup-simplify]: Simplify PI into PI
5.216 * [taylor]: Taking taylor expansion of n in n
5.216 * [backup-simplify]: Simplify 0 into 0
5.216 * [backup-simplify]: Simplify 1 into 1
5.217 * [backup-simplify]: Simplify (/ PI 1) into PI
5.217 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.218 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.218 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.218 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
5.219 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.220 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.220 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.220 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) in k
5.220 * [taylor]: Taking taylor expansion of (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) in k
5.220 * [taylor]: Taking taylor expansion of 1/2 in k
5.220 * [backup-simplify]: Simplify 1/2 into 1/2
5.220 * [taylor]: Taking taylor expansion of (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))) in k
5.220 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.220 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.220 * [taylor]: Taking taylor expansion of k in k
5.220 * [backup-simplify]: Simplify 0 into 0
5.220 * [backup-simplify]: Simplify 1 into 1
5.221 * [backup-simplify]: Simplify (/ 1 1) into 1
5.221 * [taylor]: Taking taylor expansion of 1 in k
5.221 * [backup-simplify]: Simplify 1 into 1
5.221 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
5.221 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
5.221 * [taylor]: Taking taylor expansion of (* -2 PI) in k
5.221 * [taylor]: Taking taylor expansion of -2 in k
5.221 * [backup-simplify]: Simplify -2 into -2
5.221 * [taylor]: Taking taylor expansion of PI in k
5.221 * [backup-simplify]: Simplify PI into PI
5.221 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.222 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.222 * [taylor]: Taking taylor expansion of (log n) in k
5.222 * [taylor]: Taking taylor expansion of n in k
5.222 * [backup-simplify]: Simplify n into n
5.222 * [backup-simplify]: Simplify (log n) into (log n)
5.222 * [backup-simplify]: Simplify (+ 1 0) into 1
5.222 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
5.223 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
5.224 * [backup-simplify]: Simplify (* 1 (- (log (* -2 PI)) (log n))) into (- (log (* -2 PI)) (log n))
5.224 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
5.225 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.226 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.226 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.227 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.228 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
5.228 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.228 * [backup-simplify]: Simplify (+ 0 0) into 0
5.228 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (+ (/ 1 k) 1))) into 0
5.229 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.230 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
5.231 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.231 * [taylor]: Taking taylor expansion of 0 in k
5.231 * [backup-simplify]: Simplify 0 into 0
5.231 * [backup-simplify]: Simplify 0 into 0
5.231 * [backup-simplify]: Simplify 0 into 0
5.232 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.233 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
5.234 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
5.235 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.235 * [backup-simplify]: Simplify (+ 0 0) into 0
5.235 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1)))) into 0
5.236 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.237 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
5.239 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
5.239 * [taylor]: Taking taylor expansion of 0 in k
5.239 * [backup-simplify]: Simplify 0 into 0
5.239 * [backup-simplify]: Simplify 0 into 0
5.239 * [backup-simplify]: Simplify 0 into 0
5.239 * [backup-simplify]: Simplify 0 into 0
5.240 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.242 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.248 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
5.248 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
5.248 * [backup-simplify]: Simplify (+ 0 0) into 0
5.250 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1))))) into 0
5.251 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.253 * [backup-simplify]: Simplify (+ (* (* 1/2 (+ (/ 1 k) 1)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
5.256 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
5.256 * [taylor]: Taking taylor expansion of 0 in k
5.256 * [backup-simplify]: Simplify 0 into 0
5.256 * [backup-simplify]: Simplify 0 into 0
5.258 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))) into (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
5.258 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1)
5.259 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
5.259 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
5.259 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.259 * [taylor]: Taking taylor expansion of 2 in n
5.259 * [backup-simplify]: Simplify 2 into 2
5.259 * [taylor]: Taking taylor expansion of (* n PI) in n
5.259 * [taylor]: Taking taylor expansion of n in n
5.259 * [backup-simplify]: Simplify 0 into 0
5.259 * [backup-simplify]: Simplify 1 into 1
5.259 * [taylor]: Taking taylor expansion of PI in n
5.259 * [backup-simplify]: Simplify PI into PI
5.259 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.259 * [taylor]: Taking taylor expansion of 2 in n
5.259 * [backup-simplify]: Simplify 2 into 2
5.259 * [taylor]: Taking taylor expansion of (* n PI) in n
5.259 * [taylor]: Taking taylor expansion of n in n
5.259 * [backup-simplify]: Simplify 0 into 0
5.259 * [backup-simplify]: Simplify 1 into 1
5.259 * [taylor]: Taking taylor expansion of PI in n
5.259 * [backup-simplify]: Simplify PI into PI
5.260 * [backup-simplify]: Simplify (* 0 PI) into 0
5.260 * [backup-simplify]: Simplify (* 2 0) into 0
5.261 * [backup-simplify]: Simplify 0 into 0
5.262 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.264 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.264 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.266 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.267 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.267 * [backup-simplify]: Simplify 0 into 0
5.268 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
5.269 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
5.269 * [backup-simplify]: Simplify 0 into 0
5.271 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.272 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
5.272 * [backup-simplify]: Simplify 0 into 0
5.274 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.276 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
5.276 * [backup-simplify]: Simplify 0 into 0
5.277 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.279 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
5.279 * [backup-simplify]: Simplify 0 into 0
5.281 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
5.283 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
5.283 * [backup-simplify]: Simplify 0 into 0
5.284 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
5.284 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 n)) into (* 2 (/ PI n))
5.285 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
5.285 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.285 * [taylor]: Taking taylor expansion of 2 in n
5.285 * [backup-simplify]: Simplify 2 into 2
5.285 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.285 * [taylor]: Taking taylor expansion of PI in n
5.285 * [backup-simplify]: Simplify PI into PI
5.285 * [taylor]: Taking taylor expansion of n in n
5.285 * [backup-simplify]: Simplify 0 into 0
5.285 * [backup-simplify]: Simplify 1 into 1
5.285 * [backup-simplify]: Simplify (/ PI 1) into PI
5.285 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.285 * [taylor]: Taking taylor expansion of 2 in n
5.285 * [backup-simplify]: Simplify 2 into 2
5.285 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.285 * [taylor]: Taking taylor expansion of PI in n
5.285 * [backup-simplify]: Simplify PI into PI
5.285 * [taylor]: Taking taylor expansion of n in n
5.285 * [backup-simplify]: Simplify 0 into 0
5.286 * [backup-simplify]: Simplify 1 into 1
5.286 * [backup-simplify]: Simplify (/ PI 1) into PI
5.287 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.287 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.288 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.289 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.289 * [backup-simplify]: Simplify 0 into 0
5.290 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.291 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
5.291 * [backup-simplify]: Simplify 0 into 0
5.292 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.294 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.294 * [backup-simplify]: Simplify 0 into 0
5.295 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.296 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.296 * [backup-simplify]: Simplify 0 into 0
5.298 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.299 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.299 * [backup-simplify]: Simplify 0 into 0
5.301 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.303 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.303 * [backup-simplify]: Simplify 0 into 0
5.303 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
5.304 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (- n))) into (* -2 (/ PI n))
5.304 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
5.304 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.304 * [taylor]: Taking taylor expansion of -2 in n
5.304 * [backup-simplify]: Simplify -2 into -2
5.304 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.304 * [taylor]: Taking taylor expansion of PI in n
5.304 * [backup-simplify]: Simplify PI into PI
5.304 * [taylor]: Taking taylor expansion of n in n
5.304 * [backup-simplify]: Simplify 0 into 0
5.304 * [backup-simplify]: Simplify 1 into 1
5.305 * [backup-simplify]: Simplify (/ PI 1) into PI
5.305 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.305 * [taylor]: Taking taylor expansion of -2 in n
5.305 * [backup-simplify]: Simplify -2 into -2
5.305 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.305 * [taylor]: Taking taylor expansion of PI in n
5.305 * [backup-simplify]: Simplify PI into PI
5.305 * [taylor]: Taking taylor expansion of n in n
5.305 * [backup-simplify]: Simplify 0 into 0
5.305 * [backup-simplify]: Simplify 1 into 1
5.305 * [backup-simplify]: Simplify (/ PI 1) into PI
5.306 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.306 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.307 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.308 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.308 * [backup-simplify]: Simplify 0 into 0
5.309 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.310 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
5.310 * [backup-simplify]: Simplify 0 into 0
5.311 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.313 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.313 * [backup-simplify]: Simplify 0 into 0
5.314 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.315 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
5.315 * [backup-simplify]: Simplify 0 into 0
5.320 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.322 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
5.322 * [backup-simplify]: Simplify 0 into 0
5.323 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.325 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
5.325 * [backup-simplify]: Simplify 0 into 0
5.325 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
5.325 * * * * [progress]: [ 3 / 4 ] generating series at (2 1)
5.326 * [backup-simplify]: Simplify (/ 1 (sqrt k)) into (sqrt (/ 1 k))
5.326 * [approximate]: Taking taylor expansion of (sqrt (/ 1 k)) in (k) around 0
5.326 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.326 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.326 * [taylor]: Taking taylor expansion of k in k
5.326 * [backup-simplify]: Simplify 0 into 0
5.326 * [backup-simplify]: Simplify 1 into 1
5.326 * [backup-simplify]: Simplify (/ 1 1) into 1
5.327 * [backup-simplify]: Simplify (sqrt 0) into 0
5.328 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.328 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.328 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.328 * [taylor]: Taking taylor expansion of k in k
5.328 * [backup-simplify]: Simplify 0 into 0
5.328 * [backup-simplify]: Simplify 1 into 1
5.328 * [backup-simplify]: Simplify (/ 1 1) into 1
5.328 * [backup-simplify]: Simplify (sqrt 0) into 0
5.329 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.329 * [backup-simplify]: Simplify 0 into 0
5.329 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.330 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
5.331 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.331 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.332 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.334 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.334 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.334 * [backup-simplify]: Simplify (+ (* +nan.0 (pow k 2)) (+ (* +nan.0 k) +nan.0)) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
5.334 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 k))) into (sqrt k)
5.334 * [approximate]: Taking taylor expansion of (sqrt k) in (k) around 0
5.334 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.334 * [taylor]: Taking taylor expansion of k in k
5.334 * [backup-simplify]: Simplify 0 into 0
5.334 * [backup-simplify]: Simplify 1 into 1
5.335 * [backup-simplify]: Simplify (sqrt 0) into 0
5.336 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.336 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.336 * [taylor]: Taking taylor expansion of k in k
5.336 * [backup-simplify]: Simplify 0 into 0
5.336 * [backup-simplify]: Simplify 1 into 1
5.336 * [backup-simplify]: Simplify (sqrt 0) into 0
5.337 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.337 * [backup-simplify]: Simplify 0 into 0
5.337 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.339 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.339 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.341 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.341 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.341 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (/ 1 k) 3)) (+ (* +nan.0 (pow (/ 1 k) 2)) (* +nan.0 (/ 1 k)))) into (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
5.341 * [backup-simplify]: Simplify (/ 1 (sqrt (/ 1 (- k)))) into (/ 1 (sqrt (/ -1 k)))
5.342 * [approximate]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in (k) around 0
5.342 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
5.342 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.342 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.342 * [taylor]: Taking taylor expansion of -1 in k
5.342 * [backup-simplify]: Simplify -1 into -1
5.342 * [taylor]: Taking taylor expansion of k in k
5.342 * [backup-simplify]: Simplify 0 into 0
5.342 * [backup-simplify]: Simplify 1 into 1
5.342 * [backup-simplify]: Simplify (/ -1 1) into -1
5.342 * [backup-simplify]: Simplify (sqrt 0) into 0
5.343 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.343 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
5.343 * [taylor]: Taking taylor expansion of (/ 1 (sqrt (/ -1 k))) in k
5.343 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.343 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.343 * [taylor]: Taking taylor expansion of -1 in k
5.343 * [backup-simplify]: Simplify -1 into -1
5.343 * [taylor]: Taking taylor expansion of k in k
5.343 * [backup-simplify]: Simplify 0 into 0
5.343 * [backup-simplify]: Simplify 1 into 1
5.344 * [backup-simplify]: Simplify (/ -1 1) into -1
5.344 * [backup-simplify]: Simplify (sqrt 0) into 0
5.345 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.345 * [backup-simplify]: Simplify (/ 1 +nan.0) into +nan.0
5.345 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.346 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
5.347 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.348 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
5.349 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
5.349 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.352 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.354 * [backup-simplify]: Simplify (- (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
5.354 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
5.355 * [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)))))
5.355 * * * * [progress]: [ 4 / 4 ] generating series at (2)
5.355 * [backup-simplify]: Simplify (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) into (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k)))
5.355 * [approximate]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in (k n) around 0
5.355 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in n
5.355 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in n
5.355 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in n
5.356 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in n
5.356 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in n
5.356 * [taylor]: Taking taylor expansion of 1/2 in n
5.356 * [backup-simplify]: Simplify 1/2 into 1/2
5.356 * [taylor]: Taking taylor expansion of (- 1 k) in n
5.356 * [taylor]: Taking taylor expansion of 1 in n
5.356 * [backup-simplify]: Simplify 1 into 1
5.356 * [taylor]: Taking taylor expansion of k in n
5.356 * [backup-simplify]: Simplify k into k
5.356 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.356 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.356 * [taylor]: Taking taylor expansion of 2 in n
5.356 * [backup-simplify]: Simplify 2 into 2
5.356 * [taylor]: Taking taylor expansion of (* n PI) in n
5.356 * [taylor]: Taking taylor expansion of n in n
5.356 * [backup-simplify]: Simplify 0 into 0
5.356 * [backup-simplify]: Simplify 1 into 1
5.356 * [taylor]: Taking taylor expansion of PI in n
5.356 * [backup-simplify]: Simplify PI into PI
5.356 * [backup-simplify]: Simplify (* 0 PI) into 0
5.357 * [backup-simplify]: Simplify (* 2 0) into 0
5.358 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.360 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.361 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.361 * [backup-simplify]: Simplify (- k) into (- k)
5.361 * [backup-simplify]: Simplify (+ 1 (- k)) into (- 1 k)
5.361 * [backup-simplify]: Simplify (* 1/2 (- 1 k)) into (* 1/2 (- 1 k))
5.363 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.364 * [backup-simplify]: Simplify (* (* 1/2 (- 1 k)) (+ (log n) (log (* 2 PI)))) into (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))
5.365 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI)))))) into (exp (* 1/2 (* (- 1 k) (+ (log n) (log (* 2 PI))))))
5.365 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
5.365 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.365 * [taylor]: Taking taylor expansion of k in n
5.365 * [backup-simplify]: Simplify k into k
5.365 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.365 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
5.365 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.366 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
5.366 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
5.366 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
5.366 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
5.366 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
5.366 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
5.366 * [taylor]: Taking taylor expansion of 1/2 in k
5.366 * [backup-simplify]: Simplify 1/2 into 1/2
5.366 * [taylor]: Taking taylor expansion of (- 1 k) in k
5.366 * [taylor]: Taking taylor expansion of 1 in k
5.366 * [backup-simplify]: Simplify 1 into 1
5.366 * [taylor]: Taking taylor expansion of k in k
5.366 * [backup-simplify]: Simplify 0 into 0
5.366 * [backup-simplify]: Simplify 1 into 1
5.366 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
5.366 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
5.366 * [taylor]: Taking taylor expansion of 2 in k
5.366 * [backup-simplify]: Simplify 2 into 2
5.366 * [taylor]: Taking taylor expansion of (* n PI) in k
5.366 * [taylor]: Taking taylor expansion of n in k
5.366 * [backup-simplify]: Simplify n into n
5.366 * [taylor]: Taking taylor expansion of PI in k
5.366 * [backup-simplify]: Simplify PI into PI
5.366 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.366 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
5.366 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
5.367 * [backup-simplify]: Simplify (- 0) into 0
5.367 * [backup-simplify]: Simplify (+ 1 0) into 1
5.368 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.368 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
5.368 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
5.368 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.368 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.368 * [taylor]: Taking taylor expansion of k in k
5.368 * [backup-simplify]: Simplify 0 into 0
5.368 * [backup-simplify]: Simplify 1 into 1
5.368 * [backup-simplify]: Simplify (/ 1 1) into 1
5.369 * [backup-simplify]: Simplify (sqrt 0) into 0
5.370 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.370 * [taylor]: Taking taylor expansion of (* (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) (sqrt (/ 1 k))) in k
5.370 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (* 1/2 (- 1 k))) in k
5.370 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 k)) (log (* 2 (* n PI))))) in k
5.370 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 k)) (log (* 2 (* n PI)))) in k
5.370 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 k)) in k
5.370 * [taylor]: Taking taylor expansion of 1/2 in k
5.370 * [backup-simplify]: Simplify 1/2 into 1/2
5.370 * [taylor]: Taking taylor expansion of (- 1 k) in k
5.370 * [taylor]: Taking taylor expansion of 1 in k
5.370 * [backup-simplify]: Simplify 1 into 1
5.370 * [taylor]: Taking taylor expansion of k in k
5.370 * [backup-simplify]: Simplify 0 into 0
5.370 * [backup-simplify]: Simplify 1 into 1
5.370 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
5.370 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
5.370 * [taylor]: Taking taylor expansion of 2 in k
5.370 * [backup-simplify]: Simplify 2 into 2
5.370 * [taylor]: Taking taylor expansion of (* n PI) in k
5.370 * [taylor]: Taking taylor expansion of n in k
5.370 * [backup-simplify]: Simplify n into n
5.370 * [taylor]: Taking taylor expansion of PI in k
5.371 * [backup-simplify]: Simplify PI into PI
5.371 * [backup-simplify]: Simplify (* n PI) into (* n PI)
5.371 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
5.371 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
5.371 * [backup-simplify]: Simplify (- 0) into 0
5.371 * [backup-simplify]: Simplify (+ 1 0) into 1
5.372 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.372 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
5.372 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
5.372 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
5.372 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.372 * [taylor]: Taking taylor expansion of k in k
5.372 * [backup-simplify]: Simplify 0 into 0
5.372 * [backup-simplify]: Simplify 1 into 1
5.373 * [backup-simplify]: Simplify (/ 1 1) into 1
5.373 * [backup-simplify]: Simplify (sqrt 0) into 0
5.374 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.374 * [backup-simplify]: Simplify (* (pow (* 2 (* n PI)) 1/2) 0) into 0
5.374 * [taylor]: Taking taylor expansion of 0 in n
5.374 * [backup-simplify]: Simplify 0 into 0
5.375 * [backup-simplify]: Simplify 0 into 0
5.375 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
5.376 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 (* n PI))) into 0
5.376 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 (* n PI)) 1)))) 1) into 0
5.377 * [backup-simplify]: Simplify (- 1) into -1
5.377 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.378 * [backup-simplify]: Simplify (+ (* 1/2 -1) (* 0 1)) into -1/2
5.378 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 (* n PI))))) into (- (* 1/2 (log (* 2 (* n PI)))))
5.379 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1)))) into (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI)))))
5.379 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) 0)) into (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))
5.379 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
5.379 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
5.379 * [taylor]: Taking taylor expansion of +nan.0 in n
5.379 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.379 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
5.379 * [taylor]: Taking taylor expansion of (sqrt 2) in n
5.379 * [taylor]: Taking taylor expansion of 2 in n
5.379 * [backup-simplify]: Simplify 2 into 2
5.380 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
5.380 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
5.380 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
5.380 * [taylor]: Taking taylor expansion of (* n PI) in n
5.380 * [taylor]: Taking taylor expansion of n in n
5.380 * [backup-simplify]: Simplify 0 into 0
5.380 * [backup-simplify]: Simplify 1 into 1
5.380 * [taylor]: Taking taylor expansion of PI in n
5.380 * [backup-simplify]: Simplify PI into PI
5.381 * [backup-simplify]: Simplify (* 0 PI) into 0
5.382 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.383 * [backup-simplify]: Simplify (sqrt 0) into 0
5.384 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
5.384 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
5.385 * [backup-simplify]: Simplify (* +nan.0 0) into 0
5.385 * [backup-simplify]: Simplify (- 0) into 0
5.385 * [backup-simplify]: Simplify 0 into 0
5.385 * [backup-simplify]: Simplify 0 into 0
5.386 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
5.389 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.389 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
5.390 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
5.392 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 1)))) 2) into 0
5.392 * [backup-simplify]: Simplify (- 0) into 0
5.393 * [backup-simplify]: Simplify (+ 0 0) into 0
5.394 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 -1) (* 0 1))) into 0
5.395 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 (* n PI)))))) into 0
5.396 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2)))
5.396 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))))
5.396 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))))) in n
5.396 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))))) in n
5.396 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
5.396 * [taylor]: Taking taylor expansion of +nan.0 in n
5.396 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.396 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
5.397 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
5.397 * [taylor]: Taking taylor expansion of (sqrt 2) in n
5.397 * [taylor]: Taking taylor expansion of 2 in n
5.397 * [backup-simplify]: Simplify 2 into 2
5.397 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
5.398 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
5.398 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.398 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.398 * [taylor]: Taking taylor expansion of 2 in n
5.398 * [backup-simplify]: Simplify 2 into 2
5.398 * [taylor]: Taking taylor expansion of (* n PI) in n
5.398 * [taylor]: Taking taylor expansion of n in n
5.398 * [backup-simplify]: Simplify 0 into 0
5.398 * [backup-simplify]: Simplify 1 into 1
5.398 * [taylor]: Taking taylor expansion of PI in n
5.398 * [backup-simplify]: Simplify PI into PI
5.398 * [backup-simplify]: Simplify (* 0 PI) into 0
5.399 * [backup-simplify]: Simplify (* 2 0) into 0
5.400 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.402 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.403 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.403 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
5.403 * [taylor]: Taking taylor expansion of (* n PI) in n
5.403 * [taylor]: Taking taylor expansion of n in n
5.403 * [backup-simplify]: Simplify 0 into 0
5.403 * [backup-simplify]: Simplify 1 into 1
5.403 * [taylor]: Taking taylor expansion of PI in n
5.403 * [backup-simplify]: Simplify PI into PI
5.404 * [backup-simplify]: Simplify (* 0 PI) into 0
5.405 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.406 * [backup-simplify]: Simplify (sqrt 0) into 0
5.407 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
5.407 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (sqrt 2) (sqrt (* n PI))))) in n
5.407 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
5.407 * [taylor]: Taking taylor expansion of +nan.0 in n
5.407 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.407 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
5.407 * [taylor]: Taking taylor expansion of (sqrt 2) in n
5.407 * [taylor]: Taking taylor expansion of 2 in n
5.407 * [backup-simplify]: Simplify 2 into 2
5.408 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
5.408 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
5.408 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
5.408 * [taylor]: Taking taylor expansion of (* n PI) in n
5.408 * [taylor]: Taking taylor expansion of n in n
5.408 * [backup-simplify]: Simplify 0 into 0
5.408 * [backup-simplify]: Simplify 1 into 1
5.408 * [taylor]: Taking taylor expansion of PI in n
5.408 * [backup-simplify]: Simplify PI into PI
5.409 * [backup-simplify]: Simplify (* 0 PI) into 0
5.410 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.411 * [backup-simplify]: Simplify (sqrt 0) into 0
5.412 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
5.413 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.414 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
5.415 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
5.415 * [backup-simplify]: Simplify (* +nan.0 0) into 0
5.415 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
5.416 * [backup-simplify]: Simplify (* +nan.0 0) into 0
5.416 * [backup-simplify]: Simplify (- 0) into 0
5.416 * [backup-simplify]: Simplify (+ 0 0) into 0
5.416 * [backup-simplify]: Simplify (- 0) into 0
5.416 * [backup-simplify]: Simplify 0 into 0
5.418 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
5.421 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
5.424 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
5.425 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) PI))) into (- (* +nan.0 (* (sqrt 2) PI)))
5.425 * [backup-simplify]: Simplify 0 into 0
5.426 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.429 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.432 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
5.433 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
5.435 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 (* n PI)) 1)))) 6) into 0
5.435 * [backup-simplify]: Simplify (- 0) into 0
5.435 * [backup-simplify]: Simplify (+ 0 0) into 0
5.436 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1)))) into 0
5.437 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (+ (* 0 0) (* 0 (log (* 2 (* n PI))))))) into 0
5.438 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 (* n PI))))) (+ (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 3) 6)) (* (/ (pow (- (* 1/2 (log (* 2 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3)))
5.439 * [backup-simplify]: Simplify (+ (* (pow (* 2 (* n PI)) 1/2) +nan.0) (+ (* (* -1/2 (* (sqrt (* PI (* n 2))) (log (* 2 (* n PI))))) +nan.0) (+ (* (* 1/8 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 2))) +nan.0) (* (* -1/48 (* (sqrt (* PI (* n 2))) (pow (log (* 2 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))))
5.439 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))))) in n
5.439 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))))) in n
5.439 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI)))) in n
5.439 * [taylor]: Taking taylor expansion of +nan.0 in n
5.439 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.439 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (log (* 2 (* n PI)))) (sqrt (* n PI))) in n
5.439 * [taylor]: Taking taylor expansion of (* (sqrt 2) (log (* 2 (* n PI)))) in n
5.439 * [taylor]: Taking taylor expansion of (sqrt 2) in n
5.439 * [taylor]: Taking taylor expansion of 2 in n
5.439 * [backup-simplify]: Simplify 2 into 2
5.439 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
5.440 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
5.440 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.440 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.440 * [taylor]: Taking taylor expansion of 2 in n
5.440 * [backup-simplify]: Simplify 2 into 2
5.440 * [taylor]: Taking taylor expansion of (* n PI) in n
5.440 * [taylor]: Taking taylor expansion of n in n
5.440 * [backup-simplify]: Simplify 0 into 0
5.440 * [backup-simplify]: Simplify 1 into 1
5.440 * [taylor]: Taking taylor expansion of PI in n
5.440 * [backup-simplify]: Simplify PI into PI
5.441 * [backup-simplify]: Simplify (* 0 PI) into 0
5.441 * [backup-simplify]: Simplify (* 2 0) into 0
5.443 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.445 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.446 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.446 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
5.446 * [taylor]: Taking taylor expansion of (* n PI) in n
5.446 * [taylor]: Taking taylor expansion of n in n
5.446 * [backup-simplify]: Simplify 0 into 0
5.446 * [backup-simplify]: Simplify 1 into 1
5.446 * [taylor]: Taking taylor expansion of PI in n
5.446 * [backup-simplify]: Simplify PI into PI
5.446 * [backup-simplify]: Simplify (* 0 PI) into 0
5.448 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.448 * [backup-simplify]: Simplify (sqrt 0) into 0
5.449 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
5.449 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))))) in n
5.449 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))))) in n
5.449 * [taylor]: Taking taylor expansion of (* +nan.0 (* (sqrt 2) (sqrt (* n PI)))) in n
5.449 * [taylor]: Taking taylor expansion of +nan.0 in n
5.449 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.449 * [taylor]: Taking taylor expansion of (* (sqrt 2) (sqrt (* n PI))) in n
5.449 * [taylor]: Taking taylor expansion of (sqrt 2) in n
5.449 * [taylor]: Taking taylor expansion of 2 in n
5.449 * [backup-simplify]: Simplify 2 into 2
5.449 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
5.449 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
5.449 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
5.449 * [taylor]: Taking taylor expansion of (* n PI) in n
5.449 * [taylor]: Taking taylor expansion of n in n
5.449 * [backup-simplify]: Simplify 0 into 0
5.450 * [backup-simplify]: Simplify 1 into 1
5.450 * [taylor]: Taking taylor expansion of PI in n
5.450 * [backup-simplify]: Simplify PI into PI
5.450 * [backup-simplify]: Simplify (* 0 PI) into 0
5.451 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.451 * [backup-simplify]: Simplify (sqrt 0) into 0
5.452 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
5.452 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))))) in n
5.452 * [taylor]: Taking taylor expansion of (* +nan.0 (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI)))) in n
5.452 * [taylor]: Taking taylor expansion of +nan.0 in n
5.452 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.452 * [taylor]: Taking taylor expansion of (* (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) (sqrt (* n PI))) in n
5.452 * [taylor]: Taking taylor expansion of (* (sqrt 2) (pow (log (* 2 (* n PI))) 2)) in n
5.452 * [taylor]: Taking taylor expansion of (sqrt 2) in n
5.452 * [taylor]: Taking taylor expansion of 2 in n
5.452 * [backup-simplify]: Simplify 2 into 2
5.452 * [backup-simplify]: Simplify (sqrt 2) into (sqrt 2)
5.453 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 2))) into 0
5.453 * [taylor]: Taking taylor expansion of (pow (log (* 2 (* n PI))) 2) in n
5.453 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
5.453 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
5.453 * [taylor]: Taking taylor expansion of 2 in n
5.453 * [backup-simplify]: Simplify 2 into 2
5.453 * [taylor]: Taking taylor expansion of (* n PI) in n
5.453 * [taylor]: Taking taylor expansion of n in n
5.453 * [backup-simplify]: Simplify 0 into 0
5.453 * [backup-simplify]: Simplify 1 into 1
5.453 * [taylor]: Taking taylor expansion of PI in n
5.453 * [backup-simplify]: Simplify PI into PI
5.453 * [backup-simplify]: Simplify (* 0 PI) into 0
5.454 * [backup-simplify]: Simplify (* 2 0) into 0
5.455 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.456 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
5.457 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.458 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.458 * [taylor]: Taking taylor expansion of (sqrt (* n PI)) in n
