50.729 * [progress]: [Phase 1 of 3] Setting up.
0.002 * * * [progress]: [1/2] Preparing points
0.178 * * * [progress]: [2/2] Setting up program.
0.186 * [progress]: [Phase 2 of 3] Improving.
0.187 * [simplify]: Simplifying:
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.187 * * [simplify]: iteration 0: 13 enodes
0.220 * * [simplify]: iteration 1: 29 enodes
0.225 * * [simplify]: iteration 2: 59 enodes
0.237 * * [simplify]: iteration 3: 120 enodes
0.279 * * [simplify]: iteration 4: 328 enodes
0.525 * * [simplify]: iteration 5: 1551 enodes
1.111 * * [simplify]: iteration complete: 5000