5.458 * [taylor]: Taking taylor expansion of (* n PI) in n
5.458 * [taylor]: Taking taylor expansion of n in n
5.458 * [backup-simplify]: Simplify 0 into 0
5.458 * [backup-simplify]: Simplify 1 into 1
5.458 * [taylor]: Taking taylor expansion of PI in n
5.458 * [backup-simplify]: Simplify PI into PI
5.458 * [backup-simplify]: Simplify (* 0 PI) into 0
5.459 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
5.459 * [backup-simplify]: Simplify (sqrt 0) into 0
5.460 * [backup-simplify]: Simplify (/ PI (* 2 (sqrt 0))) into (* +nan.0 PI)
5.461 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.462 * [backup-simplify]: Simplify (* (sqrt 2) (+ (log n) (log (* 2 PI)))) into (* (sqrt 2) (+ (log n) (log (* 2 PI))))
5.463 * [backup-simplify]: Simplify (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) 0) into 0
5.463 * [backup-simplify]: Simplify (* +nan.0 0) into 0
5.464 * [backup-simplify]: Simplify (* (sqrt 2) 0) into 0
5.464 * [backup-simplify]: Simplify (* +nan.0 0) into 0
5.465 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.466 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.467 * [backup-simplify]: Simplify (* (+ (log n) (log (* 2 PI))) (+ (log n) (log (* 2 PI)))) into (pow (+ (log n) (log (* 2 PI))) 2)
5.468 * [backup-simplify]: Simplify (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) into (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2))
5.469 * [backup-simplify]: Simplify (* (* (sqrt 2) (pow (+ (log n) (log (* 2 PI))) 2)) 0) into 0
5.469 * [backup-simplify]: Simplify (* +nan.0 0) into 0
5.470 * [backup-simplify]: Simplify (- 0) into 0
5.470 * [backup-simplify]: Simplify (+ 0 0) into 0
5.470 * [backup-simplify]: Simplify (- 0) into 0
5.470 * [backup-simplify]: Simplify (+ 0 0) into 0
5.470 * [backup-simplify]: Simplify (- 0) into 0
5.470 * [backup-simplify]: Simplify 0 into 0
5.471 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.472 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
5.473 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.474 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
5.476 * [backup-simplify]: Simplify (+ (* (sqrt 2) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
5.478 * [backup-simplify]: Simplify (+ (* (* (sqrt 2) (+ (log n) (log (* 2 PI)))) (* +nan.0 PI)) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))
5.484 * [backup-simplify]: Simplify (+ (* +nan.0 (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))) (* 0 0)) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))
5.488 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 PI)) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
5.493 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0)) into (- (* +nan.0 (* (sqrt 2) PI)))
5.497 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) PI)))) into (- (* +nan.0 (* (sqrt 2) PI)))
5.505 * [backup-simplify]: Simplify (+ (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI)))))))) (- (* +nan.0 (* (sqrt 2) PI)))) into (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))
5.514 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (sqrt 2) PI)) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))))
5.521 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) into (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI)))))))
5.522 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
5.527 * [backup-simplify]: Simplify (/ (- 0 (pow (* +nan.0 PI) 2) (+)) (* 2 0)) into (* +nan.0 (pow PI 2))
5.528 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 2))) into 0
5.533 * [backup-simplify]: Simplify (+ (* (sqrt 2) (* +nan.0 (pow PI 2))) (+ (* 0 (* +nan.0 PI)) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
5.542 * [backup-simplify]: Simplify (+ (* +nan.0 (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) (+ (* 0 (- (* +nan.0 (* (sqrt 2) PI)))) (* 0 0))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
5.547 * [backup-simplify]: Simplify (- (- (* +nan.0 (* (sqrt 2) (pow PI 2))))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
5.555 * [backup-simplify]: Simplify (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) into (- (* +nan.0 (* (sqrt 2) (pow PI 2))))
5.571 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (sqrt 2) (pow PI 2)))) (pow (* n 1) 2)) (+ (* (- (+ (* +nan.0 (* (sqrt 2) (* PI (log (* 2 PI))))) (- (+ (* +nan.0 (* (sqrt 2) (* PI (log n)))) (- (* +nan.0 (* (sqrt 2) PI))))))) (* n k)) (* (- (* +nan.0 (* (sqrt 2) PI))) (* n 1)))) into (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))))))
5.571 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 k))) (pow (* (* 2 PI) (/ 1 n)) (/ (- 1 (/ 1 k)) 2))) into (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k))
5.572 * [approximate]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in (k n) around 0
5.572 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in n
5.572 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in n
5.572 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in n
5.572 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in n
5.572 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in n
5.572 * [taylor]: Taking taylor expansion of 1/2 in n
5.572 * [backup-simplify]: Simplify 1/2 into 1/2
5.572 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.572 * [taylor]: Taking taylor expansion of 1 in n
5.572 * [backup-simplify]: Simplify 1 into 1
5.572 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.572 * [taylor]: Taking taylor expansion of k in n
5.572 * [backup-simplify]: Simplify k into k
5.572 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.572 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.572 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.572 * [taylor]: Taking taylor expansion of 2 in n
5.572 * [backup-simplify]: Simplify 2 into 2
5.572 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.572 * [taylor]: Taking taylor expansion of PI in n
5.572 * [backup-simplify]: Simplify PI into PI
5.572 * [taylor]: Taking taylor expansion of n in n
5.572 * [backup-simplify]: Simplify 0 into 0
5.572 * [backup-simplify]: Simplify 1 into 1
5.573 * [backup-simplify]: Simplify (/ PI 1) into PI
5.574 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.575 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.575 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.575 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.575 * [backup-simplify]: Simplify (* 1/2 (- 1 (/ 1 k))) into (* 1/2 (- 1 (/ 1 k)))
5.576 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.577 * [backup-simplify]: Simplify (* (* 1/2 (- 1 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.579 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.579 * [taylor]: Taking taylor expansion of (sqrt k) in n
5.579 * [taylor]: Taking taylor expansion of k in n
5.579 * [backup-simplify]: Simplify k into k
5.579 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
5.579 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
5.579 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
5.579 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
5.579 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
5.579 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
5.579 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
5.579 * [taylor]: Taking taylor expansion of 1/2 in k
5.579 * [backup-simplify]: Simplify 1/2 into 1/2
5.579 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
5.579 * [taylor]: Taking taylor expansion of 1 in k
5.579 * [backup-simplify]: Simplify 1 into 1
5.579 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.579 * [taylor]: Taking taylor expansion of k in k
5.579 * [backup-simplify]: Simplify 0 into 0
5.579 * [backup-simplify]: Simplify 1 into 1
5.579 * [backup-simplify]: Simplify (/ 1 1) into 1
5.580 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
5.580 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
5.580 * [taylor]: Taking taylor expansion of 2 in k
5.580 * [backup-simplify]: Simplify 2 into 2
5.580 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.580 * [taylor]: Taking taylor expansion of PI in k
5.580 * [backup-simplify]: Simplify PI into PI
5.580 * [taylor]: Taking taylor expansion of n in k
5.580 * [backup-simplify]: Simplify n into n
5.580 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.580 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
5.580 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
5.580 * [backup-simplify]: Simplify (- 1) into -1
5.581 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.581 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
5.581 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
5.581 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
5.581 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.581 * [taylor]: Taking taylor expansion of k in k
5.582 * [backup-simplify]: Simplify 0 into 0
5.582 * [backup-simplify]: Simplify 1 into 1
5.582 * [backup-simplify]: Simplify (sqrt 0) into 0
5.583 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.583 * [taylor]: Taking taylor expansion of (* (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) (sqrt k)) in k
5.583 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (* 1/2 (- 1 (/ 1 k)))) in k
5.583 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) in k
5.584 * [taylor]: Taking taylor expansion of (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n)))) in k
5.584 * [taylor]: Taking taylor expansion of (* 1/2 (- 1 (/ 1 k))) in k
5.584 * [taylor]: Taking taylor expansion of 1/2 in k
5.584 * [backup-simplify]: Simplify 1/2 into 1/2
5.584 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in k
5.584 * [taylor]: Taking taylor expansion of 1 in k
5.584 * [backup-simplify]: Simplify 1 into 1
5.584 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.584 * [taylor]: Taking taylor expansion of k in k
5.584 * [backup-simplify]: Simplify 0 into 0
5.584 * [backup-simplify]: Simplify 1 into 1
5.584 * [backup-simplify]: Simplify (/ 1 1) into 1
5.584 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
5.584 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
5.584 * [taylor]: Taking taylor expansion of 2 in k
5.584 * [backup-simplify]: Simplify 2 into 2
5.584 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.584 * [taylor]: Taking taylor expansion of PI in k
5.584 * [backup-simplify]: Simplify PI into PI
5.584 * [taylor]: Taking taylor expansion of n in k
5.584 * [backup-simplify]: Simplify n into n
5.584 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.585 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
5.585 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
5.585 * [backup-simplify]: Simplify (- 1) into -1
5.585 * [backup-simplify]: Simplify (+ 0 -1) into -1
5.586 * [backup-simplify]: Simplify (* 1/2 -1) into -1/2
5.586 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
5.586 * [backup-simplify]: Simplify (exp (* (* 1/2 (- 1 (/ 1 k))) (log (* 2 (/ PI n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))
5.586 * [taylor]: Taking taylor expansion of (sqrt k) in k
5.586 * [taylor]: Taking taylor expansion of k in k
5.586 * [backup-simplify]: Simplify 0 into 0
5.586 * [backup-simplify]: Simplify 1 into 1
5.587 * [backup-simplify]: Simplify (sqrt 0) into 0
5.588 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
5.588 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) 0) into 0
5.588 * [taylor]: Taking taylor expansion of 0 in n
5.588 * [backup-simplify]: Simplify 0 into 0
5.588 * [backup-simplify]: Simplify 0 into 0
5.589 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
5.589 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
5.589 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
5.589 * [taylor]: Taking taylor expansion of +nan.0 in n
5.589 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.589 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
5.589 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
5.589 * [taylor]: Taking taylor expansion of 1/2 in n
5.589 * [backup-simplify]: Simplify 1/2 into 1/2
5.589 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
5.589 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.589 * [taylor]: Taking taylor expansion of 1 in n
5.589 * [backup-simplify]: Simplify 1 into 1
5.589 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.589 * [taylor]: Taking taylor expansion of k in n
5.589 * [backup-simplify]: Simplify k into k
5.589 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.589 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.589 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.589 * [taylor]: Taking taylor expansion of 2 in n
5.589 * [backup-simplify]: Simplify 2 into 2
5.589 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.589 * [taylor]: Taking taylor expansion of PI in n
5.589 * [backup-simplify]: Simplify PI into PI
5.589 * [taylor]: Taking taylor expansion of n in n
5.590 * [backup-simplify]: Simplify 0 into 0
5.590 * [backup-simplify]: Simplify 1 into 1
5.590 * [backup-simplify]: Simplify (/ PI 1) into PI
5.590 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.592 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.592 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.592 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.593 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.594 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
5.595 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.597 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.598 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
5.599 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
5.600 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
5.600 * [backup-simplify]: Simplify 0 into 0
5.601 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.602 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
5.602 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
5.602 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
5.602 * [taylor]: Taking taylor expansion of +nan.0 in n
5.602 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.602 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
5.602 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
5.602 * [taylor]: Taking taylor expansion of 1/2 in n
5.602 * [backup-simplify]: Simplify 1/2 into 1/2
5.602 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
5.602 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.602 * [taylor]: Taking taylor expansion of 1 in n
5.602 * [backup-simplify]: Simplify 1 into 1
5.602 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.602 * [taylor]: Taking taylor expansion of k in n
5.602 * [backup-simplify]: Simplify k into k
5.602 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.602 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.602 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.602 * [taylor]: Taking taylor expansion of 2 in n
5.602 * [backup-simplify]: Simplify 2 into 2
5.602 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.602 * [taylor]: Taking taylor expansion of PI in n
5.602 * [backup-simplify]: Simplify PI into PI
5.602 * [taylor]: Taking taylor expansion of n in n
5.602 * [backup-simplify]: Simplify 0 into 0
5.602 * [backup-simplify]: Simplify 1 into 1
5.603 * [backup-simplify]: Simplify (/ PI 1) into PI
5.603 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.604 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.604 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.604 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.605 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.605 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
5.606 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.607 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.608 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
5.608 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
5.609 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
5.610 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.610 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
5.612 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
5.612 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.612 * [backup-simplify]: Simplify (- 0) into 0
5.612 * [backup-simplify]: Simplify (+ 0 0) into 0
5.613 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.614 * [backup-simplify]: Simplify (+ (* (- 1 (/ 1 k)) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
5.615 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into 0
5.616 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.617 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into 0
5.618 * [backup-simplify]: Simplify (- 0) into 0
5.618 * [backup-simplify]: Simplify 0 into 0
5.618 * [backup-simplify]: Simplify 0 into 0
5.620 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.621 * [backup-simplify]: Simplify (+ (* (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))))
5.621 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))))) in n
5.621 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))))) in n
5.621 * [taylor]: Taking taylor expansion of +nan.0 in n
5.621 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.621 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))))) in n
5.621 * [taylor]: Taking taylor expansion of (* 1/2 (* (- 1 (/ 1 k)) (log (* 2 (/ PI n))))) in n
5.621 * [taylor]: Taking taylor expansion of 1/2 in n
5.621 * [backup-simplify]: Simplify 1/2 into 1/2
5.621 * [taylor]: Taking taylor expansion of (* (- 1 (/ 1 k)) (log (* 2 (/ PI n)))) in n
5.621 * [taylor]: Taking taylor expansion of (- 1 (/ 1 k)) in n
5.621 * [taylor]: Taking taylor expansion of 1 in n
5.621 * [backup-simplify]: Simplify 1 into 1
5.621 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.621 * [taylor]: Taking taylor expansion of k in n
5.621 * [backup-simplify]: Simplify k into k
5.621 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.621 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
5.621 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
5.621 * [taylor]: Taking taylor expansion of 2 in n
5.621 * [backup-simplify]: Simplify 2 into 2
5.621 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.621 * [taylor]: Taking taylor expansion of PI in n
5.621 * [backup-simplify]: Simplify PI into PI
5.621 * [taylor]: Taking taylor expansion of n in n
5.621 * [backup-simplify]: Simplify 0 into 0
5.621 * [backup-simplify]: Simplify 1 into 1
5.621 * [backup-simplify]: Simplify (/ PI 1) into PI
5.622 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
5.623 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
5.623 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
5.623 * [backup-simplify]: Simplify (+ 1 (- (/ 1 k))) into (- 1 (/ 1 k))
5.624 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
5.624 * [backup-simplify]: Simplify (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))) into (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))
5.625 * [backup-simplify]: Simplify (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))) into (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))
5.626 * [backup-simplify]: Simplify (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))) into (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))
5.627 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))
5.628 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
5.629 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 k)) (- (log (* 2 PI)) (log n)))))))
5.633 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 1/2 (* (- 1 (/ 1 (/ 1 k))) (- (log (* 2 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
5.634 * [backup-simplify]: Simplify (* (/ 1 (sqrt (/ 1 (- k)))) (pow (* (* 2 PI) (/ 1 (- n))) (/ (- 1 (/ 1 (- k))) 2))) into (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k)))
5.634 * [approximate]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in (k n) around 0
5.634 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in n
5.634 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in n
5.634 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in n
5.634 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in n
5.634 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in n
5.634 * [taylor]: Taking taylor expansion of 1/2 in n
5.634 * [backup-simplify]: Simplify 1/2 into 1/2
5.634 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.634 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.634 * [taylor]: Taking taylor expansion of k in n
5.634 * [backup-simplify]: Simplify k into k
5.634 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.634 * [taylor]: Taking taylor expansion of 1 in n
5.634 * [backup-simplify]: Simplify 1 into 1
5.634 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.634 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.634 * [taylor]: Taking taylor expansion of -2 in n
5.635 * [backup-simplify]: Simplify -2 into -2
5.635 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.635 * [taylor]: Taking taylor expansion of PI in n
5.635 * [backup-simplify]: Simplify PI into PI
5.635 * [taylor]: Taking taylor expansion of n in n
5.635 * [backup-simplify]: Simplify 0 into 0
5.635 * [backup-simplify]: Simplify 1 into 1
5.635 * [backup-simplify]: Simplify (/ PI 1) into PI
5.636 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.637 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.637 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.637 * [backup-simplify]: Simplify (* 1/2 (+ (/ 1 k) 1)) into (* 1/2 (+ (/ 1 k) 1))
5.638 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.639 * [backup-simplify]: Simplify (* (* 1/2 (+ (/ 1 k) 1)) (- (log (* -2 PI)) (log n))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.640 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.641 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
5.641 * [taylor]: Taking taylor expansion of (/ -1 k) in n
5.641 * [taylor]: Taking taylor expansion of -1 in n
5.641 * [backup-simplify]: Simplify -1 into -1
5.641 * [taylor]: Taking taylor expansion of k in n
5.641 * [backup-simplify]: Simplify k into k
5.641 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
5.641 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
5.641 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
5.641 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
5.642 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k))) into (/ (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (sqrt (/ -1 k)))
5.642 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
5.642 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
5.642 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
5.642 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
5.642 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
5.642 * [taylor]: Taking taylor expansion of 1/2 in k
5.642 * [backup-simplify]: Simplify 1/2 into 1/2
5.642 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.642 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.643 * [taylor]: Taking taylor expansion of k in k
5.643 * [backup-simplify]: Simplify 0 into 0
5.643 * [backup-simplify]: Simplify 1 into 1
5.643 * [backup-simplify]: Simplify (/ 1 1) into 1
5.643 * [taylor]: Taking taylor expansion of 1 in k
5.643 * [backup-simplify]: Simplify 1 into 1
5.643 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
5.643 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
5.643 * [taylor]: Taking taylor expansion of -2 in k
5.643 * [backup-simplify]: Simplify -2 into -2
5.643 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.643 * [taylor]: Taking taylor expansion of PI in k
5.643 * [backup-simplify]: Simplify PI into PI
5.643 * [taylor]: Taking taylor expansion of n in k
5.643 * [backup-simplify]: Simplify n into n
5.643 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.643 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
5.643 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
5.644 * [backup-simplify]: Simplify (+ 1 0) into 1
5.644 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.644 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
5.645 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
5.645 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.645 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.645 * [taylor]: Taking taylor expansion of -1 in k
5.645 * [backup-simplify]: Simplify -1 into -1
5.645 * [taylor]: Taking taylor expansion of k in k
5.645 * [backup-simplify]: Simplify 0 into 0
5.645 * [backup-simplify]: Simplify 1 into 1
5.645 * [backup-simplify]: Simplify (/ -1 1) into -1
5.646 * [backup-simplify]: Simplify (sqrt 0) into 0
5.647 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.647 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
5.648 * [taylor]: Taking taylor expansion of (/ (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) (sqrt (/ -1 k))) in k
5.648 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (* 1/2 (+ (/ 1 k) 1))) in k
5.648 * [taylor]: Taking taylor expansion of (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) in k
5.648 * [taylor]: Taking taylor expansion of (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n)))) in k
5.648 * [taylor]: Taking taylor expansion of (* 1/2 (+ (/ 1 k) 1)) in k
5.648 * [taylor]: Taking taylor expansion of 1/2 in k
5.648 * [backup-simplify]: Simplify 1/2 into 1/2
5.648 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in k
5.648 * [taylor]: Taking taylor expansion of (/ 1 k) in k
5.648 * [taylor]: Taking taylor expansion of k in k
5.648 * [backup-simplify]: Simplify 0 into 0
5.648 * [backup-simplify]: Simplify 1 into 1
5.648 * [backup-simplify]: Simplify (/ 1 1) into 1
5.648 * [taylor]: Taking taylor expansion of 1 in k
5.648 * [backup-simplify]: Simplify 1 into 1
5.649 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
5.649 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
5.649 * [taylor]: Taking taylor expansion of -2 in k
5.649 * [backup-simplify]: Simplify -2 into -2
5.649 * [taylor]: Taking taylor expansion of (/ PI n) in k
5.649 * [taylor]: Taking taylor expansion of PI in k
5.649 * [backup-simplify]: Simplify PI into PI
5.649 * [taylor]: Taking taylor expansion of n in k
5.649 * [backup-simplify]: Simplify n into n
5.649 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
5.649 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
5.649 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
5.649 * [backup-simplify]: Simplify (+ 1 0) into 1
5.650 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
5.650 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
5.650 * [backup-simplify]: Simplify (exp (* (* 1/2 (+ (/ 1 k) 1)) (log (* -2 (/ PI n))))) into (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))
5.650 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
5.650 * [taylor]: Taking taylor expansion of (/ -1 k) in k
5.650 * [taylor]: Taking taylor expansion of -1 in k
5.650 * [backup-simplify]: Simplify -1 into -1
5.650 * [taylor]: Taking taylor expansion of k in k
5.650 * [backup-simplify]: Simplify 0 into 0
5.650 * [backup-simplify]: Simplify 1 into 1
5.651 * [backup-simplify]: Simplify (/ -1 1) into -1
5.651 * [backup-simplify]: Simplify (sqrt 0) into 0
5.652 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
5.652 * [backup-simplify]: Simplify (/ (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) +nan.0) into (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))
5.652 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
5.652 * [taylor]: Taking taylor expansion of +nan.0 in n
5.652 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.652 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
5.652 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
5.652 * [taylor]: Taking taylor expansion of 1/2 in n
5.652 * [backup-simplify]: Simplify 1/2 into 1/2
5.652 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
5.652 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.652 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.652 * [taylor]: Taking taylor expansion of -2 in n
5.652 * [backup-simplify]: Simplify -2 into -2
5.652 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.652 * [taylor]: Taking taylor expansion of PI in n
5.652 * [backup-simplify]: Simplify PI into PI
5.652 * [taylor]: Taking taylor expansion of n in n
5.652 * [backup-simplify]: Simplify 0 into 0
5.652 * [backup-simplify]: Simplify 1 into 1
5.653 * [backup-simplify]: Simplify (/ PI 1) into PI
5.653 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.654 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.654 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.654 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.654 * [taylor]: Taking taylor expansion of k in n
5.654 * [backup-simplify]: Simplify k into k
5.654 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.654 * [taylor]: Taking taylor expansion of 1 in n
5.654 * [backup-simplify]: Simplify 1 into 1
5.655 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.655 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.655 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
5.656 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.657 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.658 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
5.658 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
5.659 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
5.661 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
5.661 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))
5.661 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
5.661 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
5.661 * [taylor]: Taking taylor expansion of +nan.0 in n
5.662 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.662 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
5.662 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
5.662 * [taylor]: Taking taylor expansion of 1/2 in n
5.662 * [backup-simplify]: Simplify 1/2 into 1/2
5.662 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
5.662 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.662 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.662 * [taylor]: Taking taylor expansion of -2 in n
5.662 * [backup-simplify]: Simplify -2 into -2
5.662 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.662 * [taylor]: Taking taylor expansion of PI in n
5.662 * [backup-simplify]: Simplify PI into PI
5.662 * [taylor]: Taking taylor expansion of n in n
5.662 * [backup-simplify]: Simplify 0 into 0
5.662 * [backup-simplify]: Simplify 1 into 1
5.662 * [backup-simplify]: Simplify (/ PI 1) into PI
5.662 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.663 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.663 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.663 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.663 * [taylor]: Taking taylor expansion of k in n
5.663 * [backup-simplify]: Simplify k into k
5.663 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.663 * [taylor]: Taking taylor expansion of 1 in n
5.663 * [backup-simplify]: Simplify 1 into 1
5.664 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.664 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.665 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
5.666 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.666 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.670 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
5.671 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
5.672 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
5.673 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.673 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
5.673 * [backup-simplify]: Simplify (+ 0 0) into 0
5.674 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
5.674 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
5.675 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
5.676 * [backup-simplify]: Simplify (+ (* (- (log (* -2 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1))) into 0
5.677 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into 0
5.678 * [backup-simplify]: Simplify (* (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
5.679 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into 0
5.679 * [backup-simplify]: Simplify 0 into 0
5.681 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
5.685 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
5.686 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))))
5.686 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))))) in n
5.686 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))))) in n
5.686 * [taylor]: Taking taylor expansion of +nan.0 in n
5.686 * [backup-simplify]: Simplify +nan.0 into +nan.0
5.687 * [taylor]: Taking taylor expansion of (exp (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)))) in n
5.687 * [taylor]: Taking taylor expansion of (* 1/2 (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1))) in n
5.687 * [taylor]: Taking taylor expansion of 1/2 in n
5.687 * [backup-simplify]: Simplify 1/2 into 1/2
5.687 * [taylor]: Taking taylor expansion of (* (log (* -2 (/ PI n))) (+ (/ 1 k) 1)) in n
5.687 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
5.687 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
5.687 * [taylor]: Taking taylor expansion of -2 in n
5.687 * [backup-simplify]: Simplify -2 into -2
5.687 * [taylor]: Taking taylor expansion of (/ PI n) in n
5.687 * [taylor]: Taking taylor expansion of PI in n
5.687 * [backup-simplify]: Simplify PI into PI
5.687 * [taylor]: Taking taylor expansion of n in n
5.687 * [backup-simplify]: Simplify 0 into 0
5.687 * [backup-simplify]: Simplify 1 into 1
5.687 * [backup-simplify]: Simplify (/ PI 1) into PI
5.688 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
5.688 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
5.688 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1) in n
5.688 * [taylor]: Taking taylor expansion of (/ 1 k) in n
5.688 * [taylor]: Taking taylor expansion of k in n
5.688 * [backup-simplify]: Simplify k into k
5.688 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
5.688 * [taylor]: Taking taylor expansion of 1 in n
5.688 * [backup-simplify]: Simplify 1 into 1
5.689 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
5.689 * [backup-simplify]: Simplify (+ (/ 1 k) 1) into (+ (/ 1 k) 1)
5.690 * [backup-simplify]: Simplify (* (- (log (* -2 PI)) (log n)) (+ (/ 1 k) 1)) into (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))
5.691 * [backup-simplify]: Simplify (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))) into (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))
5.691 * [backup-simplify]: Simplify (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))) into (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))
5.692 * [backup-simplify]: Simplify (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))) into (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))
5.693 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
5.694 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n))))))) into (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 k) 1) (- (log (* -2 PI)) (log n)))))))
5.697 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n))))))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 1/2 (* (+ (/ 1 (/ 1 (- k))) 1) (- (log (* -2 PI)) (log (/ 1 (- n)))))))))) into (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
5.697 * * * [progress]: simplifying candidates
5.697 * * * * [progress]: [ 1 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
5.697 * * * * [progress]: [ 2 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
5.697 * * * * [progress]: [ 3 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
5.697 * * * * [progress]: [ 4 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
5.697 * * * * [progress]: [ 5 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
5.697 * * * * [progress]: [ 6 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
5.697 * * * * [progress]: [ 7 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (* 1 (/ (- 1 k) 2)))))>
5.697 * * * * [progress]: [ 8 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (/ (pow (* (* 2 PI) n) (/ 1 2)) (pow (* (* 2 PI) n) (/ k 2)))))>
5.697 * * * * [progress]: [ 9 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2)))) (cbrt (/ (- 1 k) 2)))))>
5.697 * * * * [progress]: [ 10 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2))) (sqrt (/ (- 1 k) 2)))))>
5.698 * * * * [progress]: [ 11 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2)))) (/ (cbrt (- 1 k)) (cbrt 2)))))>
5.698 * * * * [progress]: [ 12 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2))) (/ (cbrt (- 1 k)) (sqrt 2)))))>
5.698 * * * * [progress]: [ 13 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1)) (/ (cbrt (- 1 k)) 2))))>
5.698 * * * * [progress]: [ 14 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2)))) (/ (sqrt (- 1 k)) (cbrt 2)))))>
5.698 * * * * [progress]: [ 15 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (sqrt 2))) (/ (sqrt (- 1 k)) (sqrt 2)))))>
5.698 * * * * [progress]: [ 16 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) 1)) (/ (sqrt (- 1 k)) 2))))>
5.698 * * * * [progress]: [ 17 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2)))))>
5.698 * * * * [progress]: [ 18 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
5.698 * * * * [progress]: [ 19 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (- 1 k) 2))))>
5.698 * * * * [progress]: [ 20 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- (sqrt 1) (sqrt k)) (cbrt 2)))))>
5.698 * * * * [progress]: [ 21 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2))) (/ (- (sqrt 1) (sqrt k)) (sqrt 2)))))>
5.698 * * * * [progress]: [ 22 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) 1)) (/ (- (sqrt 1) (sqrt k)) 2))))>
5.698 * * * * [progress]: [ 23 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2)))) (/ (- 1 (sqrt k)) (cbrt 2)))))>
5.698 * * * * [progress]: [ 24 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (sqrt 2))) (/ (- 1 (sqrt k)) (sqrt 2)))))>
5.698 * * * * [progress]: [ 25 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) 1)) (/ (- 1 (sqrt k)) 2))))>
5.698 * * * * [progress]: [ 26 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2)))) (/ (- 1 k) (cbrt 2)))))>
5.698 * * * * [progress]: [ 27 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 (sqrt 2))) (/ (- 1 k) (sqrt 2)))))>
5.698 * * * * [progress]: [ 28 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ 1 1)) (/ (- 1 k) 2))))>
5.698 * * * * [progress]: [ 29 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
5.698 * * * * [progress]: [ 30 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (- 1 k)) (/ 1 2))))>
5.698 * * * * [progress]: [ 31 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* 2 PI) (/ (- 1 k) 2)) (pow n (/ (- 1 k) 2)))))>
5.698 * * * * [progress]: [ 32 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) (/ (- 1 k) 2)) 1)))>
5.698 * * * * [progress]: [ 33 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.698 * * * * [progress]: [ 34 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (log (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.698 * * * * [progress]: [ 35 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.699 * * * * [progress]: [ 36 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (cbrt (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.699 * * * * [progress]: [ 37 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.699 * * * * [progress]: [ 38 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.699 * * * * [progress]: [ 39 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
5.699 * * * * [progress]: [ 40 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (posit16->real (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.699 * * * * [progress]: [ 41 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 42 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 43 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (pow (* (* 2 PI) n) 1) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 44 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (+ (+ (log 2) (log PI)) (log n))) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 45 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (+ (log (* 2 PI)) (log n))) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 46 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (exp (log (* (* 2 PI) n))) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 47 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (log (exp (* (* 2 PI) n))) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 48 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 49 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 50 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n))) (cbrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 51 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (cbrt (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 52 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (sqrt (* (* 2 PI) n)) (sqrt (* (* 2 PI) n))) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 53 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 1 (* (* 2 PI) n)) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 54 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (* (cbrt n) (cbrt n))) (cbrt n)) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 55 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) (sqrt n)) (sqrt n)) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 56 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* (* 2 PI) 1) n) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 57 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* PI n)) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 58 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (posit16->real (real->posit16 (* (* 2 PI) n))) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 59 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 60 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) -1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.699 * * * * [progress]: [ 61 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow k (- 1/2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 62 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (sqrt k) (- 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 63 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow k (- (/ 1 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 64 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (/ 1 (sqrt k)) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 65 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (- (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 66 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (- 0 (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 67 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (- (log 1) (log (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 68 / 188 ] simplifiying candidate #<alt (λ (k n) (* (exp (log (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 69 / 188 ] simplifiying candidate #<alt (λ (k n) (* (log (exp (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 70 / 188 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 71 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (cbrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 72 / 188 ] simplifiying candidate #<alt (λ (k n) (* (cbrt (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 73 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 74 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (- 1) (- (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 75 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (cbrt 1) (cbrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 76 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (/ (cbrt 1) (sqrt (cbrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 77 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 78 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (/ (cbrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 79 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (/ (cbrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 80 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 81 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (sqrt 1) (cbrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 82 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))) (/ (sqrt 1) (sqrt (cbrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 83 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 84 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt 1)) (/ (sqrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 85 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (/ (sqrt 1) (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 86 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) 1) (/ (sqrt 1) (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.700 * * * * [progress]: [ 87 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ 1 (cbrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.701 * * * * [progress]: [ 88 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (/ 1 (sqrt (cbrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.701 * * * * [progress]: [ 89 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.701 * * * * [progress]: [ 90 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt 1)) (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.701 * * * * [progress]: [ 91 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (/ 1 (sqrt (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.701 * * * * [progress]: [ 92 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 1) (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.701 * * * * [progress]: [ 93 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* 1 (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.701 * * * * [progress]: [ 94 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* 1 (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.701 * * * * [progress]: [ 95 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt k) 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.701 * * * * [progress]: [ 96 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.701 * * * * [progress]: [ 97 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.701 * * * * [progress]: [ 98 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt (sqrt k))) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.701 * * * * [progress]: [ 99 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 (sqrt 1)) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
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5.701 * * * * [progress]: [ 101 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (/ 1 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.701 * * * * [progress]: [ 102 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (/ (sqrt k) (cbrt 1))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.701 * * * * [progress]: [ 103 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (/ (sqrt k) (sqrt 1))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.701 * * * * [progress]: [ 104 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (/ (sqrt k) 1)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.701 * * * * [progress]: [ 105 / 188 ] simplifiying candidate #<alt (λ (k n) (* (posit16->real (real->posit16 (/ 1 (sqrt k)))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.701 * * * * [progress]: [ 106 / 188 ] simplifiying candidate #<alt (λ (k n) (pow (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) 1))>
5.701 * * * * [progress]: [ 107 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
5.701 * * * * [progress]: [ 108 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
5.701 * * * * [progress]: [ 109 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
5.701 * * * * [progress]: [ 110 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
5.701 * * * * [progress]: [ 111 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.701 * * * * [progress]: [ 112 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
5.701 * * * * [progress]: [ 113 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
5.702 * * * * [progress]: [ 114 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
5.702 * * * * [progress]: [ 115 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
5.702 * * * * [progress]: [ 116 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- 0 (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.702 * * * * [progress]: [ 117 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
5.702 * * * * [progress]: [ 118 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
5.702 * * * * [progress]: [ 119 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
5.702 * * * * [progress]: [ 120 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
5.702 * * * * [progress]: [ 121 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (- (log 1) (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.702 * * * * [progress]: [ 122 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))))>
5.702 * * * * [progress]: [ 123 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))))>
5.702 * * * * [progress]: [ 124 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
5.702 * * * * [progress]: [ 125 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))))>
5.702 * * * * [progress]: [ 126 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.702 * * * * [progress]: [ 127 / 188 ] simplifiying candidate #<alt (λ (k n) (exp (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.702 * * * * [progress]: [ 128 / 188 ] simplifiying candidate #<alt (λ (k n) (log (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.702 * * * * [progress]: [ 129 / 188 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.702 * * * * [progress]: [ 130 / 188 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.702 * * * * [progress]: [ 131 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.702 * * * * [progress]: [ 132 / 188 ] simplifiying candidate #<alt (λ (k n) (cbrt (* (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.702 * * * * [progress]: [ 133 / 188 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.702 * * * * [progress]: [ 134 / 188 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ 1 2))) (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))))>
5.702 * * * * [progress]: [ 135 / 188 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.702 * * * * [progress]: [ 136 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.702 * * * * [progress]: [ 137 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
5.702 * * * * [progress]: [ 138 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.702 * * * * [progress]: [ 139 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
5.703 * * * * [progress]: [ 140 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.703 * * * * [progress]: [ 141 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
5.703 * * * * [progress]: [ 142 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.703 * * * * [progress]: [ 143 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
5.703 * * * * [progress]: [ 144 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.703 * * * * [progress]: [ 145 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))))>
5.703 * * * * [progress]: [ 146 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2))) (pow n (/ (- 1 k) 2))))>
5.703 * * * * [progress]: [ 147 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.703 * * * * [progress]: [ 148 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.703 * * * * [progress]: [ 149 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) 1) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.703 * * * * [progress]: [ 150 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))))>
5.703 * * * * [progress]: [ 151 / 188 ] simplifiying candidate #<alt (λ (k n) (* (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k)))) (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.703 * * * * [progress]: [ 152 / 188 ] simplifiying candidate #<alt (λ (k n) (* (sqrt (/ 1 (sqrt k))) (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.703 * * * * [progress]: [ 153 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ (cbrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.703 * * * * [progress]: [ 154 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k)))) (* (/ (cbrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.703 * * * * [progress]: [ 155 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.703 * * * * [progress]: [ 156 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)) (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.703 * * * * [progress]: [ 157 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k))) (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.703 * * * * [progress]: [ 158 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (* (cbrt 1) (cbrt 1)) 1) (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.703 * * * * [progress]: [ 159 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ (sqrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.703 * * * * [progress]: [ 160 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k)))) (* (/ (sqrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.703 * * * * [progress]: [ 161 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (sqrt k))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.703 * * * * [progress]: [ 162 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt 1)) (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.703 * * * * [progress]: [ 163 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) (sqrt (sqrt k))) (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.703 * * * * [progress]: [ 164 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ (sqrt 1) 1) (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.704 * * * * [progress]: [ 165 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (* (/ 1 (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.704 * * * * [progress]: [ 166 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (* (cbrt k) (cbrt k)))) (* (/ 1 (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.704 * * * * [progress]: [ 167 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.704 * * * * [progress]: [ 168 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt 1)) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.704 * * * * [progress]: [ 169 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt (sqrt k))) (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.704 * * * * [progress]: [ 170 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 1) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.704 * * * * [progress]: [ 171 / 188 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.704 * * * * [progress]: [ 172 / 188 ] simplifiying candidate #<alt (λ (k n) (* 1 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))>
5.704 * * * * [progress]: [ 173 / 188 ] simplifiying candidate #<alt (λ (k n) (/ (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2))) (pow (* (* 2 PI) n) (/ k 2))))>
5.704 * * * * [progress]: [ 174 / 188 ] simplifiying candidate #<alt (λ (k n) (/ (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (sqrt k)))>
5.704 * * * * [progress]: [ 175 / 188 ] simplifiying candidate #<alt (λ (k n) (posit16->real (real->posit16 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))))>
5.704 * * * * [progress]: [ 176 / 188 ] simplifiying candidate #<alt (λ (k n) (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (/ 1 (sqrt k))))>
5.704 * * * * [progress]: [ 177 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))))>
5.704 * * * * [progress]: [ 178 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))))>
5.704 * * * * [progress]: [ 179 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))>
5.704 * * * * [progress]: [ 180 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
5.704 * * * * [progress]: [ 181 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
5.704 * * * * [progress]: [ 182 / 188 ] simplifiying candidate #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* 2 (* n PI)) (/ (- 1 k) 2))))>
5.704 * * * * [progress]: [ 183 / 188 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k)))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.704 * * * * [progress]: [ 184 / 188 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3)))))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.704 * * * * [progress]: [ 185 / 188 ] simplifiying candidate #<alt (λ (k n) (* (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0))))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))>
5.704 * * * * [progress]: [ 186 / 188 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2))))))))))))))>
5.704 * * * * [progress]: [ 187 / 188 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3)))))))))>
5.704 * * * * [progress]: [ 188 / 188 ] simplifiying candidate #<alt (λ (k n) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))))))))))>
5.706 * [simplify]: Simplifying:
  (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2))
  (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2))
  (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
  (* (log (* (* 2 PI) n)) (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (* 1 (/ (- 1 k) 2))
  (pow (* (* 2 PI) n) (/ 1 2))
  (pow (* (* 2 PI) n) (/ k 2))
  (pow (* (* 2 PI) n) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* (* 2 PI) n) (sqrt (/ (- 1 k) 2)))
  (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (* (cbrt (- 1 k)) (cbrt (- 1 k))) 1))
  (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (sqrt (- 1 k)) 1))
  (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ 1 (sqrt 2)))
  (pow (* (* 2 PI) n) (/ 1 1))
  (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (+ (sqrt 1) (sqrt k)) 1))
  (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) (sqrt 2)))
  (pow (* (* 2 PI) n) (/ (+ 1 (sqrt k)) 1))
  (pow (* (* 2 PI) n) (/ 1 (* (cbrt 2) (cbrt 2))))
  (pow (* (* 2 PI) n) (/ 1 (sqrt 2)))
  (pow (* (* 2 PI) n) (/ 1 1))
  (pow (* (* 2 PI) n) 1)
  (pow (* (* 2 PI) n) (- 1 k))
  (pow (* 2 PI) (/ (- 1 k) 2))
  (pow n (/ (- 1 k) 2))
  (log (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (exp (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
  (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
  (real->posit16 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (* 2 PI) n)
  (* (* 2 PI) n)
  (+ (+ (log 2) (log PI)) (log n))
  (+ (log (* 2 PI)) (log n))
  (log (* (* 2 PI) n))
  (exp (* (* 2 PI) n))
  (* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))
  (* (cbrt (* (* 2 PI) n)) (cbrt (* (* 2 PI) n)))
  (cbrt (* (* 2 PI) n))
  (* (* (* (* 2 PI) n) (* (* 2 PI) n)) (* (* 2 PI) n))
  (sqrt (* (* 2 PI) n))
  (sqrt (* (* 2 PI) n))
  (* (* 2 PI) (* (cbrt n) (cbrt n)))
  (* (* 2 PI) (sqrt n))
  (* (* 2 PI) 1)
  (* PI n)
  (real->posit16 (* (* 2 PI) n))
  (- 1/2)
  (- 1)
  (- (/ 1 2))
  (- (log (sqrt k)))
  (- 0 (log (sqrt k)))
  (- (log 1) (log (sqrt k)))
  (log (/ 1 (sqrt k)))
  (exp (/ 1 (sqrt k)))
  (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
  (cbrt (/ 1 (sqrt k)))
  (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (- 1)
  (- (sqrt k))
  (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt 1) (cbrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt 1) (sqrt (cbrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt 1))
  (/ (cbrt 1) (sqrt k))
  (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt k)))
  (/ (cbrt 1) (sqrt (sqrt k)))
  (/ (* (cbrt 1) (cbrt 1)) 1)
  (/ (cbrt 1) (sqrt k))
  (/ (sqrt 1) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1) (cbrt (sqrt k)))
  (/ (sqrt 1) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt 1) (sqrt (cbrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt 1))
  (/ (sqrt 1) (sqrt k))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) (sqrt (sqrt k)))
  (/ (sqrt 1) 1)
  (/ (sqrt 1) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 1)
  (/ 1 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1)
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 1)
  (/ (sqrt k) (cbrt 1))
  (/ (sqrt k) (sqrt 1))
  (/ (sqrt k) 1)
  (real->posit16 (/ 1 (sqrt k)))
  (+ (- (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (+ (- 0 (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- 0 (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (+ (- (log 1) (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (- (log 1) (log (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (+ (log (/ 1 (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (* (+ (log (* 2 PI)) (log n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (* (log (* (* 2 PI) n)) (/ (- 1 k) 2)))
  (+ (log (/ 1 (sqrt k))) (log (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (log (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (exp (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (* (* 1 1) 1) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))
  (cbrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (* (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (sqrt (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* 1 (pow (* (* 2 PI) n) (/ 1 2)))
  (* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (/ 1 (sqrt k)) (pow (* 2 PI) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (* (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))))
  (* (/ 1 (sqrt k)) (sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (* (/ 1 (sqrt k)) 1)
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
  (* (cbrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (sqrt (/ 1 (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (cbrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ (sqrt 1) (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (cbrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt (cbrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt (sqrt k))) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ 1 2)))
  (* 1 (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
  (real->posit16 (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
  (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
  (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI k)))) (- (+ (* +nan.0 (* (sqrt 2) (* n PI))) (- (+ (* +nan.0 (* (log (* 2 PI)) (* (sqrt 2) (* n (* PI k))))) (- (+ (* +nan.0 (* (sqrt 2) (* n (* PI (* (log n) k))))) (- (* +nan.0 (* (sqrt 2) (* (pow n 2) (pow PI 2)))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 2))) (- (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) k)) (- (+ (* +nan.0 (/ (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n)))))) (pow k 2))) (- (* +nan.0 (exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))))))))
5.709 * * [simplify]: iteration 1: (345 enodes)
5.945 * * [simplify]: iteration 2: (922 enodes)
6.631 * * [simplify]: Extracting #0: cost 94 inf + 0
6.632 * * [simplify]: Extracting #1: cost 421 inf + 3
6.635 * * [simplify]: Extracting #2: cost 699 inf + 5459
6.642 * * [simplify]: Extracting #3: cost 633 inf + 50506
6.674 * * [simplify]: Extracting #4: cost 314 inf + 163558
6.716 * * [simplify]: Extracting #5: cost 151 inf + 230840
6.770 * * [simplify]: Extracting #6: cost 58 inf + 265745
6.829 * * [simplify]: Extracting #7: cost 33 inf + 274956
6.903 * * [simplify]: Extracting #8: cost 5 inf + 291468
6.974 * * [simplify]: Extracting #9: cost 0 inf + 293017
7.056 * * [simplify]: Extracting #10: cost 0 inf + 292497
7.143 * [simplify]: Simplified to:
  (* (/ (- 1 k) 2) (log (* n (* 2 PI))))
  (* (/ (- 1 k) 2) (log (* n (* 2 PI))))
  (* (/ (- 1 k) 2) (log (* n (* 2 PI))))
  (* (/ (- 1 k) 2) (log (* n (* 2 PI))))
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (/ (- 1 k) 2)
  (sqrt (* n (* 2 PI)))
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (/ (- 1 k) 2)) (cbrt (/ (- 1 k) 2))))
  (pow (* n (* 2 PI)) (sqrt (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (* (/ (cbrt (- 1 k)) (cbrt 2)) (/ (cbrt (- 1 k)) (cbrt 2))))
  (pow (* n (* 2 PI)) (* (/ (cbrt (- 1 k)) (sqrt 2)) (cbrt (- 1 k))))
  (pow (* n (* 2 PI)) (* (cbrt (- 1 k)) (cbrt (- 1 k))))
  (pow (* n (* 2 PI)) (/ (/ (sqrt (- 1 k)) (cbrt 2)) (cbrt 2)))
  (pow (* n (* 2 PI)) (/ (sqrt (- 1 k)) (sqrt 2)))
  (pow (* n (* 2 PI)) (sqrt (- 1 k)))
  (pow (* n (* 2 PI)) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (* n (* 2 PI))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow (* n (* 2 PI)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* n (* 2 PI)) (+ (sqrt k) 1))
  (pow (* n (* 2 PI)) (/ (/ (+ (sqrt k) 1) (cbrt 2)) (cbrt 2)))
  (pow (* n (* 2 PI)) (/ (+ (sqrt k) 1) (sqrt 2)))
  (pow (* n (* 2 PI)) (+ (sqrt k) 1))
  (pow (* n (* 2 PI)) (/ (/ 1 (cbrt 2)) (cbrt 2)))
  (pow (* n (* 2 PI)) (/ 1 (sqrt 2)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (pow (* n (* 2 PI)) (- 1 k))
  (pow (* 2 PI) (/ (- 1 k) 2))
  (pow n (/ (- 1 k) 2))
  (* (/ (- 1 k) 2) (log (* n (* 2 PI))))
  (exp (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
  (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 3)
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (pow (* n (* 2 PI)) (/ (- 1 k) 4))
  (pow (* n (* 2 PI)) (/ (- 1 k) 4))
  (real->posit16 (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (log (* n (* 2 PI)))
  (log (* n (* 2 PI)))
  (log (* n (* 2 PI)))
  (* (exp (* PI n)) (exp (* PI n)))
  (* n (* (* (* (* PI PI) PI) 8) (* n n)))
  (* (* PI n) (* 2 (* (* (* PI n) (* PI n)) 4)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* PI n) (* 2 (* (* (* PI n) (* PI n)) 4)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* (* 2 PI) (* (cbrt n) (cbrt n)))
  (* (* 2 PI) (sqrt n))
  (* 2 PI)
  (* PI n)
  (real->posit16 (* n (* 2 PI)))
  -1/2
  -1
  -1/2
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (- (log (sqrt k)))
  (exp (/ 1 (sqrt k)))
  (/ 1 (* (sqrt k) k))
  (* (cbrt (/ 1 (sqrt k))) (cbrt (/ 1 (sqrt k))))
  (cbrt (/ 1 (sqrt k)))
  (* (/ (/ 1 (sqrt k)) (sqrt k)) (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  (sqrt (/ 1 (sqrt k)))
  -1
  (- (sqrt k))
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ 1 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt k))
  (/ 1 (sqrt k))
  (sqrt k)
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  1
  (/ 1 (sqrt (sqrt k)))
  1
  (sqrt k)
  (sqrt k)
  (sqrt k)
  (real->posit16 (/ 1 (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (- (* (/ (- 1 k) 2) (log (* n (* 2 PI)))) (log (sqrt k)))
  (exp (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (/ (pow (pow (* n (* 2 PI)) (/ (- 1 k) 2)) 3) (* (sqrt k) k))
  (* (/ (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))) (sqrt k)) (/ (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k)))
  (* (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))) (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))))
  (cbrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (* (/ (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k))) (sqrt k)) (/ (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (sqrt (* n (* 2 PI)))
  (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))
  (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k))))
  (* (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (/ 1 (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (/ 1 (sqrt k))))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (/ 1 (sqrt k))))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt (sqrt k)))
  (/ (pow (* 2 PI) (/ (- 1 k) 2)) (sqrt k))
  (/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt k))
  (/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt k))
  (/ 1 (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 4)) (sqrt k))
  (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (/ 1 (sqrt k))))
  (* (sqrt (/ 1 (sqrt k))) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
  (/ (sqrt (* n (* 2 PI))) (sqrt k))
  (pow (* n (* 2 PI)) (/ (- 1 k) 2))
  (real->posit16 (/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k)))
  (+ (+ (+ (sqrt (* n (* 2 PI))) (* (* (* (log n) (* k k)) (log n)) (* 1/8 (sqrt (* n (* 2 PI)))))) (* 1/8 (* (* (log (* 2 PI)) (log (* 2 PI))) (* (sqrt (* n (* 2 PI))) (* k k))))) (+ (* (* (log (* 2 PI)) 1/4) (* (log n) (* (sqrt (* n (* 2 PI))) (* k k)))) (* -1/2 (* k (+ (* (sqrt (* n (* 2 PI))) (log n)) (* (log (* 2 PI)) (sqrt (* n (* 2 PI)))))))))
  (exp (* (* 1/2 (- 1 k)) (log (* n (* 2 PI)))))
  (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n)))))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (* +nan.0 (- (* k k))) (- +nan.0 (* k +nan.0)))
  (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) (/ +nan.0 (* (* k k) k))))
  (- (+ (- (/ +nan.0 (* k k)) (/ +nan.0 k)) +nan.0))
  (+ (- (* (* (* n PI) k) (* (sqrt 2) +nan.0))) (+ (- (* (* (sqrt 2) +nan.0) (* PI n)) (* (* (* (* n PI) k) (* (sqrt 2) +nan.0)) (log (* 2 PI)))) (* (* (sqrt 2) +nan.0) (- (* (* n PI) (* k (log n))) (* (* n PI) (* n PI))))))
  (+ (* (/ (exp (* (* 1/2 (- 1 k)) (log (* n (* 2 PI))))) k) (- +nan.0)) (* +nan.0 (- (/ (exp (* (* 1/2 (- 1 k)) (log (* n (* 2 PI))))) (* k k)) (/ (/ (exp (* (* 1/2 (- 1 k)) (log (* n (* 2 PI))))) (* k k)) k))))
  (- (- (/ (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))) (/ k +nan.0)) (* +nan.0 (- (/ (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n))))) (* k k)) (exp (* (* 1/2 (- 1 k)) (- (log (* PI -2)) (log (/ -1 n)))))))))
7.154 * * * [progress]: adding candidates to table
9.153 * * [progress]: iteration 3 / 4
9.153 * * * [progress]: picking best candidate
9.192 * * * * [pick]: Picked  #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.192 * * * [progress]: localizing error
9.220 * * * [progress]: generating rewritten candidates
9.220 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 2 1)
9.252 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1)
9.278 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1 1)
9.305 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1)
9.333 * * * [progress]: generating series expansions
9.333 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 2 1)
9.334 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
9.334 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
9.334 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
9.334 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
9.334 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
9.334 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
9.334 * [taylor]: Taking taylor expansion of 1/2 in k
9.334 * [backup-simplify]: Simplify 1/2 into 1/2
9.334 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
9.334 * [taylor]: Taking taylor expansion of 1/2 in k
9.334 * [backup-simplify]: Simplify 1/2 into 1/2
9.334 * [taylor]: Taking taylor expansion of k in k
9.334 * [backup-simplify]: Simplify 0 into 0
9.334 * [backup-simplify]: Simplify 1 into 1
9.334 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
9.334 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
9.334 * [taylor]: Taking taylor expansion of 2 in k
9.334 * [backup-simplify]: Simplify 2 into 2
9.334 * [taylor]: Taking taylor expansion of (* n PI) in k
9.335 * [taylor]: Taking taylor expansion of n in k
9.335 * [backup-simplify]: Simplify n into n
9.335 * [taylor]: Taking taylor expansion of PI in k
9.335 * [backup-simplify]: Simplify PI into PI
9.335 * [backup-simplify]: Simplify (* n PI) into (* n PI)
9.335 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
9.335 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
9.335 * [backup-simplify]: Simplify (* 1/2 0) into 0
9.336 * [backup-simplify]: Simplify (- 0) into 0
9.336 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.336 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
9.336 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
9.336 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
9.337 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
9.337 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
9.337 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
9.337 * [taylor]: Taking taylor expansion of 1/2 in n
9.337 * [backup-simplify]: Simplify 1/2 into 1/2
9.337 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
9.337 * [taylor]: Taking taylor expansion of 1/2 in n
9.337 * [backup-simplify]: Simplify 1/2 into 1/2
9.337 * [taylor]: Taking taylor expansion of k in n
9.337 * [backup-simplify]: Simplify k into k
9.337 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.337 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.337 * [taylor]: Taking taylor expansion of 2 in n
9.337 * [backup-simplify]: Simplify 2 into 2
9.337 * [taylor]: Taking taylor expansion of (* n PI) in n
9.337 * [taylor]: Taking taylor expansion of n in n
9.337 * [backup-simplify]: Simplify 0 into 0
9.337 * [backup-simplify]: Simplify 1 into 1
9.337 * [taylor]: Taking taylor expansion of PI in n
9.337 * [backup-simplify]: Simplify PI into PI
9.338 * [backup-simplify]: Simplify (* 0 PI) into 0
9.338 * [backup-simplify]: Simplify (* 2 0) into 0
9.340 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.342 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.343 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.343 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
9.343 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
9.344 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
9.345 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.346 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
9.348 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
9.348 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
9.348 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
9.348 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
9.348 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
9.348 * [taylor]: Taking taylor expansion of 1/2 in n
9.348 * [backup-simplify]: Simplify 1/2 into 1/2
9.348 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
9.348 * [taylor]: Taking taylor expansion of 1/2 in n
9.348 * [backup-simplify]: Simplify 1/2 into 1/2
9.348 * [taylor]: Taking taylor expansion of k in n
9.348 * [backup-simplify]: Simplify k into k
9.348 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.348 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.348 * [taylor]: Taking taylor expansion of 2 in n
9.348 * [backup-simplify]: Simplify 2 into 2
9.348 * [taylor]: Taking taylor expansion of (* n PI) in n
9.348 * [taylor]: Taking taylor expansion of n in n
9.348 * [backup-simplify]: Simplify 0 into 0
9.348 * [backup-simplify]: Simplify 1 into 1
9.348 * [taylor]: Taking taylor expansion of PI in n
9.348 * [backup-simplify]: Simplify PI into PI
9.349 * [backup-simplify]: Simplify (* 0 PI) into 0
9.349 * [backup-simplify]: Simplify (* 2 0) into 0
9.353 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.354 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.355 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.355 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
9.355 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
9.355 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
9.356 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.356 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
9.357 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
9.357 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
9.357 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
9.357 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
9.357 * [taylor]: Taking taylor expansion of 1/2 in k
9.357 * [backup-simplify]: Simplify 1/2 into 1/2
9.357 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
9.357 * [taylor]: Taking taylor expansion of 1/2 in k
9.357 * [backup-simplify]: Simplify 1/2 into 1/2
9.357 * [taylor]: Taking taylor expansion of k in k
9.357 * [backup-simplify]: Simplify 0 into 0
9.357 * [backup-simplify]: Simplify 1 into 1
9.357 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
9.357 * [taylor]: Taking taylor expansion of (log n) in k
9.357 * [taylor]: Taking taylor expansion of n in k
9.357 * [backup-simplify]: Simplify n into n
9.357 * [backup-simplify]: Simplify (log n) into (log n)
9.357 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.357 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.357 * [taylor]: Taking taylor expansion of 2 in k
9.358 * [backup-simplify]: Simplify 2 into 2
9.358 * [taylor]: Taking taylor expansion of PI in k
9.358 * [backup-simplify]: Simplify PI into PI
9.358 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.358 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.359 * [backup-simplify]: Simplify (* 1/2 0) into 0
9.359 * [backup-simplify]: Simplify (- 0) into 0
9.359 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.360 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.361 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
9.361 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
9.362 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
9.363 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
9.363 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
9.364 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.365 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
9.365 * [backup-simplify]: Simplify (- 0) into 0
9.365 * [backup-simplify]: Simplify (+ 0 0) into 0
9.366 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.367 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
9.368 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.368 * [taylor]: Taking taylor expansion of 0 in k
9.368 * [backup-simplify]: Simplify 0 into 0
9.368 * [backup-simplify]: Simplify 0 into 0
9.369 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
9.369 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.370 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.371 * [backup-simplify]: Simplify (+ 0 0) into 0
9.371 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
9.371 * [backup-simplify]: Simplify (- 1/2) into -1/2
9.372 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
9.372 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
9.374 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.376 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.377 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
9.378 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
9.379 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.380 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
9.380 * [backup-simplify]: Simplify (- 0) into 0
9.380 * [backup-simplify]: Simplify (+ 0 0) into 0
9.381 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.382 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
9.384 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.384 * [taylor]: Taking taylor expansion of 0 in k
9.384 * [backup-simplify]: Simplify 0 into 0
9.384 * [backup-simplify]: Simplify 0 into 0
9.384 * [backup-simplify]: Simplify 0 into 0
9.385 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
9.385 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.387 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.388 * [backup-simplify]: Simplify (+ 0 0) into 0
9.388 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
9.388 * [backup-simplify]: Simplify (- 0) into 0
9.389 * [backup-simplify]: Simplify (+ 0 0) into 0
9.390 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
9.393 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
9.398 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
9.408 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
9.408 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
9.408 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
9.408 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
9.408 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
9.408 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
9.408 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
9.408 * [taylor]: Taking taylor expansion of 1/2 in k
9.408 * [backup-simplify]: Simplify 1/2 into 1/2
9.409 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.409 * [taylor]: Taking taylor expansion of 1/2 in k
9.409 * [backup-simplify]: Simplify 1/2 into 1/2
9.409 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.409 * [taylor]: Taking taylor expansion of k in k
9.409 * [backup-simplify]: Simplify 0 into 0
9.409 * [backup-simplify]: Simplify 1 into 1
9.409 * [backup-simplify]: Simplify (/ 1 1) into 1
9.409 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
9.409 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
9.409 * [taylor]: Taking taylor expansion of 2 in k
9.409 * [backup-simplify]: Simplify 2 into 2
9.409 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.409 * [taylor]: Taking taylor expansion of PI in k
9.409 * [backup-simplify]: Simplify PI into PI
9.409 * [taylor]: Taking taylor expansion of n in k
9.409 * [backup-simplify]: Simplify n into n
9.409 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.409 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
9.409 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
9.410 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.410 * [backup-simplify]: Simplify (- 1/2) into -1/2
9.411 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
9.411 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
9.411 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
9.411 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
9.411 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
9.411 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
9.411 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
9.411 * [taylor]: Taking taylor expansion of 1/2 in n
9.411 * [backup-simplify]: Simplify 1/2 into 1/2
9.411 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.411 * [taylor]: Taking taylor expansion of 1/2 in n
9.411 * [backup-simplify]: Simplify 1/2 into 1/2
9.411 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.411 * [taylor]: Taking taylor expansion of k in n
9.411 * [backup-simplify]: Simplify k into k
9.411 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.411 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.411 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.411 * [taylor]: Taking taylor expansion of 2 in n
9.411 * [backup-simplify]: Simplify 2 into 2
9.411 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.411 * [taylor]: Taking taylor expansion of PI in n
9.411 * [backup-simplify]: Simplify PI into PI
9.411 * [taylor]: Taking taylor expansion of n in n
9.412 * [backup-simplify]: Simplify 0 into 0
9.412 * [backup-simplify]: Simplify 1 into 1
9.412 * [backup-simplify]: Simplify (/ PI 1) into PI
9.413 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.414 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.414 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.414 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
9.414 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
9.416 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.417 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
9.418 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.418 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
9.418 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
9.418 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
9.418 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
9.418 * [taylor]: Taking taylor expansion of 1/2 in n
9.418 * [backup-simplify]: Simplify 1/2 into 1/2
9.418 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.418 * [taylor]: Taking taylor expansion of 1/2 in n
9.418 * [backup-simplify]: Simplify 1/2 into 1/2
9.418 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.418 * [taylor]: Taking taylor expansion of k in n
9.418 * [backup-simplify]: Simplify k into k
9.419 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.419 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.419 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.419 * [taylor]: Taking taylor expansion of 2 in n
9.419 * [backup-simplify]: Simplify 2 into 2
9.419 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.419 * [taylor]: Taking taylor expansion of PI in n
9.419 * [backup-simplify]: Simplify PI into PI
9.419 * [taylor]: Taking taylor expansion of n in n
9.419 * [backup-simplify]: Simplify 0 into 0
9.419 * [backup-simplify]: Simplify 1 into 1
9.419 * [backup-simplify]: Simplify (/ PI 1) into PI
9.420 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.421 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.421 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.421 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
9.421 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
9.423 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.424 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
9.425 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.425 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
9.425 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
9.425 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
9.425 * [taylor]: Taking taylor expansion of 1/2 in k
9.425 * [backup-simplify]: Simplify 1/2 into 1/2
9.425 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.425 * [taylor]: Taking taylor expansion of 1/2 in k
9.425 * [backup-simplify]: Simplify 1/2 into 1/2
9.425 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.425 * [taylor]: Taking taylor expansion of k in k
9.425 * [backup-simplify]: Simplify 0 into 0
9.425 * [backup-simplify]: Simplify 1 into 1
9.426 * [backup-simplify]: Simplify (/ 1 1) into 1
9.426 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
9.426 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.426 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.426 * [taylor]: Taking taylor expansion of 2 in k
9.426 * [backup-simplify]: Simplify 2 into 2
9.426 * [taylor]: Taking taylor expansion of PI in k
9.426 * [backup-simplify]: Simplify PI into PI
9.427 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.428 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.428 * [taylor]: Taking taylor expansion of (log n) in k
9.428 * [taylor]: Taking taylor expansion of n in k
9.428 * [backup-simplify]: Simplify n into n
9.428 * [backup-simplify]: Simplify (log n) into (log n)
9.428 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.429 * [backup-simplify]: Simplify (- 1/2) into -1/2
9.429 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
9.429 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.430 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
9.431 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
9.433 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.435 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.436 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.437 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.439 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.439 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.439 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
9.440 * [backup-simplify]: Simplify (- 0) into 0
9.440 * [backup-simplify]: Simplify (+ 0 0) into 0
9.441 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.443 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
9.444 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
9.444 * [taylor]: Taking taylor expansion of 0 in k
9.444 * [backup-simplify]: Simplify 0 into 0
9.445 * [backup-simplify]: Simplify 0 into 0
9.445 * [backup-simplify]: Simplify 0 into 0
9.446 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.447 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.450 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.450 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.451 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
9.452 * [backup-simplify]: Simplify (- 0) into 0
9.452 * [backup-simplify]: Simplify (+ 0 0) into 0
9.454 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.455 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
9.457 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.457 * [taylor]: Taking taylor expansion of 0 in k
9.457 * [backup-simplify]: Simplify 0 into 0
9.458 * [backup-simplify]: Simplify 0 into 0
9.458 * [backup-simplify]: Simplify 0 into 0
9.458 * [backup-simplify]: Simplify 0 into 0
9.459 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.460 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.466 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
9.466 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.470 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
9.471 * [backup-simplify]: Simplify (- 0) into 0
9.471 * [backup-simplify]: Simplify (+ 0 0) into 0
9.473 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.474 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
9.476 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.476 * [taylor]: Taking taylor expansion of 0 in k
9.476 * [backup-simplify]: Simplify 0 into 0
9.476 * [backup-simplify]: Simplify 0 into 0
9.477 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
9.477 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
9.477 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
9.477 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
9.477 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
9.477 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
9.478 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
9.478 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.478 * [taylor]: Taking taylor expansion of 1/2 in k
9.478 * [backup-simplify]: Simplify 1/2 into 1/2
9.478 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.478 * [taylor]: Taking taylor expansion of k in k
9.478 * [backup-simplify]: Simplify 0 into 0
9.478 * [backup-simplify]: Simplify 1 into 1
9.478 * [backup-simplify]: Simplify (/ 1 1) into 1
9.478 * [taylor]: Taking taylor expansion of 1/2 in k
9.478 * [backup-simplify]: Simplify 1/2 into 1/2
9.478 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
9.478 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
9.478 * [taylor]: Taking taylor expansion of -2 in k
9.478 * [backup-simplify]: Simplify -2 into -2
9.478 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.478 * [taylor]: Taking taylor expansion of PI in k
9.478 * [backup-simplify]: Simplify PI into PI
9.478 * [taylor]: Taking taylor expansion of n in k
9.478 * [backup-simplify]: Simplify n into n
9.478 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.478 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
9.478 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
9.478 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.479 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.479 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
9.479 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
9.479 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
9.479 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
9.479 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
9.479 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
9.479 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.479 * [taylor]: Taking taylor expansion of 1/2 in n
9.479 * [backup-simplify]: Simplify 1/2 into 1/2
9.479 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.479 * [taylor]: Taking taylor expansion of k in n
9.479 * [backup-simplify]: Simplify k into k
9.479 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.479 * [taylor]: Taking taylor expansion of 1/2 in n
9.479 * [backup-simplify]: Simplify 1/2 into 1/2
9.479 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.479 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.479 * [taylor]: Taking taylor expansion of -2 in n
9.479 * [backup-simplify]: Simplify -2 into -2
9.479 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.479 * [taylor]: Taking taylor expansion of PI in n
9.479 * [backup-simplify]: Simplify PI into PI
9.479 * [taylor]: Taking taylor expansion of n in n
9.479 * [backup-simplify]: Simplify 0 into 0
9.479 * [backup-simplify]: Simplify 1 into 1
9.480 * [backup-simplify]: Simplify (/ PI 1) into PI
9.480 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.481 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.481 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.481 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
9.482 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.482 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
9.483 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.483 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
9.483 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
9.483 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
9.483 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
9.483 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.483 * [taylor]: Taking taylor expansion of 1/2 in n
9.483 * [backup-simplify]: Simplify 1/2 into 1/2
9.483 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.483 * [taylor]: Taking taylor expansion of k in n
9.483 * [backup-simplify]: Simplify k into k
9.483 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.483 * [taylor]: Taking taylor expansion of 1/2 in n
9.483 * [backup-simplify]: Simplify 1/2 into 1/2
9.483 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.483 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.483 * [taylor]: Taking taylor expansion of -2 in n
9.483 * [backup-simplify]: Simplify -2 into -2
9.484 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.484 * [taylor]: Taking taylor expansion of PI in n
9.484 * [backup-simplify]: Simplify PI into PI
9.484 * [taylor]: Taking taylor expansion of n in n
9.484 * [backup-simplify]: Simplify 0 into 0
9.484 * [backup-simplify]: Simplify 1 into 1
9.484 * [backup-simplify]: Simplify (/ PI 1) into PI
9.484 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.485 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.485 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.485 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
9.486 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.486 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
9.487 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.487 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
9.487 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
9.487 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
9.487 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.487 * [taylor]: Taking taylor expansion of 1/2 in k
9.487 * [backup-simplify]: Simplify 1/2 into 1/2
9.487 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.487 * [taylor]: Taking taylor expansion of k in k
9.487 * [backup-simplify]: Simplify 0 into 0
9.487 * [backup-simplify]: Simplify 1 into 1
9.488 * [backup-simplify]: Simplify (/ 1 1) into 1
9.488 * [taylor]: Taking taylor expansion of 1/2 in k
9.488 * [backup-simplify]: Simplify 1/2 into 1/2
9.488 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
9.488 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
9.488 * [taylor]: Taking taylor expansion of (* -2 PI) in k
9.488 * [taylor]: Taking taylor expansion of -2 in k
9.488 * [backup-simplify]: Simplify -2 into -2
9.488 * [taylor]: Taking taylor expansion of PI in k
9.488 * [backup-simplify]: Simplify PI into PI
9.488 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.489 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.489 * [taylor]: Taking taylor expansion of (log n) in k
9.489 * [taylor]: Taking taylor expansion of n in k
9.489 * [backup-simplify]: Simplify n into n
9.489 * [backup-simplify]: Simplify (log n) into (log n)
9.489 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.489 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.489 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.490 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
9.491 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
9.492 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.493 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.493 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.494 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
9.495 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
9.495 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.495 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
9.495 * [backup-simplify]: Simplify (+ 0 0) into 0
9.496 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.497 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
9.498 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
9.498 * [taylor]: Taking taylor expansion of 0 in k
9.498 * [backup-simplify]: Simplify 0 into 0
9.498 * [backup-simplify]: Simplify 0 into 0
9.498 * [backup-simplify]: Simplify 0 into 0
9.499 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.499 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
9.501 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
9.502 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.502 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
9.502 * [backup-simplify]: Simplify (+ 0 0) into 0
9.503 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.504 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
9.506 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.506 * [taylor]: Taking taylor expansion of 0 in k
9.506 * [backup-simplify]: Simplify 0 into 0
9.506 * [backup-simplify]: Simplify 0 into 0
9.506 * [backup-simplify]: Simplify 0 into 0
9.506 * [backup-simplify]: Simplify 0 into 0
9.506 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.507 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.514 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
9.514 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.515 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
9.516 * [backup-simplify]: Simplify (+ 0 0) into 0
9.518 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.520 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
9.523 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.523 * [taylor]: Taking taylor expansion of 0 in k
9.523 * [backup-simplify]: Simplify 0 into 0
9.523 * [backup-simplify]: Simplify 0 into 0
9.524 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
9.524 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1)
9.525 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
9.525 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
9.525 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
9.525 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
9.525 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
9.525 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
9.525 * [taylor]: Taking taylor expansion of 1/2 in k
9.525 * [backup-simplify]: Simplify 1/2 into 1/2
9.525 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
9.525 * [taylor]: Taking taylor expansion of 1/2 in k
9.525 * [backup-simplify]: Simplify 1/2 into 1/2
9.525 * [taylor]: Taking taylor expansion of k in k
9.525 * [backup-simplify]: Simplify 0 into 0
9.525 * [backup-simplify]: Simplify 1 into 1
9.525 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
9.525 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
9.525 * [taylor]: Taking taylor expansion of 2 in k
9.525 * [backup-simplify]: Simplify 2 into 2
9.525 * [taylor]: Taking taylor expansion of (* n PI) in k
9.525 * [taylor]: Taking taylor expansion of n in k
9.525 * [backup-simplify]: Simplify n into n
9.525 * [taylor]: Taking taylor expansion of PI in k
9.526 * [backup-simplify]: Simplify PI into PI
9.526 * [backup-simplify]: Simplify (* n PI) into (* n PI)
9.526 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
9.526 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
9.526 * [backup-simplify]: Simplify (* 1/2 0) into 0
9.527 * [backup-simplify]: Simplify (- 0) into 0
9.527 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.527 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
9.527 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
9.527 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
9.527 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
9.527 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
9.527 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
9.527 * [taylor]: Taking taylor expansion of 1/2 in n
9.528 * [backup-simplify]: Simplify 1/2 into 1/2
9.528 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
9.528 * [taylor]: Taking taylor expansion of 1/2 in n
9.528 * [backup-simplify]: Simplify 1/2 into 1/2
9.528 * [taylor]: Taking taylor expansion of k in n
9.528 * [backup-simplify]: Simplify k into k
9.528 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.528 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.528 * [taylor]: Taking taylor expansion of 2 in n
9.528 * [backup-simplify]: Simplify 2 into 2
9.528 * [taylor]: Taking taylor expansion of (* n PI) in n
9.528 * [taylor]: Taking taylor expansion of n in n
9.528 * [backup-simplify]: Simplify 0 into 0
9.528 * [backup-simplify]: Simplify 1 into 1
9.528 * [taylor]: Taking taylor expansion of PI in n
9.528 * [backup-simplify]: Simplify PI into PI
9.528 * [backup-simplify]: Simplify (* 0 PI) into 0
9.529 * [backup-simplify]: Simplify (* 2 0) into 0
9.530 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.532 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.533 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.533 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
9.533 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
9.534 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
9.535 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.536 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
9.537 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
9.537 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
9.537 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
9.538 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
9.538 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
9.538 * [taylor]: Taking taylor expansion of 1/2 in n
9.538 * [backup-simplify]: Simplify 1/2 into 1/2
9.538 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
9.538 * [taylor]: Taking taylor expansion of 1/2 in n
9.538 * [backup-simplify]: Simplify 1/2 into 1/2
9.538 * [taylor]: Taking taylor expansion of k in n
9.538 * [backup-simplify]: Simplify k into k
9.538 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
9.538 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.538 * [taylor]: Taking taylor expansion of 2 in n
9.538 * [backup-simplify]: Simplify 2 into 2
9.538 * [taylor]: Taking taylor expansion of (* n PI) in n
9.538 * [taylor]: Taking taylor expansion of n in n
9.538 * [backup-simplify]: Simplify 0 into 0
9.538 * [backup-simplify]: Simplify 1 into 1
9.538 * [taylor]: Taking taylor expansion of PI in n
9.538 * [backup-simplify]: Simplify PI into PI
9.539 * [backup-simplify]: Simplify (* 0 PI) into 0
9.539 * [backup-simplify]: Simplify (* 2 0) into 0
9.541 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.542 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.543 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.543 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
9.543 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
9.543 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
9.544 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.545 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
9.546 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
9.546 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
9.546 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
9.546 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
9.546 * [taylor]: Taking taylor expansion of 1/2 in k
9.546 * [backup-simplify]: Simplify 1/2 into 1/2
9.546 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
9.546 * [taylor]: Taking taylor expansion of 1/2 in k
9.546 * [backup-simplify]: Simplify 1/2 into 1/2
9.546 * [taylor]: Taking taylor expansion of k in k
9.546 * [backup-simplify]: Simplify 0 into 0
9.546 * [backup-simplify]: Simplify 1 into 1
9.546 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
9.546 * [taylor]: Taking taylor expansion of (log n) in k
9.546 * [taylor]: Taking taylor expansion of n in k
9.546 * [backup-simplify]: Simplify n into n
9.546 * [backup-simplify]: Simplify (log n) into (log n)
9.546 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.546 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.546 * [taylor]: Taking taylor expansion of 2 in k
9.546 * [backup-simplify]: Simplify 2 into 2
9.546 * [taylor]: Taking taylor expansion of PI in k
9.546 * [backup-simplify]: Simplify PI into PI
9.546 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.547 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.547 * [backup-simplify]: Simplify (* 1/2 0) into 0
9.547 * [backup-simplify]: Simplify (- 0) into 0
9.548 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.548 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.549 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
9.550 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
9.550 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
9.551 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
9.552 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
9.553 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.553 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
9.553 * [backup-simplify]: Simplify (- 0) into 0
9.553 * [backup-simplify]: Simplify (+ 0 0) into 0
9.554 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.555 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
9.556 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
9.556 * [taylor]: Taking taylor expansion of 0 in k
9.556 * [backup-simplify]: Simplify 0 into 0
9.556 * [backup-simplify]: Simplify 0 into 0
9.557 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
9.557 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.558 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.558 * [backup-simplify]: Simplify (+ 0 0) into 0
9.559 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
9.559 * [backup-simplify]: Simplify (- 1/2) into -1/2
9.559 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
9.560 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
9.562 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.564 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
9.565 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
9.566 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
9.568 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.568 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
9.569 * [backup-simplify]: Simplify (- 0) into 0
9.569 * [backup-simplify]: Simplify (+ 0 0) into 0
9.570 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
9.571 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
9.574 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.574 * [taylor]: Taking taylor expansion of 0 in k
9.574 * [backup-simplify]: Simplify 0 into 0
9.575 * [backup-simplify]: Simplify 0 into 0
9.575 * [backup-simplify]: Simplify 0 into 0
9.576 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
9.576 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.579 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.579 * [backup-simplify]: Simplify (+ 0 0) into 0
9.580 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
9.580 * [backup-simplify]: Simplify (- 0) into 0
9.580 * [backup-simplify]: Simplify (+ 0 0) into 0
9.581 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
9.584 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
9.588 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
9.594 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
9.594 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
9.594 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
9.594 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
9.594 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
9.594 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
9.594 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
9.594 * [taylor]: Taking taylor expansion of 1/2 in k
9.594 * [backup-simplify]: Simplify 1/2 into 1/2
9.594 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.594 * [taylor]: Taking taylor expansion of 1/2 in k
9.594 * [backup-simplify]: Simplify 1/2 into 1/2
9.594 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.594 * [taylor]: Taking taylor expansion of k in k
9.594 * [backup-simplify]: Simplify 0 into 0
9.594 * [backup-simplify]: Simplify 1 into 1
9.595 * [backup-simplify]: Simplify (/ 1 1) into 1
9.595 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
9.595 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
9.595 * [taylor]: Taking taylor expansion of 2 in k
9.595 * [backup-simplify]: Simplify 2 into 2
9.595 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.595 * [taylor]: Taking taylor expansion of PI in k
9.595 * [backup-simplify]: Simplify PI into PI
9.595 * [taylor]: Taking taylor expansion of n in k
9.595 * [backup-simplify]: Simplify n into n
9.595 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.595 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
9.595 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
9.595 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.596 * [backup-simplify]: Simplify (- 1/2) into -1/2
9.596 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
9.596 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
9.596 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
9.596 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
9.597 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
9.597 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
9.597 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
9.597 * [taylor]: Taking taylor expansion of 1/2 in n
9.597 * [backup-simplify]: Simplify 1/2 into 1/2
9.597 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.597 * [taylor]: Taking taylor expansion of 1/2 in n
9.597 * [backup-simplify]: Simplify 1/2 into 1/2
9.597 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.597 * [taylor]: Taking taylor expansion of k in n
9.597 * [backup-simplify]: Simplify k into k
9.597 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.597 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.597 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.597 * [taylor]: Taking taylor expansion of 2 in n
9.597 * [backup-simplify]: Simplify 2 into 2
9.597 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.597 * [taylor]: Taking taylor expansion of PI in n
9.597 * [backup-simplify]: Simplify PI into PI
9.597 * [taylor]: Taking taylor expansion of n in n
9.597 * [backup-simplify]: Simplify 0 into 0
9.597 * [backup-simplify]: Simplify 1 into 1
9.598 * [backup-simplify]: Simplify (/ PI 1) into PI
9.598 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.599 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.599 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.599 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
9.599 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
9.601 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.602 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
9.603 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.603 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
9.603 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
9.603 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
9.603 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
9.603 * [taylor]: Taking taylor expansion of 1/2 in n
9.603 * [backup-simplify]: Simplify 1/2 into 1/2
9.603 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.603 * [taylor]: Taking taylor expansion of 1/2 in n
9.603 * [backup-simplify]: Simplify 1/2 into 1/2
9.603 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.603 * [taylor]: Taking taylor expansion of k in n
9.603 * [backup-simplify]: Simplify k into k
9.603 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.603 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
9.603 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.603 * [taylor]: Taking taylor expansion of 2 in n
9.604 * [backup-simplify]: Simplify 2 into 2
9.604 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.604 * [taylor]: Taking taylor expansion of PI in n
9.604 * [backup-simplify]: Simplify PI into PI
9.604 * [taylor]: Taking taylor expansion of n in n
9.604 * [backup-simplify]: Simplify 0 into 0
9.604 * [backup-simplify]: Simplify 1 into 1
9.604 * [backup-simplify]: Simplify (/ PI 1) into PI
9.605 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.606 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.606 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.606 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
9.606 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
9.607 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.608 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
9.610 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.610 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
9.610 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
9.610 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
9.610 * [taylor]: Taking taylor expansion of 1/2 in k
9.610 * [backup-simplify]: Simplify 1/2 into 1/2
9.610 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.610 * [taylor]: Taking taylor expansion of 1/2 in k
9.610 * [backup-simplify]: Simplify 1/2 into 1/2
9.610 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.610 * [taylor]: Taking taylor expansion of k in k
9.610 * [backup-simplify]: Simplify 0 into 0
9.610 * [backup-simplify]: Simplify 1 into 1
9.610 * [backup-simplify]: Simplify (/ 1 1) into 1
9.610 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
9.610 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
9.610 * [taylor]: Taking taylor expansion of (* 2 PI) in k
9.610 * [taylor]: Taking taylor expansion of 2 in k
9.610 * [backup-simplify]: Simplify 2 into 2
9.610 * [taylor]: Taking taylor expansion of PI in k
9.610 * [backup-simplify]: Simplify PI into PI
9.611 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.612 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
9.612 * [taylor]: Taking taylor expansion of (log n) in k
9.612 * [taylor]: Taking taylor expansion of n in k
9.612 * [backup-simplify]: Simplify n into n
9.612 * [backup-simplify]: Simplify (log n) into (log n)
9.612 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.613 * [backup-simplify]: Simplify (- 1/2) into -1/2
9.613 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
9.613 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.614 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
9.615 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
9.617 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.618 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
9.619 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.620 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.622 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
9.622 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.622 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
9.623 * [backup-simplify]: Simplify (- 0) into 0
9.623 * [backup-simplify]: Simplify (+ 0 0) into 0
9.625 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.626 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
9.628 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
9.628 * [taylor]: Taking taylor expansion of 0 in k
9.628 * [backup-simplify]: Simplify 0 into 0
9.628 * [backup-simplify]: Simplify 0 into 0
9.628 * [backup-simplify]: Simplify 0 into 0
9.629 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.630 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.634 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
9.634 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.635 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
9.635 * [backup-simplify]: Simplify (- 0) into 0
9.636 * [backup-simplify]: Simplify (+ 0 0) into 0
9.637 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.639 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
9.641 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.641 * [taylor]: Taking taylor expansion of 0 in k
9.641 * [backup-simplify]: Simplify 0 into 0
9.641 * [backup-simplify]: Simplify 0 into 0
9.641 * [backup-simplify]: Simplify 0 into 0
9.641 * [backup-simplify]: Simplify 0 into 0
9.642 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.644 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.649 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
9.649 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.650 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
9.651 * [backup-simplify]: Simplify (- 0) into 0
9.651 * [backup-simplify]: Simplify (+ 0 0) into 0
9.653 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
9.654 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
9.657 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.657 * [taylor]: Taking taylor expansion of 0 in k
9.657 * [backup-simplify]: Simplify 0 into 0
9.657 * [backup-simplify]: Simplify 0 into 0
9.659 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
9.659 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
9.659 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
9.659 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
9.659 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
9.659 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
9.659 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
9.659 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.659 * [taylor]: Taking taylor expansion of 1/2 in k
9.659 * [backup-simplify]: Simplify 1/2 into 1/2
9.660 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.660 * [taylor]: Taking taylor expansion of k in k
9.660 * [backup-simplify]: Simplify 0 into 0
9.660 * [backup-simplify]: Simplify 1 into 1
9.660 * [backup-simplify]: Simplify (/ 1 1) into 1
9.660 * [taylor]: Taking taylor expansion of 1/2 in k
9.660 * [backup-simplify]: Simplify 1/2 into 1/2
9.660 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
9.660 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
9.660 * [taylor]: Taking taylor expansion of -2 in k
9.660 * [backup-simplify]: Simplify -2 into -2
9.660 * [taylor]: Taking taylor expansion of (/ PI n) in k
9.660 * [taylor]: Taking taylor expansion of PI in k
9.660 * [backup-simplify]: Simplify PI into PI
9.660 * [taylor]: Taking taylor expansion of n in k
9.660 * [backup-simplify]: Simplify n into n
9.660 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
9.660 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
9.660 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
9.661 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.661 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.661 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
9.662 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
9.662 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
9.662 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
9.662 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
9.662 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
9.662 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.662 * [taylor]: Taking taylor expansion of 1/2 in n
9.662 * [backup-simplify]: Simplify 1/2 into 1/2
9.662 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.662 * [taylor]: Taking taylor expansion of k in n
9.662 * [backup-simplify]: Simplify k into k
9.662 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.662 * [taylor]: Taking taylor expansion of 1/2 in n
9.662 * [backup-simplify]: Simplify 1/2 into 1/2
9.662 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.662 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.662 * [taylor]: Taking taylor expansion of -2 in n
9.662 * [backup-simplify]: Simplify -2 into -2
9.662 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.662 * [taylor]: Taking taylor expansion of PI in n
9.662 * [backup-simplify]: Simplify PI into PI
9.662 * [taylor]: Taking taylor expansion of n in n
9.662 * [backup-simplify]: Simplify 0 into 0
9.662 * [backup-simplify]: Simplify 1 into 1
9.663 * [backup-simplify]: Simplify (/ PI 1) into PI
9.663 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.664 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.664 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.664 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
9.666 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.667 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
9.668 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.668 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
9.668 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
9.668 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
9.668 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
9.668 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
9.668 * [taylor]: Taking taylor expansion of 1/2 in n
9.668 * [backup-simplify]: Simplify 1/2 into 1/2
9.668 * [taylor]: Taking taylor expansion of (/ 1 k) in n
9.668 * [taylor]: Taking taylor expansion of k in n
9.668 * [backup-simplify]: Simplify k into k
9.668 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
9.668 * [taylor]: Taking taylor expansion of 1/2 in n
9.668 * [backup-simplify]: Simplify 1/2 into 1/2
9.668 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
9.669 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.669 * [taylor]: Taking taylor expansion of -2 in n
9.669 * [backup-simplify]: Simplify -2 into -2
9.669 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.669 * [taylor]: Taking taylor expansion of PI in n
9.669 * [backup-simplify]: Simplify PI into PI
9.669 * [taylor]: Taking taylor expansion of n in n
9.669 * [backup-simplify]: Simplify 0 into 0
9.669 * [backup-simplify]: Simplify 1 into 1
9.669 * [backup-simplify]: Simplify (/ PI 1) into PI
9.670 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.671 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.671 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
9.671 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
9.672 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.673 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
9.674 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.675 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
9.675 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
9.675 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
9.675 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
9.675 * [taylor]: Taking taylor expansion of 1/2 in k
9.675 * [backup-simplify]: Simplify 1/2 into 1/2
9.675 * [taylor]: Taking taylor expansion of (/ 1 k) in k
9.675 * [taylor]: Taking taylor expansion of k in k
9.675 * [backup-simplify]: Simplify 0 into 0
9.675 * [backup-simplify]: Simplify 1 into 1
9.675 * [backup-simplify]: Simplify (/ 1 1) into 1
9.675 * [taylor]: Taking taylor expansion of 1/2 in k
9.675 * [backup-simplify]: Simplify 1/2 into 1/2
9.675 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
9.675 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
9.675 * [taylor]: Taking taylor expansion of (* -2 PI) in k
9.675 * [taylor]: Taking taylor expansion of -2 in k
9.675 * [backup-simplify]: Simplify -2 into -2
9.675 * [taylor]: Taking taylor expansion of PI in k
9.676 * [backup-simplify]: Simplify PI into PI
9.676 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.678 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
9.678 * [taylor]: Taking taylor expansion of (log n) in k
9.678 * [taylor]: Taking taylor expansion of n in k
9.678 * [backup-simplify]: Simplify n into n
9.678 * [backup-simplify]: Simplify (log n) into (log n)
9.678 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
9.679 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
9.679 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
9.680 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
9.681 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
9.682 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.683 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
9.684 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.685 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
9.687 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
9.687 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
9.687 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
9.688 * [backup-simplify]: Simplify (+ 0 0) into 0
9.689 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.690 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
9.692 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
9.692 * [taylor]: Taking taylor expansion of 0 in k
9.692 * [backup-simplify]: Simplify 0 into 0
9.692 * [backup-simplify]: Simplify 0 into 0
9.692 * [backup-simplify]: Simplify 0 into 0
9.693 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.695 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
9.698 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
9.698 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.699 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
9.699 * [backup-simplify]: Simplify (+ 0 0) into 0
9.701 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.702 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
9.708 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
9.708 * [taylor]: Taking taylor expansion of 0 in k
9.708 * [backup-simplify]: Simplify 0 into 0
9.708 * [backup-simplify]: Simplify 0 into 0
9.708 * [backup-simplify]: Simplify 0 into 0
9.708 * [backup-simplify]: Simplify 0 into 0
9.709 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.710 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.716 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
9.716 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
9.717 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
9.717 * [backup-simplify]: Simplify (+ 0 0) into 0
9.718 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
9.719 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
9.721 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
9.721 * [taylor]: Taking taylor expansion of 0 in k
9.721 * [backup-simplify]: Simplify 0 into 0
9.721 * [backup-simplify]: Simplify 0 into 0
9.722 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
9.722 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1 1)
9.722 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
9.722 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
9.722 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.722 * [taylor]: Taking taylor expansion of 2 in n
9.722 * [backup-simplify]: Simplify 2 into 2
9.722 * [taylor]: Taking taylor expansion of (* n PI) in n
9.722 * [taylor]: Taking taylor expansion of n in n
9.722 * [backup-simplify]: Simplify 0 into 0
9.722 * [backup-simplify]: Simplify 1 into 1
9.722 * [taylor]: Taking taylor expansion of PI in n
9.722 * [backup-simplify]: Simplify PI into PI
9.722 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.723 * [taylor]: Taking taylor expansion of 2 in n
9.723 * [backup-simplify]: Simplify 2 into 2
9.723 * [taylor]: Taking taylor expansion of (* n PI) in n
9.723 * [taylor]: Taking taylor expansion of n in n
9.723 * [backup-simplify]: Simplify 0 into 0
9.723 * [backup-simplify]: Simplify 1 into 1
9.723 * [taylor]: Taking taylor expansion of PI in n
9.723 * [backup-simplify]: Simplify PI into PI
9.723 * [backup-simplify]: Simplify (* 0 PI) into 0
9.723 * [backup-simplify]: Simplify (* 2 0) into 0
9.723 * [backup-simplify]: Simplify 0 into 0
9.724 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.725 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.726 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.726 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
9.727 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
9.727 * [backup-simplify]: Simplify 0 into 0
9.728 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
9.729 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
9.729 * [backup-simplify]: Simplify 0 into 0
9.729 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.730 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
9.730 * [backup-simplify]: Simplify 0 into 0
9.731 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
9.732 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
9.732 * [backup-simplify]: Simplify 0 into 0
9.733 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
9.734 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
9.734 * [backup-simplify]: Simplify 0 into 0
9.735 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
9.736 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
9.737 * [backup-simplify]: Simplify 0 into 0
9.737 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
9.738 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
9.738 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
9.738 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.738 * [taylor]: Taking taylor expansion of 2 in n
9.738 * [backup-simplify]: Simplify 2 into 2
9.738 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.738 * [taylor]: Taking taylor expansion of PI in n
9.738 * [backup-simplify]: Simplify PI into PI
9.738 * [taylor]: Taking taylor expansion of n in n
9.738 * [backup-simplify]: Simplify 0 into 0
9.738 * [backup-simplify]: Simplify 1 into 1
9.738 * [backup-simplify]: Simplify (/ PI 1) into PI
9.738 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.738 * [taylor]: Taking taylor expansion of 2 in n
9.738 * [backup-simplify]: Simplify 2 into 2
9.738 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.738 * [taylor]: Taking taylor expansion of PI in n
9.738 * [backup-simplify]: Simplify PI into PI
9.738 * [taylor]: Taking taylor expansion of n in n
9.738 * [backup-simplify]: Simplify 0 into 0
9.738 * [backup-simplify]: Simplify 1 into 1
9.739 * [backup-simplify]: Simplify (/ PI 1) into PI
9.739 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.739 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.740 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.740 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.740 * [backup-simplify]: Simplify 0 into 0
9.741 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.742 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.742 * [backup-simplify]: Simplify 0 into 0
9.742 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.743 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.743 * [backup-simplify]: Simplify 0 into 0
9.744 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.744 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.744 * [backup-simplify]: Simplify 0 into 0
9.745 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.746 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
9.746 * [backup-simplify]: Simplify 0 into 0
9.747 * [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
9.748 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
9.748 * [backup-simplify]: Simplify 0 into 0
9.748 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
9.748 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
9.748 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
9.748 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.748 * [taylor]: Taking taylor expansion of -2 in n
9.748 * [backup-simplify]: Simplify -2 into -2
9.749 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.749 * [taylor]: Taking taylor expansion of PI in n
9.749 * [backup-simplify]: Simplify PI into PI
9.749 * [taylor]: Taking taylor expansion of n in n
9.749 * [backup-simplify]: Simplify 0 into 0
9.749 * [backup-simplify]: Simplify 1 into 1
9.749 * [backup-simplify]: Simplify (/ PI 1) into PI
9.749 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.749 * [taylor]: Taking taylor expansion of -2 in n
9.749 * [backup-simplify]: Simplify -2 into -2
9.749 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.749 * [taylor]: Taking taylor expansion of PI in n
9.749 * [backup-simplify]: Simplify PI into PI
9.749 * [taylor]: Taking taylor expansion of n in n
9.749 * [backup-simplify]: Simplify 0 into 0
9.749 * [backup-simplify]: Simplify 1 into 1
9.749 * [backup-simplify]: Simplify (/ PI 1) into PI
9.750 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.750 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.751 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.751 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
9.751 * [backup-simplify]: Simplify 0 into 0
9.752 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.753 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
9.753 * [backup-simplify]: Simplify 0 into 0
9.754 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.756 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.756 * [backup-simplify]: Simplify 0 into 0
9.757 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.758 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.758 * [backup-simplify]: Simplify 0 into 0
9.759 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.760 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
9.761 * [backup-simplify]: Simplify 0 into 0
9.762 * [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
9.763 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
9.763 * [backup-simplify]: Simplify 0 into 0
9.764 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
9.764 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1)
9.764 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
9.765 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
9.765 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.765 * [taylor]: Taking taylor expansion of 2 in n
9.765 * [backup-simplify]: Simplify 2 into 2
9.765 * [taylor]: Taking taylor expansion of (* n PI) in n
9.765 * [taylor]: Taking taylor expansion of n in n
9.765 * [backup-simplify]: Simplify 0 into 0
9.765 * [backup-simplify]: Simplify 1 into 1
9.765 * [taylor]: Taking taylor expansion of PI in n
9.765 * [backup-simplify]: Simplify PI into PI
9.765 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
9.765 * [taylor]: Taking taylor expansion of 2 in n
9.765 * [backup-simplify]: Simplify 2 into 2
9.765 * [taylor]: Taking taylor expansion of (* n PI) in n
9.765 * [taylor]: Taking taylor expansion of n in n
9.765 * [backup-simplify]: Simplify 0 into 0
9.765 * [backup-simplify]: Simplify 1 into 1
9.765 * [taylor]: Taking taylor expansion of PI in n
9.765 * [backup-simplify]: Simplify PI into PI
9.765 * [backup-simplify]: Simplify (* 0 PI) into 0
9.766 * [backup-simplify]: Simplify (* 2 0) into 0
9.766 * [backup-simplify]: Simplify 0 into 0
9.767 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
9.769 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
9.769 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.770 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
9.771 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
9.771 * [backup-simplify]: Simplify 0 into 0
9.773 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
9.774 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
9.774 * [backup-simplify]: Simplify 0 into 0
9.776 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.777 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
9.777 * [backup-simplify]: Simplify 0 into 0
9.780 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
9.781 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
9.781 * [backup-simplify]: Simplify 0 into 0
9.783 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
9.785 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
9.785 * [backup-simplify]: Simplify 0 into 0
9.787 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
9.790 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
9.790 * [backup-simplify]: Simplify 0 into 0
9.790 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
9.791 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
9.791 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
9.791 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.791 * [taylor]: Taking taylor expansion of 2 in n
9.791 * [backup-simplify]: Simplify 2 into 2
9.791 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.791 * [taylor]: Taking taylor expansion of PI in n
9.791 * [backup-simplify]: Simplify PI into PI
9.791 * [taylor]: Taking taylor expansion of n in n
9.791 * [backup-simplify]: Simplify 0 into 0
9.791 * [backup-simplify]: Simplify 1 into 1
9.792 * [backup-simplify]: Simplify (/ PI 1) into PI
9.792 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
9.792 * [taylor]: Taking taylor expansion of 2 in n
9.792 * [backup-simplify]: Simplify 2 into 2
9.792 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.792 * [taylor]: Taking taylor expansion of PI in n
9.792 * [backup-simplify]: Simplify PI into PI
9.792 * [taylor]: Taking taylor expansion of n in n
9.792 * [backup-simplify]: Simplify 0 into 0
9.792 * [backup-simplify]: Simplify 1 into 1
9.793 * [backup-simplify]: Simplify (/ PI 1) into PI
9.793 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.794 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
9.795 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.796 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
9.796 * [backup-simplify]: Simplify 0 into 0
9.797 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.798 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
9.798 * [backup-simplify]: Simplify 0 into 0
9.800 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.801 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.801 * [backup-simplify]: Simplify 0 into 0
9.802 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.804 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.804 * [backup-simplify]: Simplify 0 into 0
9.805 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.807 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
9.807 * [backup-simplify]: Simplify 0 into 0
9.808 * [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
9.810 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
9.810 * [backup-simplify]: Simplify 0 into 0
9.811 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
9.812 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
9.812 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
9.812 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.812 * [taylor]: Taking taylor expansion of -2 in n
9.812 * [backup-simplify]: Simplify -2 into -2
9.812 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.812 * [taylor]: Taking taylor expansion of PI in n
9.812 * [backup-simplify]: Simplify PI into PI
9.812 * [taylor]: Taking taylor expansion of n in n
9.812 * [backup-simplify]: Simplify 0 into 0
9.812 * [backup-simplify]: Simplify 1 into 1
9.813 * [backup-simplify]: Simplify (/ PI 1) into PI
9.813 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
9.813 * [taylor]: Taking taylor expansion of -2 in n
9.813 * [backup-simplify]: Simplify -2 into -2
9.813 * [taylor]: Taking taylor expansion of (/ PI n) in n
9.813 * [taylor]: Taking taylor expansion of PI in n
9.813 * [backup-simplify]: Simplify PI into PI
9.813 * [taylor]: Taking taylor expansion of n in n
9.813 * [backup-simplify]: Simplify 0 into 0
9.813 * [backup-simplify]: Simplify 1 into 1
9.813 * [backup-simplify]: Simplify (/ PI 1) into PI
9.814 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.814 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
9.816 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
9.816 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
9.816 * [backup-simplify]: Simplify 0 into 0
9.818 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.819 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
9.819 * [backup-simplify]: Simplify 0 into 0
9.820 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.820 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
9.820 * [backup-simplify]: Simplify 0 into 0
9.821 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.822 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
9.822 * [backup-simplify]: Simplify 0 into 0
9.822 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
9.823 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
9.823 * [backup-simplify]: Simplify 0 into 0
9.824 * [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
9.825 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
9.825 * [backup-simplify]: Simplify 0 into 0
9.826 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
9.826 * * * [progress]: simplifying candidates
9.826 * * * * [progress]: [ 1 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (exp (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))))))))>
9.826 * * * * [progress]: [ 2 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (exp (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))))))))>
9.826 * * * * [progress]: [ 3 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))))))))>
9.826 * * * * [progress]: [ 4 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))))))))>
9.826 * * * * [progress]: [ 5 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2))))))))>
9.826 * * * * [progress]: [ 6 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2))))))))>
9.826 * * * * [progress]: [ 7 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2))))))))>
9.826 * * * * [progress]: [ 8 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (/ (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2)))))))>
9.826 * * * * [progress]: [ 9 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2))))))))>
9.826 * * * * [progress]: [ 10 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2))))))))>
9.826 * * * * [progress]: [ 11 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))))))>
9.826 * * * * [progress]: [ 12 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2))))))))>
9.826 * * * * [progress]: [ 13 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))))))))>
9.826 * * * * [progress]: [ 14 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))))))>
9.826 * * * * [progress]: [ 15 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2))))))))>
9.826 * * * * [progress]: [ 16 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2))))))))>
9.826 * * * * [progress]: [ 17 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
9.826 * * * * [progress]: [ 18 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1)))))>
9.827 * * * * [progress]: [ 19 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (exp (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))))>
9.827 * * * * [progress]: [ 20 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (log (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))))>
9.827 * * * * [progress]: [ 21 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))))>
9.827 * * * * [progress]: [ 22 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (cbrt (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))))>
9.827 * * * * [progress]: [ 23 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))))>
9.827 * * * * [progress]: [ 24 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))))))>
9.827 * * * * [progress]: [ 25 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))))))>
9.827 * * * * [progress]: [ 26 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (posit16->real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))))>
9.827 * * * * [progress]: [ 27 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (exp (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.827 * * * * [progress]: [ 28 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (exp (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.827 * * * * [progress]: [ 29 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.827 * * * * [progress]: [ 30 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.827 * * * * [progress]: [ 31 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.827 * * * * [progress]: [ 32 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.827 * * * * [progress]: [ 33 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.827 * * * * [progress]: [ 34 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (/ (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.827 * * * * [progress]: [ 35 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.827 * * * * [progress]: [ 36 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.827 * * * * [progress]: [ 37 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.827 * * * * [progress]: [ 38 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.827 * * * * [progress]: [ 39 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.827 * * * * [progress]: [ 40 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.827 * * * * [progress]: [ 41 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.827 * * * * [progress]: [ 42 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 43 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 44 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1)) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 45 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (exp (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 46 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (log (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 47 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (* (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 48 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (cbrt (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 49 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (* (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 50 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (* 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 51 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 52 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (posit16->real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 53 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 54 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 55 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 56 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (exp (+ (log n) (+ (log 2) (log PI)))) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 57 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (exp (+ (log n) (log (* 2 PI)))) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 58 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (exp (log (* n (* 2 PI)))) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 59 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (log (exp (* n (* 2 PI)))) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 60 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (- 1/2 (/ k 2)))))))>
9.828 * * * * [progress]: [ 61 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 62 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 63 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 64 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 65 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 66 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 67 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 68 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 69 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 70 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 71 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 72 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 73 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 74 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 75 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (exp (+ (log n) (+ (log 2) (log PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 76 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (exp (+ (log n) (log (* 2 PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 77 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (exp (log (* n (* 2 PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 78 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (log (exp (* n (* 2 PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 79 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 80 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 81 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 82 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.829 * * * * [progress]: [ 83 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.830 * * * * [progress]: [ 84 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.830 * * * * [progress]: [ 85 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.830 * * * * [progress]: [ 86 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.830 * * * * [progress]: [ 87 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.830 * * * * [progress]: [ 88 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.830 * * * * [progress]: [ 89 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.830 * * * * [progress]: [ 90 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.830 * * * * [progress]: [ 91 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))))))>
9.830 * * * * [progress]: [ 92 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))))))>
9.830 * * * * [progress]: [ 93 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))))))>
9.830 * * * * [progress]: [ 94 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.830 * * * * [progress]: [ 95 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.830 * * * * [progress]: [ 96 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.830 * * * * [progress]: [ 97 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))))>
9.830 * * * * [progress]: [ 98 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))))>
9.830 * * * * [progress]: [ 99 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))))))>
9.830 * * * * [progress]: [ 100 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.830 * * * * [progress]: [ 101 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.830 * * * * [progress]: [ 102 / 102 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))))>
9.834 * [simplify]: Simplifying:
  (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))
  (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* 2 PI) (- 1/2 (/ k 2)))
  (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))
  (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* 2 PI) (- 1/2 (/ k 2)))
  (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
9.835 * * [simplify]: iteration 1: (123 enodes)
9.881 * * [simplify]: iteration 2: (338 enodes)
10.237 * * [simplify]: iteration 3: (1097 enodes)
11.400 * * [simplify]: Extracting #0: cost 31 inf + 0
11.402 * * [simplify]: Extracting #1: cost 329 inf + 0
11.407 * * [simplify]: Extracting #2: cost 757 inf + 4110
11.430 * * [simplify]: Extracting #3: cost 833 inf + 50054
11.488 * * [simplify]: Extracting #4: cost 431 inf + 181247
11.572 * * [simplify]: Extracting #5: cost 129 inf + 281537
11.671 * * [simplify]: Extracting #6: cost 23 inf + 318846
11.781 * * [simplify]: Extracting #7: cost 3 inf + 326788
11.862 * * [simplify]: Extracting #8: cost 0 inf + 327772
11.949 * [simplify]: Simplified to:
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* 2 (* PI n)))
  (pow (* 2 (* PI n)) (/ k 2))
  (pow (* 2 (* PI n)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* 2 (* PI n)) (sqrt (- 1/2 (/ k 2))))
  (* 2 (* PI n))
  (pow (* 2 (* PI n)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* 2 (* PI n)) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* 2 (* PI n))
  (sqrt (* 2 (* PI n)))
  (pow (* 2 (* PI n)) (/ (- k) 2))
  (sqrt (* 2 (* PI n)))
  (pow (* 2 (* PI n)) (/ (- k) 2))
  (pow n (- 1/2 (/ k 2)))
  (pow (* PI 2) (- 1/2 (/ k 2)))
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (exp (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (* (* (pow (* 2 (* PI n)) (- 1/2 (/ k 2))) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))
  (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* 2 (* PI n)))
  (pow (* 2 (* PI n)) (/ k 2))
  (pow (* 2 (* PI n)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* 2 (* PI n)) (sqrt (- 1/2 (/ k 2))))
  (* 2 (* PI n))
  (pow (* 2 (* PI n)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* 2 (* PI n)) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* 2 (* PI n))
  (sqrt (* 2 (* PI n)))
  (pow (* 2 (* PI n)) (/ (- k) 2))
  (sqrt (* 2 (* PI n)))
  (pow (* 2 (* PI n)) (/ (- k) 2))
  (pow n (- 1/2 (/ k 2)))
  (pow (* PI 2) (- 1/2 (/ k 2)))
  (* (log (* 2 (* PI n))) (- 1/2 (/ k 2)))
  (exp (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (* (* (pow (* 2 (* PI n)) (- 1/2 (/ k 2))) (pow (* 2 (* PI n)) (- 1/2 (/ k 2)))) (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (sqrt (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))
  (pow (* 2 (* PI n)) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* 2 (* PI n)) (- 1/2 (/ k 2))))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (log (* 2 (* PI n)))
  (log (* 2 (* PI n)))
  (log (* 2 (* PI n)))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* (* (* PI n) (* PI n)) 8) (* PI n))
  (* (* (* (* PI n) (* PI n)) 8) (* PI n))
  (* (cbrt (* 2 (* PI n))) (cbrt (* 2 (* PI n))))
  (cbrt (* 2 (* PI n)))
  (* (* (* (* PI n) (* PI n)) 8) (* PI n))
  (sqrt (* 2 (* PI n)))
  (sqrt (* 2 (* PI n)))
  (* n 2)
  (* (cbrt n) (* PI 2))
  (* (sqrt n) (* PI 2))
  (* 2 (* PI n))
  (real->posit16 (* 2 (* PI n)))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (log (* 2 (* PI n)))
  (log (* 2 (* PI n)))
  (log (* 2 (* PI n)))
  (* (exp (* PI n)) (exp (* PI n)))
  (* (* (* (* PI n) (* PI n)) 8) (* PI n))
  (* (* (* (* PI n) (* PI n)) 8) (* PI n))
  (* (cbrt (* 2 (* PI n))) (cbrt (* 2 (* PI n))))
  (cbrt (* 2 (* PI n)))
  (* (* (* (* PI n) (* PI n)) 8) (* PI n))
  (sqrt (* 2 (* PI n)))
  (sqrt (* 2 (* PI n)))
  (* n 2)
  (* (cbrt n) (* PI 2))
  (* (sqrt n) (* PI 2))
  (* 2 (* PI n))
  (real->posit16 (* 2 (* PI n)))
  (- (+ (+ (sqrt (* 2 (* PI n))) (* (* 1/8 (sqrt (* 2 (* PI n)))) (* (* k (log (* PI 2))) (* k (log (* PI 2)))))) (* (* k k) (+ (* (* 1/8 (* (log n) (sqrt (* 2 (* PI n))))) (log n)) (* (* (log n) (sqrt (* 2 (* PI n)))) (* 1/4 (log (* PI 2))))))) (* (* k 1/2) (* (sqrt (* 2 (* PI n))) (+ (log n) (log (* PI 2))))))
  (exp (* (log (* 2 (* PI n))) (- 1/2 (* k 1/2))))
  (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))
  (- (+ (+ (sqrt (* 2 (* PI n))) (* (* 1/8 (sqrt (* 2 (* PI n)))) (* (* k (log (* PI 2))) (* k (log (* PI 2)))))) (* (* k k) (+ (* (* 1/8 (* (log n) (sqrt (* 2 (* PI n))))) (log n)) (* (* (log n) (sqrt (* 2 (* PI n)))) (* 1/4 (log (* PI 2))))))) (* (* k 1/2) (* (sqrt (* 2 (* PI n))) (+ (log n) (log (* PI 2))))))
  (exp (* (log (* 2 (* PI n))) (- 1/2 (* k 1/2))))
  (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (* 2 (* PI n))
  (* 2 (* PI n))
11.958 * * * [progress]: adding candidates to table
13.371 * * [progress]: iteration 4 / 4
13.371 * * * [progress]: picking best candidate
13.397 * * * * [pick]: Picked  #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.397 * * * [progress]: localizing error
13.439 * * * [progress]: generating rewritten candidates
13.439 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1 1)
13.458 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 2 1 1)
13.469 * * * * [progress]: [ 3 / 4 ] rewriting at (2 2 2 1 2)
13.486 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1 1)
13.513 * * * [progress]: generating series expansions
13.513 * * * * [progress]: [ 1 / 4 ] generating series at (2 1 1)
13.514 * [backup-simplify]: Simplify (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) into (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k)))
13.514 * [approximate]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in (n k) around 0
13.514 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in k
13.515 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in k
13.515 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in k
13.515 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
13.515 * [taylor]: Taking taylor expansion of 1/2 in k
13.515 * [backup-simplify]: Simplify 1/2 into 1/2
13.515 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
13.515 * [taylor]: Taking taylor expansion of 1/2 in k
13.515 * [backup-simplify]: Simplify 1/2 into 1/2
13.515 * [taylor]: Taking taylor expansion of k in k
13.515 * [backup-simplify]: Simplify 0 into 0
13.515 * [backup-simplify]: Simplify 1 into 1
13.515 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in k
13.515 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in k
13.515 * [taylor]: Taking taylor expansion of 2 in k
13.515 * [backup-simplify]: Simplify 2 into 2
13.515 * [taylor]: Taking taylor expansion of (* n PI) in k
13.515 * [taylor]: Taking taylor expansion of n in k
13.515 * [backup-simplify]: Simplify n into n
13.515 * [taylor]: Taking taylor expansion of PI in k
13.515 * [backup-simplify]: Simplify PI into PI
13.515 * [backup-simplify]: Simplify (* n PI) into (* n PI)
13.515 * [backup-simplify]: Simplify (* 2 (* n PI)) into (* 2 (* n PI))
13.515 * [backup-simplify]: Simplify (log (* 2 (* n PI))) into (log (* 2 (* n PI)))
13.516 * [backup-simplify]: Simplify (* 1/2 0) into 0
13.516 * [backup-simplify]: Simplify (- 0) into 0
13.517 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.517 * [backup-simplify]: Simplify (* 1/2 (log (* 2 (* n PI)))) into (* 1/2 (log (* 2 (* n PI))))
13.517 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 (* n PI))))) into (pow (* 2 (* n PI)) 1/2)
13.517 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
13.517 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
13.517 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
13.517 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
13.517 * [taylor]: Taking taylor expansion of 1/2 in n
13.517 * [backup-simplify]: Simplify 1/2 into 1/2
13.517 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
13.517 * [taylor]: Taking taylor expansion of 1/2 in n
13.517 * [backup-simplify]: Simplify 1/2 into 1/2
13.517 * [taylor]: Taking taylor expansion of k in n
13.517 * [backup-simplify]: Simplify k into k
13.517 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.517 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.517 * [taylor]: Taking taylor expansion of 2 in n
13.517 * [backup-simplify]: Simplify 2 into 2
13.517 * [taylor]: Taking taylor expansion of (* n PI) in n
13.517 * [taylor]: Taking taylor expansion of n in n
13.517 * [backup-simplify]: Simplify 0 into 0
13.517 * [backup-simplify]: Simplify 1 into 1
13.517 * [taylor]: Taking taylor expansion of PI in n
13.517 * [backup-simplify]: Simplify PI into PI
13.518 * [backup-simplify]: Simplify (* 0 PI) into 0
13.518 * [backup-simplify]: Simplify (* 2 0) into 0
13.520 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.522 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.523 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.523 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
13.523 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
13.523 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
13.524 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.526 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
13.527 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
13.527 * [taylor]: Taking taylor expansion of (pow (* 2 (* n PI)) (- 1/2 (* 1/2 k))) in n
13.527 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI))))) in n
13.527 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 (* n PI)))) in n
13.527 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
13.527 * [taylor]: Taking taylor expansion of 1/2 in n
13.527 * [backup-simplify]: Simplify 1/2 into 1/2
13.527 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
13.527 * [taylor]: Taking taylor expansion of 1/2 in n
13.527 * [backup-simplify]: Simplify 1/2 into 1/2
13.527 * [taylor]: Taking taylor expansion of k in n
13.527 * [backup-simplify]: Simplify k into k
13.527 * [taylor]: Taking taylor expansion of (log (* 2 (* n PI))) in n
13.527 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.527 * [taylor]: Taking taylor expansion of 2 in n
13.527 * [backup-simplify]: Simplify 2 into 2
13.527 * [taylor]: Taking taylor expansion of (* n PI) in n
13.527 * [taylor]: Taking taylor expansion of n in n
13.527 * [backup-simplify]: Simplify 0 into 0
13.527 * [backup-simplify]: Simplify 1 into 1
13.527 * [taylor]: Taking taylor expansion of PI in n
13.527 * [backup-simplify]: Simplify PI into PI
13.528 * [backup-simplify]: Simplify (* 0 PI) into 0
13.528 * [backup-simplify]: Simplify (* 2 0) into 0
13.530 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.531 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.532 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.533 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
13.533 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
13.533 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
13.534 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.535 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) into (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))
13.536 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) into (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))))
13.537 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) in k
13.537 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI)))) in k
13.537 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
13.537 * [taylor]: Taking taylor expansion of 1/2 in k
13.537 * [backup-simplify]: Simplify 1/2 into 1/2
13.537 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
13.537 * [taylor]: Taking taylor expansion of 1/2 in k
13.537 * [backup-simplify]: Simplify 1/2 into 1/2
13.537 * [taylor]: Taking taylor expansion of k in k
13.537 * [backup-simplify]: Simplify 0 into 0
13.537 * [backup-simplify]: Simplify 1 into 1
13.537 * [taylor]: Taking taylor expansion of (+ (log n) (log (* 2 PI))) in k
13.537 * [taylor]: Taking taylor expansion of (log n) in k
13.537 * [taylor]: Taking taylor expansion of n in k
13.537 * [backup-simplify]: Simplify n into n
13.537 * [backup-simplify]: Simplify (log n) into (log n)
13.537 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
13.537 * [taylor]: Taking taylor expansion of (* 2 PI) in k
13.537 * [taylor]: Taking taylor expansion of 2 in k
13.537 * [backup-simplify]: Simplify 2 into 2
13.537 * [taylor]: Taking taylor expansion of PI in k
13.537 * [backup-simplify]: Simplify PI into PI
13.538 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.539 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.539 * [backup-simplify]: Simplify (* 1/2 0) into 0
13.540 * [backup-simplify]: Simplify (- 0) into 0
13.540 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.541 * [backup-simplify]: Simplify (+ (log n) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.542 * [backup-simplify]: Simplify (* 1/2 (+ (log n) (log (* 2 PI)))) into (* 1/2 (+ (log n) (log (* 2 PI))))
13.543 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
13.545 * [backup-simplify]: Simplify (exp (* 1/2 (+ (log n) (log (* 2 PI))))) into (exp (* 1/2 (+ (log n) (log (* 2 PI)))))
13.546 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.547 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
13.549 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.549 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
13.550 * [backup-simplify]: Simplify (- 0) into 0
13.550 * [backup-simplify]: Simplify (+ 0 0) into 0
13.551 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.553 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (+ (log n) (log (* 2 PI))))) into 0
13.554 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 1) 1)))) into 0
13.554 * [taylor]: Taking taylor expansion of 0 in k
13.554 * [backup-simplify]: Simplify 0 into 0
13.554 * [backup-simplify]: Simplify 0 into 0
13.555 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
13.556 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.558 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.558 * [backup-simplify]: Simplify (+ 0 0) into 0
13.559 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
13.559 * [backup-simplify]: Simplify (- 1/2) into -1/2
13.560 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
13.561 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (+ (log n) (log (* 2 PI))))) into (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n))))
13.564 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 1) 1)))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
13.567 * [backup-simplify]: Simplify (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI)))))))
13.569 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.570 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.574 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.575 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
13.575 * [backup-simplify]: Simplify (- 0) into 0
13.576 * [backup-simplify]: Simplify (+ 0 0) into 0
13.577 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2 PI))) into (+ (log n) (log (* 2 PI)))
13.579 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
13.581 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.581 * [taylor]: Taking taylor expansion of 0 in k
13.581 * [backup-simplify]: Simplify 0 into 0
13.581 * [backup-simplify]: Simplify 0 into 0
13.581 * [backup-simplify]: Simplify 0 into 0
13.590 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
13.591 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
13.594 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.595 * [backup-simplify]: Simplify (+ 0 0) into 0
13.596 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
13.596 * [backup-simplify]: Simplify (- 0) into 0
13.597 * [backup-simplify]: Simplify (+ 0 0) into 0
13.598 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (+ (log n) (log (* 2 PI)))))) into 0
13.602 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* (/ (pow (- (+ (* 1/2 (log (* 2 PI))) (* 1/2 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
13.608 * [backup-simplify]: Simplify (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) into (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2)))))
13.617 * [backup-simplify]: Simplify (+ (* (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (+ (* 1/8 (pow (log n) 2)) (+ (* 1/4 (* (log n) (log (* 2 PI)))) (* 1/8 (pow (log (* 2 PI)) 2))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 1/2 (log n)) (* 1/2 (log (* 2 PI)))) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) (* k 1)) (exp (* 1/2 (+ (log n) (log (* 2 PI))))))) into (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
13.618 * [backup-simplify]: Simplify (pow (* (/ 1 n) (* 2 PI)) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
13.618 * [approximate]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
13.618 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in k
13.618 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in k
13.618 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in k
13.618 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
13.618 * [taylor]: Taking taylor expansion of 1/2 in k
13.618 * [backup-simplify]: Simplify 1/2 into 1/2
13.618 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.618 * [taylor]: Taking taylor expansion of 1/2 in k
13.618 * [backup-simplify]: Simplify 1/2 into 1/2
13.618 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.618 * [taylor]: Taking taylor expansion of k in k
13.618 * [backup-simplify]: Simplify 0 into 0
13.619 * [backup-simplify]: Simplify 1 into 1
13.619 * [backup-simplify]: Simplify (/ 1 1) into 1
13.619 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in k
13.619 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in k
13.619 * [taylor]: Taking taylor expansion of 2 in k
13.619 * [backup-simplify]: Simplify 2 into 2
13.619 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.619 * [taylor]: Taking taylor expansion of PI in k
13.619 * [backup-simplify]: Simplify PI into PI
13.619 * [taylor]: Taking taylor expansion of n in k
13.619 * [backup-simplify]: Simplify n into n
13.619 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.619 * [backup-simplify]: Simplify (* 2 (/ PI n)) into (* 2 (/ PI n))
13.619 * [backup-simplify]: Simplify (log (* 2 (/ PI n))) into (log (* 2 (/ PI n)))
13.620 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.620 * [backup-simplify]: Simplify (- 1/2) into -1/2
13.620 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
13.621 * [backup-simplify]: Simplify (* -1/2 (log (* 2 (/ PI n)))) into (* -1/2 (log (* 2 (/ PI n))))
13.621 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) into (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k))))
13.621 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
13.621 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.621 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.621 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
13.621 * [taylor]: Taking taylor expansion of 1/2 in n
13.621 * [backup-simplify]: Simplify 1/2 into 1/2
13.621 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.621 * [taylor]: Taking taylor expansion of 1/2 in n
13.621 * [backup-simplify]: Simplify 1/2 into 1/2
13.621 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.621 * [taylor]: Taking taylor expansion of k in n
13.621 * [backup-simplify]: Simplify k into k
13.621 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.621 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.621 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.621 * [taylor]: Taking taylor expansion of 2 in n
13.621 * [backup-simplify]: Simplify 2 into 2
13.621 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.621 * [taylor]: Taking taylor expansion of PI in n
13.621 * [backup-simplify]: Simplify PI into PI
13.621 * [taylor]: Taking taylor expansion of n in n
13.621 * [backup-simplify]: Simplify 0 into 0
13.621 * [backup-simplify]: Simplify 1 into 1
13.622 * [backup-simplify]: Simplify (/ PI 1) into PI
13.623 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.624 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.624 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.624 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
13.624 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
13.625 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.626 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
13.628 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
13.628 * [taylor]: Taking taylor expansion of (pow (* 2 (/ PI n)) (- 1/2 (* 1/2 (/ 1 k)))) in n
13.628 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n))))) in n
13.628 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 (/ PI n)))) in n
13.628 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
13.628 * [taylor]: Taking taylor expansion of 1/2 in n
13.628 * [backup-simplify]: Simplify 1/2 into 1/2
13.628 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.628 * [taylor]: Taking taylor expansion of 1/2 in n
13.628 * [backup-simplify]: Simplify 1/2 into 1/2
13.628 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.628 * [taylor]: Taking taylor expansion of k in n
13.628 * [backup-simplify]: Simplify k into k
13.628 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.628 * [taylor]: Taking taylor expansion of (log (* 2 (/ PI n))) in n
13.628 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.628 * [taylor]: Taking taylor expansion of 2 in n
13.628 * [backup-simplify]: Simplify 2 into 2
13.628 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.628 * [taylor]: Taking taylor expansion of PI in n
13.628 * [backup-simplify]: Simplify PI into PI
13.628 * [taylor]: Taking taylor expansion of n in n
13.628 * [backup-simplify]: Simplify 0 into 0
13.628 * [backup-simplify]: Simplify 1 into 1
13.629 * [backup-simplify]: Simplify (/ PI 1) into PI
13.629 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.630 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.630 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.631 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
13.631 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
13.632 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.634 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) into (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))
13.635 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
13.635 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) in k
13.635 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))) in k
13.635 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
13.635 * [taylor]: Taking taylor expansion of 1/2 in k
13.635 * [backup-simplify]: Simplify 1/2 into 1/2
13.635 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.635 * [taylor]: Taking taylor expansion of 1/2 in k
13.635 * [backup-simplify]: Simplify 1/2 into 1/2
13.635 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.635 * [taylor]: Taking taylor expansion of k in k
13.635 * [backup-simplify]: Simplify 0 into 0
13.635 * [backup-simplify]: Simplify 1 into 1
13.636 * [backup-simplify]: Simplify (/ 1 1) into 1
13.636 * [taylor]: Taking taylor expansion of (- (log (* 2 PI)) (log n)) in k
13.636 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
13.636 * [taylor]: Taking taylor expansion of (* 2 PI) in k
13.636 * [taylor]: Taking taylor expansion of 2 in k
13.636 * [backup-simplify]: Simplify 2 into 2
13.636 * [taylor]: Taking taylor expansion of PI in k
13.636 * [backup-simplify]: Simplify PI into PI
13.636 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.638 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.638 * [taylor]: Taking taylor expansion of (log n) in k
13.638 * [taylor]: Taking taylor expansion of n in k
13.638 * [backup-simplify]: Simplify n into n
13.638 * [backup-simplify]: Simplify (log n) into (log n)
13.638 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.639 * [backup-simplify]: Simplify (- 1/2) into -1/2
13.639 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
13.639 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.640 * [backup-simplify]: Simplify (+ (log (* 2 PI)) (- (log n))) into (- (log (* 2 PI)) (log n))
13.641 * [backup-simplify]: Simplify (* -1/2 (- (log (* 2 PI)) (log n))) into (* -1/2 (- (log (* 2 PI)) (log n)))
13.642 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
13.643 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) into (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n))))
13.644 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.645 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.647 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.647 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.648 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
13.648 * [backup-simplify]: Simplify (- 0) into 0
13.648 * [backup-simplify]: Simplify (+ 0 0) into 0
13.650 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.651 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log (* 2 PI)) (log n)))) into 0
13.653 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
13.653 * [taylor]: Taking taylor expansion of 0 in k
13.653 * [backup-simplify]: Simplify 0 into 0
13.653 * [backup-simplify]: Simplify 0 into 0
13.653 * [backup-simplify]: Simplify 0 into 0
13.654 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.655 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
13.658 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.658 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.659 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
13.660 * [backup-simplify]: Simplify (- 0) into 0
13.660 * [backup-simplify]: Simplify (+ 0 0) into 0
13.661 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.663 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n))))) into 0
13.664 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.664 * [taylor]: Taking taylor expansion of 0 in k
13.664 * [backup-simplify]: Simplify 0 into 0
13.664 * [backup-simplify]: Simplify 0 into 0
13.664 * [backup-simplify]: Simplify 0 into 0
13.665 * [backup-simplify]: Simplify 0 into 0
13.665 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.666 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.669 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2 PI) 1)))) 6) into 0
13.669 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.670 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
13.671 * [backup-simplify]: Simplify (- 0) into 0
13.671 * [backup-simplify]: Simplify (+ 0 0) into 0
13.672 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2 PI))) into (- (log (* 2 PI)) (log n))
13.673 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2 PI)) (log n)))))) into 0
13.674 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 (/ 1 k))) (- (log (* 2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.674 * [taylor]: Taking taylor expansion of 0 in k
13.674 * [backup-simplify]: Simplify 0 into 0
13.674 * [backup-simplify]: Simplify 0 into 0
13.675 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (- (log (* 2 PI)) (log (/ 1 n))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
13.676 * [backup-simplify]: Simplify (pow (* (/ 1 (- n)) (* 2 PI)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2))
13.676 * [approximate]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
13.676 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in k
13.676 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in k
13.676 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in k
13.676 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
13.676 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.676 * [taylor]: Taking taylor expansion of 1/2 in k
13.676 * [backup-simplify]: Simplify 1/2 into 1/2
13.676 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.676 * [taylor]: Taking taylor expansion of k in k
13.676 * [backup-simplify]: Simplify 0 into 0
13.676 * [backup-simplify]: Simplify 1 into 1
13.676 * [backup-simplify]: Simplify (/ 1 1) into 1
13.676 * [taylor]: Taking taylor expansion of 1/2 in k
13.676 * [backup-simplify]: Simplify 1/2 into 1/2
13.676 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in k
13.676 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in k
13.676 * [taylor]: Taking taylor expansion of -2 in k
13.676 * [backup-simplify]: Simplify -2 into -2
13.676 * [taylor]: Taking taylor expansion of (/ PI n) in k
13.676 * [taylor]: Taking taylor expansion of PI in k
13.676 * [backup-simplify]: Simplify PI into PI
13.676 * [taylor]: Taking taylor expansion of n in k
13.676 * [backup-simplify]: Simplify n into n
13.676 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
13.676 * [backup-simplify]: Simplify (* -2 (/ PI n)) into (* -2 (/ PI n))
13.676 * [backup-simplify]: Simplify (log (* -2 (/ PI n))) into (log (* -2 (/ PI n)))
13.677 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.677 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.677 * [backup-simplify]: Simplify (* 1/2 (log (* -2 (/ PI n)))) into (* 1/2 (log (* -2 (/ PI n))))
13.677 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) into (exp (* (log (* -2 (/ PI n))) (+ (* 1/2 (/ 1 k)) 1/2)))
13.677 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
13.677 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
13.677 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
13.677 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
13.677 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.677 * [taylor]: Taking taylor expansion of 1/2 in n
13.677 * [backup-simplify]: Simplify 1/2 into 1/2
13.677 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.677 * [taylor]: Taking taylor expansion of k in n
13.677 * [backup-simplify]: Simplify k into k
13.677 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.677 * [taylor]: Taking taylor expansion of 1/2 in n
13.677 * [backup-simplify]: Simplify 1/2 into 1/2
13.677 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.677 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.677 * [taylor]: Taking taylor expansion of -2 in n
13.677 * [backup-simplify]: Simplify -2 into -2
13.677 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.678 * [taylor]: Taking taylor expansion of PI in n
13.678 * [backup-simplify]: Simplify PI into PI
13.678 * [taylor]: Taking taylor expansion of n in n
13.678 * [backup-simplify]: Simplify 0 into 0
13.678 * [backup-simplify]: Simplify 1 into 1
13.678 * [backup-simplify]: Simplify (/ PI 1) into PI
13.678 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.679 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.679 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.679 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
13.680 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.681 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
13.681 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
13.681 * [taylor]: Taking taylor expansion of (pow (* -2 (/ PI n)) (+ (* 1/2 (/ 1 k)) 1/2)) in n
13.681 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n))))) in n
13.681 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* -2 (/ PI n)))) in n
13.681 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
13.681 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.681 * [taylor]: Taking taylor expansion of 1/2 in n
13.681 * [backup-simplify]: Simplify 1/2 into 1/2
13.681 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.681 * [taylor]: Taking taylor expansion of k in n
13.681 * [backup-simplify]: Simplify k into k
13.681 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.681 * [taylor]: Taking taylor expansion of 1/2 in n
13.682 * [backup-simplify]: Simplify 1/2 into 1/2
13.682 * [taylor]: Taking taylor expansion of (log (* -2 (/ PI n))) in n
13.682 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.682 * [taylor]: Taking taylor expansion of -2 in n
13.682 * [backup-simplify]: Simplify -2 into -2
13.682 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.682 * [taylor]: Taking taylor expansion of PI in n
13.682 * [backup-simplify]: Simplify PI into PI
13.682 * [taylor]: Taking taylor expansion of n in n
13.682 * [backup-simplify]: Simplify 0 into 0
13.682 * [backup-simplify]: Simplify 1 into 1
13.682 * [backup-simplify]: Simplify (/ PI 1) into PI
13.682 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.683 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.683 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.683 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
13.684 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.685 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))
13.685 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
13.685 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) in k
13.685 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))) in k
13.685 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
13.686 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.686 * [taylor]: Taking taylor expansion of 1/2 in k
13.686 * [backup-simplify]: Simplify 1/2 into 1/2
13.686 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.686 * [taylor]: Taking taylor expansion of k in k
13.686 * [backup-simplify]: Simplify 0 into 0
13.686 * [backup-simplify]: Simplify 1 into 1
13.686 * [backup-simplify]: Simplify (/ 1 1) into 1
13.686 * [taylor]: Taking taylor expansion of 1/2 in k
13.686 * [backup-simplify]: Simplify 1/2 into 1/2
13.686 * [taylor]: Taking taylor expansion of (- (log (* -2 PI)) (log n)) in k
13.686 * [taylor]: Taking taylor expansion of (log (* -2 PI)) in k
13.686 * [taylor]: Taking taylor expansion of (* -2 PI) in k
13.686 * [taylor]: Taking taylor expansion of -2 in k
13.686 * [backup-simplify]: Simplify -2 into -2
13.686 * [taylor]: Taking taylor expansion of PI in k
13.686 * [backup-simplify]: Simplify PI into PI
13.686 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.687 * [backup-simplify]: Simplify (log (* -2 PI)) into (log (* -2 PI))
13.687 * [taylor]: Taking taylor expansion of (log n) in k
13.687 * [taylor]: Taking taylor expansion of n in k
13.687 * [backup-simplify]: Simplify n into n
13.687 * [backup-simplify]: Simplify (log n) into (log n)
13.687 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.688 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.688 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.688 * [backup-simplify]: Simplify (+ (log (* -2 PI)) (- (log n))) into (- (log (* -2 PI)) (log n))
13.689 * [backup-simplify]: Simplify (* 1/2 (- (log (* -2 PI)) (log n))) into (* 1/2 (- (log (* -2 PI)) (log n)))
13.690 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
13.691 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n))))
13.692 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.693 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
13.695 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2 PI) 1)))) 1) into 0
13.695 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.695 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
13.696 * [backup-simplify]: Simplify (+ 0 0) into 0
13.697 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.698 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log (* -2 PI)) (log n)))) into 0
13.700 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
13.700 * [taylor]: Taking taylor expansion of 0 in k
13.700 * [backup-simplify]: Simplify 0 into 0
13.701 * [backup-simplify]: Simplify 0 into 0
13.701 * [backup-simplify]: Simplify 0 into 0
13.702 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.703 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
13.707 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2 PI) 1)))) 2) into 0
13.707 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.708 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
13.708 * [backup-simplify]: Simplify (+ 0 0) into 0
13.709 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.712 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n))))) into 0
13.714 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.714 * [taylor]: Taking taylor expansion of 0 in k
13.714 * [backup-simplify]: Simplify 0 into 0
13.714 * [backup-simplify]: Simplify 0 into 0
13.714 * [backup-simplify]: Simplify 0 into 0
13.714 * [backup-simplify]: Simplify 0 into 0
13.715 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.716 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.720 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2 PI) 1)))) 6) into 0
13.720 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.721 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
13.721 * [backup-simplify]: Simplify (+ 0 0) into 0
13.722 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2 PI))) into (- (log (* -2 PI)) (log n))
13.723 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2 PI)) (log n)))))) into 0
13.725 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log (* -2 PI)) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.725 * [taylor]: Taking taylor expansion of 0 in k
13.725 * [backup-simplify]: Simplify 0 into 0
13.725 * [backup-simplify]: Simplify 0 into 0
13.726 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log (* -2 PI)) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
13.726 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 2 1 1)
13.726 * [backup-simplify]: Simplify (pow n (- 1/2 (/ k 2))) into (pow n (- 1/2 (* 1/2 k)))
13.726 * [approximate]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in (n k) around 0
13.726 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k
13.726 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k
13.726 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k
13.726 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
13.726 * [taylor]: Taking taylor expansion of 1/2 in k
13.726 * [backup-simplify]: Simplify 1/2 into 1/2
13.726 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
13.726 * [taylor]: Taking taylor expansion of 1/2 in k
13.726 * [backup-simplify]: Simplify 1/2 into 1/2
13.726 * [taylor]: Taking taylor expansion of k in k
13.726 * [backup-simplify]: Simplify 0 into 0
13.726 * [backup-simplify]: Simplify 1 into 1
13.726 * [taylor]: Taking taylor expansion of (log n) in k
13.726 * [taylor]: Taking taylor expansion of n in k
13.726 * [backup-simplify]: Simplify n into n
13.726 * [backup-simplify]: Simplify (log n) into (log n)
13.726 * [backup-simplify]: Simplify (* 1/2 0) into 0
13.727 * [backup-simplify]: Simplify (- 0) into 0
13.727 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.727 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n))
13.727 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
13.727 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n
13.727 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n
13.727 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n
13.727 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
13.727 * [taylor]: Taking taylor expansion of 1/2 in n
13.727 * [backup-simplify]: Simplify 1/2 into 1/2
13.727 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
13.727 * [taylor]: Taking taylor expansion of 1/2 in n
13.727 * [backup-simplify]: Simplify 1/2 into 1/2
13.727 * [taylor]: Taking taylor expansion of k in n
13.727 * [backup-simplify]: Simplify k into k
13.727 * [taylor]: Taking taylor expansion of (log n) in n
13.727 * [taylor]: Taking taylor expansion of n in n
13.727 * [backup-simplify]: Simplify 0 into 0
13.727 * [backup-simplify]: Simplify 1 into 1
13.728 * [backup-simplify]: Simplify (log 1) into 0
13.728 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
13.728 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
13.728 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
13.728 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
13.728 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n))
13.728 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k)))
13.728 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in n
13.728 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in n
13.728 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in n
13.728 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in n
13.728 * [taylor]: Taking taylor expansion of 1/2 in n
13.728 * [backup-simplify]: Simplify 1/2 into 1/2
13.728 * [taylor]: Taking taylor expansion of (* 1/2 k) in n
13.728 * [taylor]: Taking taylor expansion of 1/2 in n
13.728 * [backup-simplify]: Simplify 1/2 into 1/2
13.728 * [taylor]: Taking taylor expansion of k in n
13.728 * [backup-simplify]: Simplify k into k
13.728 * [taylor]: Taking taylor expansion of (log n) in n
13.728 * [taylor]: Taking taylor expansion of n in n
13.729 * [backup-simplify]: Simplify 0 into 0
13.729 * [backup-simplify]: Simplify 1 into 1
13.729 * [backup-simplify]: Simplify (log 1) into 0
13.729 * [backup-simplify]: Simplify (* 1/2 k) into (* 1/2 k)
13.729 * [backup-simplify]: Simplify (- (* 1/2 k)) into (- (* 1/2 k))
13.729 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 k))) into (- 1/2 (* 1/2 k))
13.729 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
13.729 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 k)) (log n)) into (* (- 1/2 (* 1/2 k)) (log n))
13.729 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 k)) (log n))) into (pow n (- 1/2 (* 1/2 k)))
13.729 * [taylor]: Taking taylor expansion of (pow n (- 1/2 (* 1/2 k))) in k
13.729 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log n))) in k
13.729 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log n)) in k
13.729 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
13.729 * [taylor]: Taking taylor expansion of 1/2 in k
13.729 * [backup-simplify]: Simplify 1/2 into 1/2
13.729 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
13.730 * [taylor]: Taking taylor expansion of 1/2 in k
13.730 * [backup-simplify]: Simplify 1/2 into 1/2
13.730 * [taylor]: Taking taylor expansion of k in k
13.730 * [backup-simplify]: Simplify 0 into 0
13.730 * [backup-simplify]: Simplify 1 into 1
13.730 * [taylor]: Taking taylor expansion of (log n) in k
13.730 * [taylor]: Taking taylor expansion of n in k
13.730 * [backup-simplify]: Simplify n into n
13.730 * [backup-simplify]: Simplify (log n) into (log n)
13.730 * [backup-simplify]: Simplify (* 1/2 0) into 0
13.730 * [backup-simplify]: Simplify (- 0) into 0
13.730 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.730 * [backup-simplify]: Simplify (* 1/2 (log n)) into (* 1/2 (log n))
13.731 * [backup-simplify]: Simplify (exp (* 1/2 (log n))) into (pow n 1/2)
13.731 * [backup-simplify]: Simplify (pow n 1/2) into (pow n 1/2)
13.731 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
13.732 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 k)) into 0
13.732 * [backup-simplify]: Simplify (- 0) into 0
13.732 * [backup-simplify]: Simplify (+ 0 0) into 0
13.732 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
13.732 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (* 0 (log n))) into 0
13.733 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 1) 1)))) into 0
13.733 * [taylor]: Taking taylor expansion of 0 in k
13.733 * [backup-simplify]: Simplify 0 into 0
13.733 * [backup-simplify]: Simplify 0 into 0
13.734 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
13.734 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
13.734 * [backup-simplify]: Simplify (- 1/2) into -1/2
13.734 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
13.735 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log n))) into (- (* 1/2 (log n)))
13.735 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 1) 1)))) into (* -1/2 (* (sqrt n) (log n)))
13.735 * [backup-simplify]: Simplify (* -1/2 (* (sqrt n) (log n))) into (* -1/2 (* (sqrt n) (log n)))
13.738 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
13.739 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 k))) into 0
13.740 * [backup-simplify]: Simplify (- 0) into 0
13.740 * [backup-simplify]: Simplify (+ 0 0) into 0
13.741 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
13.742 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 k)) 0) (+ (* 0 0) (* 0 (log n)))) into 0
13.743 * [backup-simplify]: Simplify (* (exp (* (- 1/2 (* 1/2 k)) (log n))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.743 * [taylor]: Taking taylor expansion of 0 in k
13.743 * [backup-simplify]: Simplify 0 into 0
13.743 * [backup-simplify]: Simplify 0 into 0
13.743 * [backup-simplify]: Simplify 0 into 0
13.745 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
13.746 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
13.747 * [backup-simplify]: Simplify (- 0) into 0
13.747 * [backup-simplify]: Simplify (+ 0 0) into 0
13.748 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log n)))) into 0
13.749 * [backup-simplify]: Simplify (* (exp (* 1/2 (log n))) (+ (* (/ (pow (- (* 1/2 (log n))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt n) (pow (log n) 2)))
13.749 * [backup-simplify]: Simplify (* 1/8 (* (sqrt n) (pow (log n) 2))) into (* 1/8 (* (sqrt n) (pow (log n) 2)))
13.750 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (sqrt n) (pow (log n) 2))) (pow (* k 1) 2)) (+ (* (* -1/2 (* (sqrt n) (log n))) (* k 1)) (pow n 1/2))) into (- (+ (pow n 1/2) (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2))))) (* 1/2 (* (sqrt n) (* (log n) k))))
13.750 * [backup-simplify]: Simplify (pow (/ 1 n) (- 1/2 (/ (/ 1 k) 2))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))
13.750 * [approximate]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in (n k) around 0
13.750 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in k
13.750 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in k
13.750 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in k
13.750 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
13.750 * [taylor]: Taking taylor expansion of 1/2 in k
13.750 * [backup-simplify]: Simplify 1/2 into 1/2
13.750 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.751 * [taylor]: Taking taylor expansion of 1/2 in k
13.751 * [backup-simplify]: Simplify 1/2 into 1/2
13.751 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.751 * [taylor]: Taking taylor expansion of k in k
13.751 * [backup-simplify]: Simplify 0 into 0
13.751 * [backup-simplify]: Simplify 1 into 1
13.751 * [backup-simplify]: Simplify (/ 1 1) into 1
13.751 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in k
13.751 * [taylor]: Taking taylor expansion of (/ 1 n) in k
13.751 * [taylor]: Taking taylor expansion of n in k
13.751 * [backup-simplify]: Simplify n into n
13.751 * [backup-simplify]: Simplify (/ 1 n) into (/ 1 n)
13.751 * [backup-simplify]: Simplify (log (/ 1 n)) into (log (/ 1 n))
13.752 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.752 * [backup-simplify]: Simplify (- 1/2) into -1/2
13.753 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
13.753 * [backup-simplify]: Simplify (* -1/2 (log (/ 1 n))) into (* -1/2 (log (/ 1 n)))
13.753 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) into (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k))))
13.753 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n
13.753 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n
13.753 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n
13.753 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
13.753 * [taylor]: Taking taylor expansion of 1/2 in n
13.753 * [backup-simplify]: Simplify 1/2 into 1/2
13.753 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.753 * [taylor]: Taking taylor expansion of 1/2 in n
13.753 * [backup-simplify]: Simplify 1/2 into 1/2
13.753 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.753 * [taylor]: Taking taylor expansion of k in n
13.753 * [backup-simplify]: Simplify k into k
13.753 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.754 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n
13.754 * [taylor]: Taking taylor expansion of (/ 1 n) in n
13.754 * [taylor]: Taking taylor expansion of n in n
13.754 * [backup-simplify]: Simplify 0 into 0
13.754 * [backup-simplify]: Simplify 1 into 1
13.754 * [backup-simplify]: Simplify (/ 1 1) into 1
13.754 * [backup-simplify]: Simplify (log 1) into 0
13.755 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.755 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
13.755 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
13.755 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
13.755 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))
13.756 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))
13.756 * [taylor]: Taking taylor expansion of (pow (/ 1 n) (- 1/2 (* 1/2 (/ 1 k)))) in n
13.756 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n)))) in n
13.756 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (/ 1 n))) in n
13.756 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in n
13.756 * [taylor]: Taking taylor expansion of 1/2 in n
13.756 * [backup-simplify]: Simplify 1/2 into 1/2
13.756 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.756 * [taylor]: Taking taylor expansion of 1/2 in n
13.756 * [backup-simplify]: Simplify 1/2 into 1/2
13.756 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.756 * [taylor]: Taking taylor expansion of k in n
13.756 * [backup-simplify]: Simplify k into k
13.756 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.756 * [taylor]: Taking taylor expansion of (log (/ 1 n)) in n
13.756 * [taylor]: Taking taylor expansion of (/ 1 n) in n
13.756 * [taylor]: Taking taylor expansion of n in n
13.756 * [backup-simplify]: Simplify 0 into 0
13.756 * [backup-simplify]: Simplify 1 into 1
13.757 * [backup-simplify]: Simplify (/ 1 1) into 1
13.757 * [backup-simplify]: Simplify (log 1) into 0
13.757 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.757 * [backup-simplify]: Simplify (- (/ 1/2 k)) into (- (* 1/2 (/ 1 k)))
13.757 * [backup-simplify]: Simplify (+ 1/2 (- (* 1/2 (/ 1 k)))) into (- 1/2 (* 1/2 (/ 1 k)))
13.758 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
13.758 * [backup-simplify]: Simplify (* (- 1/2 (* 1/2 (/ 1 k))) (- (log n))) into (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))
13.758 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))
13.758 * [taylor]: Taking taylor expansion of (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) in k
13.758 * [taylor]: Taking taylor expansion of (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))) in k
13.758 * [taylor]: Taking taylor expansion of -1 in k
13.758 * [backup-simplify]: Simplify -1 into -1
13.758 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log n)) in k
13.758 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
13.758 * [taylor]: Taking taylor expansion of 1/2 in k
13.758 * [backup-simplify]: Simplify 1/2 into 1/2
13.759 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.759 * [taylor]: Taking taylor expansion of 1/2 in k
13.759 * [backup-simplify]: Simplify 1/2 into 1/2
13.759 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.759 * [taylor]: Taking taylor expansion of k in k
13.759 * [backup-simplify]: Simplify 0 into 0
13.759 * [backup-simplify]: Simplify 1 into 1
13.759 * [backup-simplify]: Simplify (/ 1 1) into 1
13.759 * [taylor]: Taking taylor expansion of (log n) in k
13.759 * [taylor]: Taking taylor expansion of n in k
13.759 * [backup-simplify]: Simplify n into n
13.759 * [backup-simplify]: Simplify (log n) into (log n)
13.760 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.760 * [backup-simplify]: Simplify (- 1/2) into -1/2
13.761 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
13.761 * [backup-simplify]: Simplify (* -1/2 (log n)) into (* -1/2 (log n))
13.761 * [backup-simplify]: Simplify (* -1 (* -1/2 (log n))) into (* 1/2 (log n))
13.761 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))
13.761 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) into (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n))))
13.762 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
13.764 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
13.764 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.764 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
13.765 * [backup-simplify]: Simplify (- 0) into 0
13.765 * [backup-simplify]: Simplify (+ 0 0) into 0
13.766 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
13.766 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (* 0 (- (log n)))) into 0
13.767 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
13.767 * [taylor]: Taking taylor expansion of 0 in k
13.767 * [backup-simplify]: Simplify 0 into 0
13.767 * [backup-simplify]: Simplify 0 into 0
13.767 * [backup-simplify]: Simplify 0 into 0
13.768 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.771 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow 1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow 1 1)))) 2) into 0
13.771 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.772 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
13.772 * [backup-simplify]: Simplify (- 0) into 0
13.773 * [backup-simplify]: Simplify (+ 0 0) into 0
13.773 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
13.774 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log n))))) into 0
13.775 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.775 * [taylor]: Taking taylor expansion of 0 in k
13.775 * [backup-simplify]: Simplify 0 into 0
13.776 * [backup-simplify]: Simplify 0 into 0
13.776 * [backup-simplify]: Simplify 0 into 0
13.776 * [backup-simplify]: Simplify 0 into 0
13.777 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.782 * [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
13.782 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.784 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
13.784 * [backup-simplify]: Simplify (- 0) into 0
13.784 * [backup-simplify]: Simplify (+ 0 0) into 0
13.785 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) 0) into (- (log n))
13.785 * [backup-simplify]: Simplify (+ (* (- 1/2 (* 1/2 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log n)))))) into 0
13.787 * [backup-simplify]: Simplify (* (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 k))) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.787 * [taylor]: Taking taylor expansion of 0 in k
13.787 * [backup-simplify]: Simplify 0 into 0
13.787 * [backup-simplify]: Simplify 0 into 0
13.788 * [backup-simplify]: Simplify (exp (* -1 (* (- 1/2 (* 1/2 (/ 1 (/ 1 k)))) (log (/ 1 n))))) into (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n)))))
13.788 * [backup-simplify]: Simplify (pow (/ 1 (- n)) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))
13.788 * [approximate]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in (n k) around 0
13.788 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in k
13.788 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in k
13.788 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in k
13.788 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
13.788 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.788 * [taylor]: Taking taylor expansion of 1/2 in k
13.788 * [backup-simplify]: Simplify 1/2 into 1/2
13.788 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.788 * [taylor]: Taking taylor expansion of k in k
13.788 * [backup-simplify]: Simplify 0 into 0
13.788 * [backup-simplify]: Simplify 1 into 1
13.789 * [backup-simplify]: Simplify (/ 1 1) into 1
13.789 * [taylor]: Taking taylor expansion of 1/2 in k
13.789 * [backup-simplify]: Simplify 1/2 into 1/2
13.789 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in k
13.789 * [taylor]: Taking taylor expansion of (/ -1 n) in k
13.789 * [taylor]: Taking taylor expansion of -1 in k
13.789 * [backup-simplify]: Simplify -1 into -1
13.789 * [taylor]: Taking taylor expansion of n in k
13.789 * [backup-simplify]: Simplify n into n
13.789 * [backup-simplify]: Simplify (/ -1 n) into (/ -1 n)
13.789 * [backup-simplify]: Simplify (log (/ -1 n)) into (log (/ -1 n))
13.789 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.790 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.790 * [backup-simplify]: Simplify (* 1/2 (log (/ -1 n))) into (* 1/2 (log (/ -1 n)))
13.790 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) into (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2))
13.790 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n
13.790 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n
13.790 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n
13.790 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
13.790 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.790 * [taylor]: Taking taylor expansion of 1/2 in n
13.790 * [backup-simplify]: Simplify 1/2 into 1/2
13.790 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.790 * [taylor]: Taking taylor expansion of k in n
13.790 * [backup-simplify]: Simplify k into k
13.791 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.791 * [taylor]: Taking taylor expansion of 1/2 in n
13.791 * [backup-simplify]: Simplify 1/2 into 1/2
13.791 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n
13.791 * [taylor]: Taking taylor expansion of (/ -1 n) in n
13.791 * [taylor]: Taking taylor expansion of -1 in n
13.791 * [backup-simplify]: Simplify -1 into -1
13.791 * [taylor]: Taking taylor expansion of n in n
13.791 * [backup-simplify]: Simplify 0 into 0
13.791 * [backup-simplify]: Simplify 1 into 1
13.791 * [backup-simplify]: Simplify (/ -1 1) into -1
13.792 * [backup-simplify]: Simplify (log -1) into (log -1)
13.792 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.792 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
13.793 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
13.793 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))
13.794 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))
13.794 * [taylor]: Taking taylor expansion of (pow (/ -1 n) (+ (* 1/2 (/ 1 k)) 1/2)) in n
13.794 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n)))) in n
13.794 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (/ -1 n))) in n
13.794 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in n
13.794 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in n
13.794 * [taylor]: Taking taylor expansion of 1/2 in n
13.794 * [backup-simplify]: Simplify 1/2 into 1/2
13.794 * [taylor]: Taking taylor expansion of (/ 1 k) in n
13.794 * [taylor]: Taking taylor expansion of k in n
13.794 * [backup-simplify]: Simplify k into k
13.794 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
13.794 * [taylor]: Taking taylor expansion of 1/2 in n
13.794 * [backup-simplify]: Simplify 1/2 into 1/2
13.794 * [taylor]: Taking taylor expansion of (log (/ -1 n)) in n
13.794 * [taylor]: Taking taylor expansion of (/ -1 n) in n
13.794 * [taylor]: Taking taylor expansion of -1 in n
13.794 * [backup-simplify]: Simplify -1 into -1
13.794 * [taylor]: Taking taylor expansion of n in n
13.794 * [backup-simplify]: Simplify 0 into 0
13.794 * [backup-simplify]: Simplify 1 into 1
13.795 * [backup-simplify]: Simplify (/ -1 1) into -1
13.795 * [backup-simplify]: Simplify (log -1) into (log -1)
13.795 * [backup-simplify]: Simplify (* 1/2 (/ 1 k)) into (/ 1/2 k)
13.795 * [backup-simplify]: Simplify (+ (/ 1/2 k) 1/2) into (+ (* 1/2 (/ 1 k)) 1/2)
13.796 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
13.796 * [backup-simplify]: Simplify (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) into (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))
13.797 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))
13.797 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) in k
13.797 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))) in k
13.797 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
13.797 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.797 * [taylor]: Taking taylor expansion of 1/2 in k
13.797 * [backup-simplify]: Simplify 1/2 into 1/2
13.797 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.797 * [taylor]: Taking taylor expansion of k in k
13.797 * [backup-simplify]: Simplify 0 into 0
13.797 * [backup-simplify]: Simplify 1 into 1
13.798 * [backup-simplify]: Simplify (/ 1 1) into 1
13.798 * [taylor]: Taking taylor expansion of 1/2 in k
13.798 * [backup-simplify]: Simplify 1/2 into 1/2
13.798 * [taylor]: Taking taylor expansion of (- (log -1) (log n)) in k
13.798 * [taylor]: Taking taylor expansion of (log -1) in k
13.798 * [taylor]: Taking taylor expansion of -1 in k
13.798 * [backup-simplify]: Simplify -1 into -1
13.798 * [backup-simplify]: Simplify (log -1) into (log -1)
13.798 * [taylor]: Taking taylor expansion of (log n) in k
13.798 * [taylor]: Taking taylor expansion of n in k
13.798 * [backup-simplify]: Simplify n into n
13.798 * [backup-simplify]: Simplify (log n) into (log n)
13.799 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.799 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.799 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
13.800 * [backup-simplify]: Simplify (+ (log -1) (- (log n))) into (- (log -1) (log n))
13.800 * [backup-simplify]: Simplify (* 1/2 (- (log -1) (log n))) into (* 1/2 (- (log -1) (log n)))
13.801 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))
13.801 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) into (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n))))
13.802 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
13.804 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow -1 1)))) 1) into 0
13.804 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
13.804 * [backup-simplify]: Simplify (+ (* 1/2 0) (* 0 (/ 1 k))) into 0
13.805 * [backup-simplify]: Simplify (+ 0 0) into 0
13.805 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
13.806 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (* 0 (- (log -1) (log n)))) into 0
13.807 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 1) 1)))) into 0
13.807 * [taylor]: Taking taylor expansion of 0 in k
13.807 * [backup-simplify]: Simplify 0 into 0
13.807 * [backup-simplify]: Simplify 0 into 0
13.807 * [backup-simplify]: Simplify 0 into 0
13.808 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.811 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow -1 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow -1 1)))) 2) into 0
13.811 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.812 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (* 0 (/ 1 k)))) into 0
13.812 * [backup-simplify]: Simplify (+ 0 0) into 0
13.813 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
13.814 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (* 0 (- (log -1) (log n))))) into 0
13.816 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
13.816 * [taylor]: Taking taylor expansion of 0 in k
13.816 * [backup-simplify]: Simplify 0 into 0
13.816 * [backup-simplify]: Simplify 0 into 0
13.816 * [backup-simplify]: Simplify 0 into 0
13.816 * [backup-simplify]: Simplify 0 into 0
13.817 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.821 * [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
13.821 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
13.822 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 0) (+ (* 0 0) (* 0 (/ 1 k))))) into 0
13.822 * [backup-simplify]: Simplify (+ 0 0) into 0
13.822 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log -1)) into (- (log -1) (log n))
13.823 * [backup-simplify]: Simplify (+ (* (+ (* 1/2 (/ 1 k)) 1/2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log -1) (log n)))))) into 0
13.824 * [backup-simplify]: Simplify (* (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (- (log -1) (log n)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
13.824 * [taylor]: Taking taylor expansion of 0 in k
13.824 * [backup-simplify]: Simplify 0 into 0
13.824 * [backup-simplify]: Simplify 0 into 0
13.825 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2) (- (log -1) (log (/ 1 (- n)))))) into (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n)))))
13.825 * * * * [progress]: [ 3 / 4 ] generating series at (2 2 2 1 2)
13.825 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (/ k 2))) into (pow (* 2 PI) (- 1/2 (* 1/2 k)))
13.825 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in (k) around 0
13.825 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in k
13.825 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k
13.825 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k
13.825 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
13.825 * [taylor]: Taking taylor expansion of 1/2 in k
13.825 * [backup-simplify]: Simplify 1/2 into 1/2
13.825 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
13.825 * [taylor]: Taking taylor expansion of 1/2 in k
13.825 * [backup-simplify]: Simplify 1/2 into 1/2
13.825 * [taylor]: Taking taylor expansion of k in k
13.825 * [backup-simplify]: Simplify 0 into 0
13.825 * [backup-simplify]: Simplify 1 into 1
13.825 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
13.825 * [taylor]: Taking taylor expansion of (* 2 PI) in k
13.825 * [taylor]: Taking taylor expansion of 2 in k
13.825 * [backup-simplify]: Simplify 2 into 2
13.825 * [taylor]: Taking taylor expansion of PI in k
13.826 * [backup-simplify]: Simplify PI into PI
13.826 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.826 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.827 * [backup-simplify]: Simplify (* 1/2 0) into 0
13.827 * [backup-simplify]: Simplify (- 0) into 0
13.827 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.828 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
13.830 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
13.830 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 k))) in k
13.830 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 k)) (log (* 2 PI)))) in k
13.830 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 k)) (log (* 2 PI))) in k
13.830 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 k)) in k
13.830 * [taylor]: Taking taylor expansion of 1/2 in k
13.830 * [backup-simplify]: Simplify 1/2 into 1/2
13.830 * [taylor]: Taking taylor expansion of (* 1/2 k) in k
13.830 * [taylor]: Taking taylor expansion of 1/2 in k
13.830 * [backup-simplify]: Simplify 1/2 into 1/2
13.830 * [taylor]: Taking taylor expansion of k in k
13.830 * [backup-simplify]: Simplify 0 into 0
13.830 * [backup-simplify]: Simplify 1 into 1
13.830 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
13.830 * [taylor]: Taking taylor expansion of (* 2 PI) in k
13.830 * [taylor]: Taking taylor expansion of 2 in k
13.830 * [backup-simplify]: Simplify 2 into 2
13.830 * [taylor]: Taking taylor expansion of PI in k
13.830 * [backup-simplify]: Simplify PI into PI
13.830 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.831 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.831 * [backup-simplify]: Simplify (* 1/2 0) into 0
13.831 * [backup-simplify]: Simplify (- 0) into 0
13.832 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.833 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
13.834 * [backup-simplify]: Simplify (exp (* 1/2 (log (* 2 PI)))) into (pow (* 2 PI) 1/2)
13.835 * [backup-simplify]: Simplify (pow (* 2 PI) 1/2) into (pow (* 2 PI) 1/2)
13.837 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.839 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2 PI) 1)))) 1) into 0
13.839 * [backup-simplify]: Simplify (+ (* 1/2 1) (* 0 0)) into 1/2
13.839 * [backup-simplify]: Simplify (- 1/2) into -1/2
13.840 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
13.842 * [backup-simplify]: Simplify (+ (* 1/2 0) (* -1/2 (log (* 2 PI)))) into (- (* 1/2 (log (* 2 PI))))
13.849 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 1) 1)))) into (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI))))
13.852 * [backup-simplify]: Simplify (* -1/2 (* (sqrt (* PI 2)) (log (* 2 PI)))) into (* -1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI)))
13.853 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
13.857 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2 PI) 1)))) 2) into 0
13.858 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* 0 1) (* 0 0))) into 0
13.858 * [backup-simplify]: Simplify (- 0) into 0
13.859 * [backup-simplify]: Simplify (+ 0 0) into 0
13.860 * [backup-simplify]: Simplify (+ (* 1/2 0) (+ (* -1/2 0) (* 0 (log (* 2 PI))))) into 0
13.876 * [backup-simplify]: Simplify (* (exp (* 1/2 (log (* 2 PI)))) (+ (* (/ (pow (- (* 1/2 (log (* 2 PI)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2)))
13.882 * [backup-simplify]: Simplify (* 1/8 (* (sqrt (* PI 2)) (pow (log (* 2 PI)) 2))) into (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI)))
13.891 * [backup-simplify]: Simplify (+ (* (* 1/8 (* (* (sqrt 2) (pow (log (* 2 PI)) 2)) (sqrt PI))) (pow k 2)) (+ (* (* -1/2 (* (* (sqrt 2) (log (* 2 PI))) (sqrt PI))) k) (pow (* 2 PI) 1/2))) into (- (+ (* 1/8 (* (* (sqrt 2) (* (pow k 2) (pow (log (* 2 PI)) 2))) (sqrt PI))) (pow (* 2 PI) 1/2)) (* 1/2 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI))))
13.892 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (/ (/ 1 k) 2))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))
13.892 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in (k) around 0
13.892 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in k
13.892 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k
13.892 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k
13.892 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
13.892 * [taylor]: Taking taylor expansion of 1/2 in k
13.892 * [backup-simplify]: Simplify 1/2 into 1/2
13.892 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.892 * [taylor]: Taking taylor expansion of 1/2 in k
13.892 * [backup-simplify]: Simplify 1/2 into 1/2
13.892 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.892 * [taylor]: Taking taylor expansion of k in k
13.892 * [backup-simplify]: Simplify 0 into 0
13.892 * [backup-simplify]: Simplify 1 into 1
13.892 * [backup-simplify]: Simplify (/ 1 1) into 1
13.892 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
13.892 * [taylor]: Taking taylor expansion of (* 2 PI) in k
13.892 * [taylor]: Taking taylor expansion of 2 in k
13.892 * [backup-simplify]: Simplify 2 into 2
13.892 * [taylor]: Taking taylor expansion of PI in k
13.892 * [backup-simplify]: Simplify PI into PI
13.893 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.893 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.894 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.894 * [backup-simplify]: Simplify (- 1/2) into -1/2
13.894 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
13.895 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
13.896 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))
13.896 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) in k
13.896 * [taylor]: Taking taylor expansion of (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) in k
13.896 * [taylor]: Taking taylor expansion of (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI))) in k
13.896 * [taylor]: Taking taylor expansion of (- 1/2 (* 1/2 (/ 1 k))) in k
13.896 * [taylor]: Taking taylor expansion of 1/2 in k
13.896 * [backup-simplify]: Simplify 1/2 into 1/2
13.896 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.896 * [taylor]: Taking taylor expansion of 1/2 in k
13.896 * [backup-simplify]: Simplify 1/2 into 1/2
13.896 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.896 * [taylor]: Taking taylor expansion of k in k
13.896 * [backup-simplify]: Simplify 0 into 0
13.896 * [backup-simplify]: Simplify 1 into 1
13.896 * [backup-simplify]: Simplify (/ 1 1) into 1
13.896 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
13.896 * [taylor]: Taking taylor expansion of (* 2 PI) in k
13.896 * [taylor]: Taking taylor expansion of 2 in k
13.896 * [backup-simplify]: Simplify 2 into 2
13.896 * [taylor]: Taking taylor expansion of PI in k
13.896 * [backup-simplify]: Simplify PI into PI
13.897 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.897 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.898 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.898 * [backup-simplify]: Simplify (- 1/2) into -1/2
13.898 * [backup-simplify]: Simplify (+ 0 -1/2) into -1/2
13.899 * [backup-simplify]: Simplify (* -1/2 (log (* 2 PI))) into (* -1/2 (log (* 2 PI)))
13.900 * [backup-simplify]: Simplify (exp (* (- 1/2 (* 1/2 (/ 1 k))) (log (* 2 PI)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))
13.900 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k)))) into (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 k))))
13.900 * [backup-simplify]: Simplify 0 into 0
13.900 * [backup-simplify]: Simplify 0 into 0
13.900 * [backup-simplify]: Simplify 0 into 0
13.900 * [backup-simplify]: Simplify 0 into 0
13.900 * [backup-simplify]: Simplify 0 into 0
13.900 * [backup-simplify]: Simplify 0 into 0
13.901 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (* 1/2 (/ 1 (/ 1 k))))) into (pow (* 2 PI) (- 1/2 (* 1/2 k)))
13.901 * [backup-simplify]: Simplify (pow (* 2 PI) (- 1/2 (/ (/ 1 (- k)) 2))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))
13.901 * [approximate]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in (k) around 0
13.901 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in k
13.901 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k
13.901 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k
13.901 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
13.901 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.901 * [taylor]: Taking taylor expansion of 1/2 in k
13.901 * [backup-simplify]: Simplify 1/2 into 1/2
13.901 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.901 * [taylor]: Taking taylor expansion of k in k
13.901 * [backup-simplify]: Simplify 0 into 0
13.901 * [backup-simplify]: Simplify 1 into 1
13.902 * [backup-simplify]: Simplify (/ 1 1) into 1
13.902 * [taylor]: Taking taylor expansion of 1/2 in k
13.902 * [backup-simplify]: Simplify 1/2 into 1/2
13.902 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
13.902 * [taylor]: Taking taylor expansion of (* 2 PI) in k
13.902 * [taylor]: Taking taylor expansion of 2 in k
13.902 * [backup-simplify]: Simplify 2 into 2
13.902 * [taylor]: Taking taylor expansion of PI in k
13.902 * [backup-simplify]: Simplify PI into PI
13.902 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.903 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.903 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.904 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.905 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
13.905 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))
13.905 * [taylor]: Taking taylor expansion of (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) in k
13.905 * [taylor]: Taking taylor expansion of (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) in k
13.905 * [taylor]: Taking taylor expansion of (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI))) in k
13.905 * [taylor]: Taking taylor expansion of (+ (* 1/2 (/ 1 k)) 1/2) in k
13.905 * [taylor]: Taking taylor expansion of (* 1/2 (/ 1 k)) in k
13.905 * [taylor]: Taking taylor expansion of 1/2 in k
13.905 * [backup-simplify]: Simplify 1/2 into 1/2
13.905 * [taylor]: Taking taylor expansion of (/ 1 k) in k
13.905 * [taylor]: Taking taylor expansion of k in k
13.905 * [backup-simplify]: Simplify 0 into 0
13.905 * [backup-simplify]: Simplify 1 into 1
13.906 * [backup-simplify]: Simplify (/ 1 1) into 1
13.906 * [taylor]: Taking taylor expansion of 1/2 in k
13.906 * [backup-simplify]: Simplify 1/2 into 1/2
13.906 * [taylor]: Taking taylor expansion of (log (* 2 PI)) in k
13.906 * [taylor]: Taking taylor expansion of (* 2 PI) in k
13.906 * [taylor]: Taking taylor expansion of 2 in k
13.906 * [backup-simplify]: Simplify 2 into 2
13.906 * [taylor]: Taking taylor expansion of PI in k
13.906 * [backup-simplify]: Simplify PI into PI
13.906 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.907 * [backup-simplify]: Simplify (log (* 2 PI)) into (log (* 2 PI))
13.907 * [backup-simplify]: Simplify (* 1/2 1) into 1/2
13.907 * [backup-simplify]: Simplify (+ 1/2 0) into 1/2
13.908 * [backup-simplify]: Simplify (* 1/2 (log (* 2 PI))) into (* 1/2 (log (* 2 PI)))
13.909 * [backup-simplify]: Simplify (exp (* (+ (* 1/2 (/ 1 k)) 1/2) (log (* 2 PI)))) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))
13.910 * [backup-simplify]: Simplify (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2)) into (pow (* 2 PI) (+ (* 1/2 (/ 1 k)) 1/2))
13.910 * [backup-simplify]: Simplify 0 into 0
13.910 * [backup-simplify]: Simplify 0 into 0
13.910 * [backup-simplify]: Simplify 0 into 0
13.910 * [backup-simplify]: Simplify 0 into 0
13.910 * [backup-simplify]: Simplify 0 into 0
13.910 * [backup-simplify]: Simplify 0 into 0
13.910 * [backup-simplify]: Simplify (pow (* 2 PI) (+ (* 1/2 (/ 1 (/ 1 (- k)))) 1/2)) into (pow (* 2 PI) (- 1/2 (* 1/2 k)))
13.910 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1 1)
13.911 * [backup-simplify]: Simplify (* n (* 2 PI)) into (* 2 (* n PI))
13.911 * [approximate]: Taking taylor expansion of (* 2 (* n PI)) in (n) around 0
13.911 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.911 * [taylor]: Taking taylor expansion of 2 in n
13.911 * [backup-simplify]: Simplify 2 into 2
13.911 * [taylor]: Taking taylor expansion of (* n PI) in n
13.911 * [taylor]: Taking taylor expansion of n in n
13.911 * [backup-simplify]: Simplify 0 into 0
13.911 * [backup-simplify]: Simplify 1 into 1
13.911 * [taylor]: Taking taylor expansion of PI in n
13.911 * [backup-simplify]: Simplify PI into PI
13.911 * [taylor]: Taking taylor expansion of (* 2 (* n PI)) in n
13.911 * [taylor]: Taking taylor expansion of 2 in n
13.911 * [backup-simplify]: Simplify 2 into 2
13.911 * [taylor]: Taking taylor expansion of (* n PI) in n
13.911 * [taylor]: Taking taylor expansion of n in n
13.911 * [backup-simplify]: Simplify 0 into 0
13.911 * [backup-simplify]: Simplify 1 into 1
13.911 * [taylor]: Taking taylor expansion of PI in n
13.911 * [backup-simplify]: Simplify PI into PI
13.911 * [backup-simplify]: Simplify (* 0 PI) into 0
13.912 * [backup-simplify]: Simplify (* 2 0) into 0
13.912 * [backup-simplify]: Simplify 0 into 0
13.913 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
13.913 * [backup-simplify]: Simplify (+ (* 2 PI) (* 0 0)) into (* 2 PI)
13.914 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.914 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
13.915 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 PI) (* 0 0))) into 0
13.915 * [backup-simplify]: Simplify 0 into 0
13.916 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
13.917 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
13.918 * [backup-simplify]: Simplify 0 into 0
13.919 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.920 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
13.920 * [backup-simplify]: Simplify 0 into 0
13.922 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.923 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
13.923 * [backup-simplify]: Simplify 0 into 0
13.925 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.927 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
13.927 * [backup-simplify]: Simplify 0 into 0
13.929 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
13.931 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
13.931 * [backup-simplify]: Simplify 0 into 0
13.931 * [backup-simplify]: Simplify (* (* 2 PI) n) into (* 2 (* n PI))
13.932 * [backup-simplify]: Simplify (* (/ 1 n) (* 2 PI)) into (* 2 (/ PI n))
13.932 * [approximate]: Taking taylor expansion of (* 2 (/ PI n)) in (n) around 0
13.932 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.932 * [taylor]: Taking taylor expansion of 2 in n
13.932 * [backup-simplify]: Simplify 2 into 2
13.932 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.932 * [taylor]: Taking taylor expansion of PI in n
13.932 * [backup-simplify]: Simplify PI into PI
13.932 * [taylor]: Taking taylor expansion of n in n
13.932 * [backup-simplify]: Simplify 0 into 0
13.932 * [backup-simplify]: Simplify 1 into 1
13.932 * [backup-simplify]: Simplify (/ PI 1) into PI
13.932 * [taylor]: Taking taylor expansion of (* 2 (/ PI n)) in n
13.932 * [taylor]: Taking taylor expansion of 2 in n
13.932 * [backup-simplify]: Simplify 2 into 2
13.932 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.933 * [taylor]: Taking taylor expansion of PI in n
13.933 * [backup-simplify]: Simplify PI into PI
13.933 * [taylor]: Taking taylor expansion of n in n
13.933 * [backup-simplify]: Simplify 0 into 0
13.933 * [backup-simplify]: Simplify 1 into 1
13.933 * [backup-simplify]: Simplify (/ PI 1) into PI
13.934 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.934 * [backup-simplify]: Simplify (* 2 PI) into (* 2 PI)
13.935 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.936 * [backup-simplify]: Simplify (+ (* 2 0) (* 0 PI)) into 0
13.936 * [backup-simplify]: Simplify 0 into 0
13.937 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.938 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (* 0 PI))) into 0
13.938 * [backup-simplify]: Simplify 0 into 0
13.939 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.940 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.940 * [backup-simplify]: Simplify 0 into 0
13.941 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.942 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.942 * [backup-simplify]: Simplify 0 into 0
13.943 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.945 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.945 * [backup-simplify]: Simplify 0 into 0
13.946 * [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
13.948 * [backup-simplify]: Simplify (+ (* 2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.948 * [backup-simplify]: Simplify 0 into 0
13.948 * [backup-simplify]: Simplify (* (* 2 PI) (/ 1 (/ 1 n))) into (* 2 (* n PI))
13.949 * [backup-simplify]: Simplify (* (/ 1 (- n)) (* 2 PI)) into (* -2 (/ PI n))
13.949 * [approximate]: Taking taylor expansion of (* -2 (/ PI n)) in (n) around 0
13.949 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.949 * [taylor]: Taking taylor expansion of -2 in n
13.949 * [backup-simplify]: Simplify -2 into -2
13.949 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.949 * [taylor]: Taking taylor expansion of PI in n
13.949 * [backup-simplify]: Simplify PI into PI
13.949 * [taylor]: Taking taylor expansion of n in n
13.949 * [backup-simplify]: Simplify 0 into 0
13.949 * [backup-simplify]: Simplify 1 into 1
13.950 * [backup-simplify]: Simplify (/ PI 1) into PI
13.950 * [taylor]: Taking taylor expansion of (* -2 (/ PI n)) in n
13.950 * [taylor]: Taking taylor expansion of -2 in n
13.950 * [backup-simplify]: Simplify -2 into -2
13.950 * [taylor]: Taking taylor expansion of (/ PI n) in n
13.950 * [taylor]: Taking taylor expansion of PI in n
13.950 * [backup-simplify]: Simplify PI into PI
13.950 * [taylor]: Taking taylor expansion of n in n
13.950 * [backup-simplify]: Simplify 0 into 0
13.950 * [backup-simplify]: Simplify 1 into 1
13.950 * [backup-simplify]: Simplify (/ PI 1) into PI
13.951 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.951 * [backup-simplify]: Simplify (* -2 PI) into (* -2 PI)
13.952 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
13.953 * [backup-simplify]: Simplify (+ (* -2 0) (* 0 PI)) into 0
13.953 * [backup-simplify]: Simplify 0 into 0
13.958 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.959 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (* 0 PI))) into 0
13.959 * [backup-simplify]: Simplify 0 into 0
13.960 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.961 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
13.962 * [backup-simplify]: Simplify 0 into 0
13.963 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.964 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
13.964 * [backup-simplify]: Simplify 0 into 0
13.965 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
13.967 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
13.967 * [backup-simplify]: Simplify 0 into 0
13.968 * [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
13.969 * [backup-simplify]: Simplify (+ (* -2 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
13.969 * [backup-simplify]: Simplify 0 into 0
13.970 * [backup-simplify]: Simplify (* (* -2 PI) (/ 1 (/ 1 (- n)))) into (* 2 (* n PI))
13.970 * * * [progress]: simplifying candidates
13.970 * * * * [progress]: [ 1 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (exp (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.970 * * * * [progress]: [ 2 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (exp (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.970 * * * * [progress]: [ 3 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.971 * * * * [progress]: [ 4 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (exp (* (log (* n (* 2 PI))) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.971 * * * * [progress]: [ 5 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.971 * * * * [progress]: [ 6 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.971 * * * * [progress]: [ 7 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (* 1 (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.971 * * * * [progress]: [ 8 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (/ (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.971 * * * * [progress]: [ 9 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.971 * * * * [progress]: [ 10 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.971 * * * * [progress]: [ 11 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.971 * * * * [progress]: [ 12 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.971 * * * * [progress]: [ 13 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.971 * * * * [progress]: [ 14 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.971 * * * * [progress]: [ 15 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.971 * * * * [progress]: [ 16 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (* (pow (* n (* 2 PI)) 1/2) (pow (* n (* 2 PI)) (- (/ k 2))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.971 * * * * [progress]: [ 17 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.971 * * * * [progress]: [ 18 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) 1)) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.972 * * * * [progress]: [ 19 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (exp (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.972 * * * * [progress]: [ 20 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (log (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.972 * * * * [progress]: [ 21 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (* (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.972 * * * * [progress]: [ 22 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (cbrt (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.972 * * * * [progress]: [ 23 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (* (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.972 * * * * [progress]: [ 24 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (* 1 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.972 * * * * [progress]: [ 25 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.972 * * * * [progress]: [ 26 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (posit16->real (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.972 * * * * [progress]: [ 27 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (exp (* (log n) (- 1/2 (/ k 2)))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.972 * * * * [progress]: [ 28 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (exp (* (log n) (- 1/2 (/ k 2)))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.972 * * * * [progress]: [ 29 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (* 1 (- 1/2 (/ k 2)))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.972 * * * * [progress]: [ 30 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (/ (pow n 1/2) (pow n (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.972 * * * * [progress]: [ 31 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow (pow n (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.972 * * * * [progress]: [ 32 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow (pow n (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.972 * * * * [progress]: [ 33 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow (pow n 1) (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.973 * * * * [progress]: [ 34 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow (pow n (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.973 * * * * [progress]: [ 35 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow (pow n (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.973 * * * * [progress]: [ 36 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow (pow n 1) (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.973 * * * * [progress]: [ 37 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (* (pow n 1/2) (pow n (- (/ k 2)))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.973 * * * * [progress]: [ 38 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (* (pow n 1/2) (pow n (- (/ k 2)))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.973 * * * * [progress]: [ 39 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (* (pow (* (cbrt n) (cbrt n)) (- 1/2 (/ k 2))) (pow (cbrt n) (- 1/2 (/ k 2)))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.973 * * * * [progress]: [ 40 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (* (pow (sqrt n) (- 1/2 (/ k 2))) (pow (sqrt n) (- 1/2 (/ k 2)))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.973 * * * * [progress]: [ 41 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (* (pow 1 (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.973 * * * * [progress]: [ 42 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow (pow n (- 1/2 (/ k 2))) 1) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.973 * * * * [progress]: [ 43 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (exp (log (pow n (- 1/2 (/ k 2))))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.973 * * * * [progress]: [ 44 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (log (exp (pow n (- 1/2 (/ k 2))))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.973 * * * * [progress]: [ 45 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (* (* (cbrt (pow n (- 1/2 (/ k 2)))) (cbrt (pow n (- 1/2 (/ k 2))))) (cbrt (pow n (- 1/2 (/ k 2))))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.973 * * * * [progress]: [ 46 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (cbrt (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2))))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.974 * * * * [progress]: [ 47 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (* (sqrt (pow n (- 1/2 (/ k 2)))) (sqrt (pow n (- 1/2 (/ k 2))))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.974 * * * * [progress]: [ 48 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (* 1 (pow n (- 1/2 (/ k 2)))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.974 * * * * [progress]: [ 49 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow n (/ (- 1/2 (/ k 2)) 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.974 * * * * [progress]: [ 50 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (posit16->real (real->posit16 (pow n (- 1/2 (/ k 2))))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.974 * * * * [progress]: [ 51 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (exp (* (+ (log 2) (log PI)) (- 1/2 (/ k 2)))))))))>
13.974 * * * * [progress]: [ 52 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (exp (* (log (* 2 PI)) (- 1/2 (/ k 2)))))))))>
13.974 * * * * [progress]: [ 53 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (exp (* (log (* 2 PI)) (- 1/2 (/ k 2)))))))))>
13.974 * * * * [progress]: [ 54 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (* 1 (- 1/2 (/ k 2)))))))))>
13.974 * * * * [progress]: [ 55 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (* 1 (- 1/2 (/ k 2)))))))))>
13.974 * * * * [progress]: [ 56 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (/ (pow (* 2 PI) 1/2) (pow (* 2 PI) (/ k 2))))))))>
13.974 * * * * [progress]: [ 57 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (pow (* 2 PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))))))))>
13.974 * * * * [progress]: [ 58 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (pow (* 2 PI) (sqrt (- 1/2 (/ k 2)))) (sqrt (- 1/2 (/ k 2)))))))))>
13.974 * * * * [progress]: [ 59 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (pow (* 2 PI) 1) (- 1/2 (/ k 2))))))))>
13.974 * * * * [progress]: [ 60 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (pow (* 2 PI) (+ (sqrt 1/2) (sqrt (/ k 2)))) (- (sqrt 1/2) (sqrt (/ k 2)))))))))>
13.975 * * * * [progress]: [ 61 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (pow (* 2 PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2)))) (- (sqrt 1/2) (/ (sqrt k) (sqrt 2)))))))))>
13.975 * * * * [progress]: [ 62 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (pow (* 2 PI) 1) (- 1/2 (/ k 2))))))))>
13.975 * * * * [progress]: [ 63 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (* (pow (* 2 PI) 1/2) (pow (* 2 PI) (- (/ k 2)))))))))>
13.975 * * * * [progress]: [ 64 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (* (pow (* 2 PI) 1/2) (pow (* 2 PI) (- (/ k 2)))))))))>
13.975 * * * * [progress]: [ 65 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (* (pow 2 (- 1/2 (/ k 2))) (pow PI (- 1/2 (/ k 2)))))))))>
13.975 * * * * [progress]: [ 66 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (pow (* 2 PI) (- 1/2 (/ k 2))) 1))))))>
13.975 * * * * [progress]: [ 67 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (exp (log (pow (* 2 PI) (- 1/2 (/ k 2))))))))))>
13.975 * * * * [progress]: [ 68 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (log (exp (pow (* 2 PI) (- 1/2 (/ k 2))))))))))>
13.975 * * * * [progress]: [ 69 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (* (* (cbrt (pow (* 2 PI) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 PI) (- 1/2 (/ k 2))))) (cbrt (pow (* 2 PI) (- 1/2 (/ k 2))))))))))>
13.975 * * * * [progress]: [ 70 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (cbrt (* (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2)))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))))>
13.975 * * * * [progress]: [ 71 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (* (sqrt (pow (* 2 PI) (- 1/2 (/ k 2)))) (sqrt (pow (* 2 PI) (- 1/2 (/ k 2))))))))))>
13.975 * * * * [progress]: [ 72 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (* 1 (pow (* 2 PI) (- 1/2 (/ k 2)))))))))>
13.976 * * * * [progress]: [ 73 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (* (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))))))))>
13.976 * * * * [progress]: [ 74 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (posit16->real (real->posit16 (pow (* 2 PI) (- 1/2 (/ k 2))))))))))>
13.976 * * * * [progress]: [ 75 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.976 * * * * [progress]: [ 76 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.976 * * * * [progress]: [ 77 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (pow (* n (* 2 PI)) 1) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.976 * * * * [progress]: [ 78 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (exp (+ (log n) (+ (log 2) (log PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.976 * * * * [progress]: [ 79 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (exp (+ (log n) (log (* 2 PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.976 * * * * [progress]: [ 80 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (exp (log (* n (* 2 PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.976 * * * * [progress]: [ 81 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (log (exp (* n (* 2 PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.976 * * * * [progress]: [ 82 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (cbrt (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.976 * * * * [progress]: [ 83 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (cbrt (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.976 * * * * [progress]: [ 84 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (cbrt (* n (* 2 PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.976 * * * * [progress]: [ 85 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (cbrt (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.976 * * * * [progress]: [ 86 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* (sqrt (* n (* 2 PI))) (sqrt (* n (* 2 PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.977 * * * * [progress]: [ 87 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.977 * * * * [progress]: [ 88 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* (* n 2) PI) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.977 * * * * [progress]: [ 89 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* (* (cbrt n) (cbrt n)) (* (cbrt n) (* 2 PI))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.977 * * * * [progress]: [ 90 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* (sqrt n) (* (sqrt n) (* 2 PI))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.977 * * * * [progress]: [ 91 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* 1 (* n (* 2 PI))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.977 * * * * [progress]: [ 92 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (posit16->real (real->posit16 (* n (* 2 PI)))) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.977 * * * * [progress]: [ 93 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* (* 2 PI) n) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.977 * * * * [progress]: [ 94 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.977 * * * * [progress]: [ 95 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.977 * * * * [progress]: [ 96 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.977 * * * * [progress]: [ 97 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (- (+ (pow n 1/2) (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2))))) (* 1/2 (* (sqrt n) (* (log n) k)))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.977 * * * * [progress]: [ 98 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n))))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.977 * * * * [progress]: [ 99 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n))))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.978 * * * * [progress]: [ 100 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (- (+ (* 1/8 (* (* (sqrt 2) (* (pow k 2) (pow (log (* 2 PI)) 2))) (sqrt PI))) (pow (* 2 PI) 1/2)) (* 1/2 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI)))))))))>
13.978 * * * * [progress]: [ 101 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (* 1/2 k))))))))>
13.978 * * * * [progress]: [ 102 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (* 1/2 k))))))))>
13.978 * * * * [progress]: [ 103 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.978 * * * * [progress]: [ 104 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.978 * * * * [progress]: [ 105 / 105 ] simplifiying candidate #<alt (λ (k n) (/ (sqrt (pow (* 2 (* n PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))>
13.980 * [simplify]: Simplifying:
  (* (+ (log n) (+ (log 2) (log PI))) (- 1/2 (/ k 2)))
  (* (+ (log n) (log (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* (log (* n (* 2 PI))) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (/ k 2))
  (pow (* n (* 2 PI)) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* n (* 2 PI)) (sqrt (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* n (* 2 PI)) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* n (* 2 PI)) 1)
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow (* n (* 2 PI)) 1/2)
  (pow (* n (* 2 PI)) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* 2 PI) (- 1/2 (/ k 2)))
  (log (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (exp (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
  (cbrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (* (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
  (* (log n) (- 1/2 (/ k 2)))
  (* (log n) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow n 1/2)
  (pow n (/ k 2))
  (pow n (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow n (sqrt (- 1/2 (/ k 2))))
  (pow n 1)
  (pow n (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow n (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow n 1)
  (pow n 1/2)
  (pow n (- (/ k 2)))
  (pow n 1/2)
  (pow n (- (/ k 2)))
  (pow (* (cbrt n) (cbrt n)) (- 1/2 (/ k 2)))
  (pow (cbrt n) (- 1/2 (/ k 2)))
  (pow (sqrt n) (- 1/2 (/ k 2)))
  (pow (sqrt n) (- 1/2 (/ k 2)))
  (pow 1 (- 1/2 (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (log (pow n (- 1/2 (/ k 2))))
  (exp (pow n (- 1/2 (/ k 2))))
  (* (cbrt (pow n (- 1/2 (/ k 2)))) (cbrt (pow n (- 1/2 (/ k 2)))))
  (cbrt (pow n (- 1/2 (/ k 2))))
  (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2))))
  (sqrt (pow n (- 1/2 (/ k 2))))
  (sqrt (pow n (- 1/2 (/ k 2))))
  (pow n (/ (- 1/2 (/ k 2)) 2))
  (pow n (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow n (- 1/2 (/ k 2))))
  (* (+ (log 2) (log PI)) (- 1/2 (/ k 2)))
  (* (log (* 2 PI)) (- 1/2 (/ k 2)))
  (* (log (* 2 PI)) (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (* 1 (- 1/2 (/ k 2)))
  (pow (* 2 PI) 1/2)
  (pow (* 2 PI) (/ k 2))
  (pow (* 2 PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* 2 PI) (sqrt (- 1/2 (/ k 2))))
  (pow (* 2 PI) 1)
  (pow (* 2 PI) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* 2 PI) (+ (sqrt 1/2) (/ (sqrt k) (sqrt 2))))
  (pow (* 2 PI) 1)
  (pow (* 2 PI) 1/2)
  (pow (* 2 PI) (- (/ k 2)))
  (pow (* 2 PI) 1/2)
  (pow (* 2 PI) (- (/ k 2)))
  (pow 2 (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (log (pow (* 2 PI) (- 1/2 (/ k 2))))
  (exp (pow (* 2 PI) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* 2 PI) (- 1/2 (/ k 2)))) (cbrt (pow (* 2 PI) (- 1/2 (/ k 2)))))
  (cbrt (pow (* 2 PI) (- 1/2 (/ k 2))))
  (* (* (pow (* 2 PI) (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2)))) (pow (* 2 PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* 2 PI) (- 1/2 (/ k 2))))
  (sqrt (pow (* 2 PI) (- 1/2 (/ k 2))))
  (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))
  (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))
  (real->posit16 (pow (* 2 PI) (- 1/2 (/ k 2))))
  (* n (* 2 PI))
  (* n (* 2 PI))
  (+ (log n) (+ (log 2) (log PI)))
  (+ (log n) (log (* 2 PI)))
  (log (* n (* 2 PI)))
  (exp (* n (* 2 PI)))
  (* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
  (* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
  (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI))))
  (cbrt (* n (* 2 PI)))
  (* (* (* n (* 2 PI)) (* n (* 2 PI))) (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (sqrt (* n (* 2 PI)))
  (* n 2)
  (* (cbrt n) (* 2 PI))
  (* (sqrt n) (* 2 PI))
  (* n (* 2 PI))
  (real->posit16 (* n (* 2 PI)))
  (- (+ (* 1/4 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) (pow k 2))))) (+ (* 1/8 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* 1/8 (* (pow (log (* 2 PI)) 2) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (pow k 2))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) (* (log n) k))) (* 1/2 (* (log (* 2 PI)) (* (exp (* 1/2 (+ (log n) (log (* 2 PI))))) k)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* 2 PI)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log (* -2 PI)) (log (/ -1 n)))))
  (- (+ (pow n 1/2) (* 1/8 (* (sqrt n) (* (pow (log n) 2) (pow k 2))))) (* 1/2 (* (sqrt n) (* (log n) k))))
  (exp (* -1 (* (- 1/2 (* 1/2 k)) (log (/ 1 n)))))
  (exp (* (- 1/2 (* 1/2 k)) (- (log -1) (log (/ -1 n)))))
  (- (+ (* 1/8 (* (* (sqrt 2) (* (pow k 2) (pow (log (* 2 PI)) 2))) (sqrt PI))) (pow (* 2 PI) 1/2)) (* 1/2 (* (* (sqrt 2) (* k (log (* 2 PI)))) (sqrt PI))))
  (pow (* 2 PI) (- 1/2 (* 1/2 k)))
  (pow (* 2 PI) (- 1/2 (* 1/2 k)))
  (* 2 (* n PI))
  (* 2 (* n PI))
  (* 2 (* n PI))
13.983 * * [simplify]: iteration 1: (192 enodes)
14.050 * * [simplify]: iteration 2: (545 enodes)
14.772 * * [simplify]: iteration 3: (1816 enodes)
19.641 * * [simplify]: Extracting #0: cost 73 inf + 0
19.643 * * [simplify]: Extracting #1: cost 551 inf + 2
19.648 * * [simplify]: Extracting #2: cost 1195 inf + 9300
19.663 * * [simplify]: Extracting #3: cost 1495 inf + 43751
19.730 * * [simplify]: Extracting #4: cost 1003 inf + 196011
19.840 * * [simplify]: Extracting #5: cost 249 inf + 459311
19.986 * * [simplify]: Extracting #6: cost 66 inf + 530126
20.116 * * [simplify]: Extracting #7: cost 11 inf + 560207
20.275 * * [simplify]: Extracting #8: cost 0 inf + 566610
20.390 * [simplify]: Simplified to:
  (* (log (* (* PI 2) n)) (- 1/2 (/ k 2)))
  (* (log (* (* PI 2) n)) (- 1/2 (/ k 2)))
  (* (log (* (* PI 2) n)) (- 1/2 (/ k 2)))
  (* (log (* (* PI 2) n)) (- 1/2 (/ k 2)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (/ k 2))
  (pow (* (* PI 2) n) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* (* PI 2) n) (sqrt (- 1/2 (/ k 2))))
  (* (* PI 2) n)
  (pow (* (* PI 2) n) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* (* PI 2) n) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* (* PI 2) n)
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (- (/ k 2)))
  (sqrt (* (* PI 2) n))
  (pow (* (* PI 2) n) (- (/ k 2)))
  (pow n (- 1/2 (/ k 2)))
  (pow (* PI 2) (- 1/2 (* k 1/2)))
  (* (log (* (* PI 2) n)) (- 1/2 (/ k 2)))
  (exp (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))) (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2)))))
  (cbrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (pow (pow (* (* PI 2) n) (- 1/2 (/ k 2))) 3)
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (sqrt (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (pow (* (* PI 2) n) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* (* PI 2) n) (- 1/2 (/ k 2))))
  (* (log n) (- 1/2 (/ k 2)))
  (* (log n) (- 1/2 (/ k 2)))
  (- 1/2 (/ k 2))
  (sqrt n)
  (pow n (/ k 2))
  (pow n (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow n (sqrt (- 1/2 (/ k 2))))
  n
  (pow n (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow n (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  n
  (sqrt n)
  (pow n (- (/ k 2)))
  (sqrt n)
  (pow n (- (/ k 2)))
  (pow (* (cbrt n) (cbrt n)) (- 1/2 (/ k 2)))
  (pow (cbrt n) (- 1/2 (/ k 2)))
  (pow (sqrt n) (- 1/2 (/ k 2)))
  (pow (sqrt n) (- 1/2 (/ k 2)))
  1
  (pow n (- 1/2 (/ k 2)))
  (* (log n) (- 1/2 (/ k 2)))
  (exp (pow n (- 1/2 (/ k 2))))
  (* (cbrt (pow n (- 1/2 (/ k 2)))) (cbrt (pow n (- 1/2 (/ k 2)))))
  (cbrt (pow n (- 1/2 (/ k 2))))
  (* (* (pow n (- 1/2 (/ k 2))) (pow n (- 1/2 (/ k 2)))) (pow n (- 1/2 (/ k 2))))
  (fabs (pow n (- 1/4 (/ k 4))))
  (fabs (pow n (- 1/4 (/ k 4))))
  (pow n (- 1/4 (/ k 4)))
  (pow n (- 1/4 (/ k 4)))
  (real->posit16 (pow n (- 1/2 (/ k 2))))
  (* (log (* PI 2)) (- 1/2 (/ k 2)))
  (* (log (* PI 2)) (- 1/2 (/ k 2)))
  (* (log (* PI 2)) (- 1/2 (/ k 2)))
  (- 1/2 (/ k 2))
  (- 1/2 (/ k 2))
  (sqrt (* PI 2))
  (pow (* PI 2) (/ k 2))
  (pow (* PI 2) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2)))))
  (pow (* PI 2) (sqrt (- 1/2 (/ k 2))))
  (* PI 2)
  (pow (* PI 2) (+ (sqrt 1/2) (sqrt (/ k 2))))
  (pow (* PI 2) (+ (/ (sqrt k) (sqrt 2)) (sqrt 1/2)))
  (* PI 2)
  (sqrt (* PI 2))
  (pow (* PI 2) (- (/ k 2)))
  (sqrt (* PI 2))
  (pow (* PI 2) (- (/ k 2)))
  (pow 2 (- 1/2 (/ k 2)))
  (pow PI (- 1/2 (/ k 2)))
  (* (log (* PI 2)) (- 1/2 (/ k 2)))
  (exp (pow (* PI 2) (- 1/2 (* k 1/2))))
  (* (cbrt (pow (* PI 2) (- 1/2 (* k 1/2)))) (cbrt (pow (* PI 2) (- 1/2 (* k 1/2)))))
  (cbrt (pow (* PI 2) (- 1/2 (* k 1/2))))
  (* (pow (* PI 2) (- 1/2 (* k 1/2))) (* (pow (* PI 2) (- 1/2 (* k 1/2))) (pow (* PI 2) (- 1/2 (* k 1/2)))))
  (sqrt (pow (* PI 2) (- 1/2 (* k 1/2))))
  (sqrt (pow (* PI 2) (- 1/2 (* k 1/2))))
  (pow (* PI 2) (- 1/4 (/ k 4)))
  (pow (* PI 2) (- 1/4 (/ k 4)))
  (real->posit16 (pow (* PI 2) (- 1/2 (* k 1/2))))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (log (* (* PI 2) n))
  (exp (+ (* PI n) (* PI n)))
  (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n))
  (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n))
  (* (cbrt (* (* PI 2) n)) (cbrt (* (* PI 2) n)))
  (cbrt (* (* PI 2) n))
  (* (* (* (* PI 2) n) (* (* PI 2) n)) (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (sqrt (* (* PI 2) n))
  (* n 2)
  (* (cbrt n) (* PI 2))
  (* (* PI 2) (sqrt n))
  (* (* PI 2) n)
  (real->posit16 (* (* PI 2) n))
  (+ (+ (* (* (* k k) (* (sqrt (* (* PI 2) n)) 1/8)) (* (log n) (log n))) (sqrt (* (* PI 2) n))) (- (* (* k k) (+ (* (* (log (* PI 2)) (log (* PI 2))) (* (sqrt (* (* PI 2) n)) 1/8)) (* 1/4 (* (* (log n) (sqrt (* (* PI 2) n))) (log (* PI 2)))))) (* (* k 1/2) (+ (* (log n) (sqrt (* (* PI 2) n))) (* (sqrt (* (* PI 2) n)) (log (* PI 2)))))))
  (exp (* (- 1/2 (* k 1/2)) (log (* (* PI 2) n))))
  (exp (* (- (log (* PI -2)) (log (/ -1 n))) (- 1/2 (* k 1/2))))
  (+ (sqrt n) (* (sqrt n) (- (* (* (* (log n) k) (* (log n) k)) 1/8) (* k (* (log n) 1/2)))))
  (exp (* (log n) (- 1/2 (* k 1/2))))
  (exp (* (- 1/2 (* k 1/2)) (+ 0 (log n))))
  (+ (sqrt (* PI 2)) (* (sqrt PI) (+ (* (* (* 1/8 (sqrt 2)) (* (log (* PI 2)) k)) (* (log (* PI 2)) k)) (* -1/2 (* (sqrt 2) (* (log (* PI 2)) k))))))
  (pow (* PI 2) (- 1/2 (* k 1/2)))
  (pow (* PI 2) (- 1/2 (* k 1/2)))
  (* (* PI 2) n)
  (* (* PI 2) n)
  (* (* PI 2) n)
20.402 * * * [progress]: adding candidates to table
22.175 * [progress]: [Phase 3 of 3] Extracting.
22.175 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ (sqrt (* n (* 2 PI))) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))> #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))> #<alt (λ (k n) (* (/ 1 (fabs (cbrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (pow (* 2 PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))))))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>)
22.177 * * * [regime-changes]: Trying 4 branch expressions: ((* (* 2 PI) n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) n k)
22.177 * * * * [regimes]: Trying to branch on (* (* 2 PI) n) from (#<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ (sqrt (* n (* 2 PI))) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))> #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))> #<alt (λ (k n) (* (/ 1 (fabs (cbrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (pow (* 2 PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))))))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>)
22.249 * * * * [regimes]: Trying to branch on (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) from (#<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ (sqrt (* n (* 2 PI))) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))> #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))> #<alt (λ (k n) (* (/ 1 (fabs (cbrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (pow (* 2 PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))))))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>)
22.353 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ (sqrt (* n (* 2 PI))) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))> #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))> #<alt (λ (k n) (* (/ 1 (fabs (cbrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (pow (* 2 PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))))))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>)
22.404 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (sqrt (sqrt k))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (sqrt (sqrt k)))))> #<alt (λ (k n) (/ (sqrt (* n (* 2 PI))) (* (sqrt k) (pow (* n (* 2 PI)) (/ k 2)))))> #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (* 2 PI) (- 1/2 (/ k 2))))))))> #<alt (λ (k n) (* (/ 1 (fabs (cbrt k))) (/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt (cbrt k)))))> #<alt (λ (k n) (* (/ (sqrt (* (* PI 2) n)) (* (cbrt (sqrt k)) (cbrt (sqrt k)))) (/ (pow (* (* PI 2) n) (- (/ k 2))) (cbrt (sqrt k)))))> #<alt (λ (k n) (/ (sqrt (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))) (/ (sqrt k) (sqrt (* (pow n (- 1/2 (/ k 2))) (pow (pow (* 2 PI) (* (cbrt (- 1/2 (/ k 2))) (cbrt (- 1/2 (/ k 2))))) (cbrt (- 1/2 (/ k 2)))))))))> #<alt (λ (k n) (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))> #<alt (λ (k n) (* (/ (pow n (- 1/2 (/ k 2))) (sqrt (sqrt k))) (/ (pow (* 2 PI) (- 1/2 (/ k 2))) (sqrt (sqrt k)))))>)
22.473 * * * [regime]: Found split indices: #<option (#s(si 6 255))>
22.473 * [simplify]: Simplifying:
  (* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
22.473 * * [simplify]: iteration 1: (13 enodes)
22.476 * * [simplify]: iteration 2: (16 enodes)
22.477 * * [simplify]: Extracting #0: cost 1 inf + 0
22.478 * * [simplify]: Extracting #1: cost 3 inf + 0
22.478 * * [simplify]: Extracting #2: cost 7 inf + 0
22.478 * * [simplify]: Extracting #3: cost 11 inf + 1
22.478 * * [simplify]: Extracting #4: cost 5 inf + 252
22.478 * * [simplify]: Extracting #5: cost 4 inf + 253
22.478 * * [simplify]: Extracting #6: cost 1 inf + 753
22.478 * * [simplify]: Extracting #7: cost 0 inf + 1248
22.479 * [simplify]: Simplified to:
  (* (/ 1 (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
31.060 * [regime-testing]: Baseline error score: 0.3728699545150107
31.065 * [regime-testing]: Oracle error score: 0.02679583072920173
31.070 * [regime-testing]: End program error score: 0.3728699545150107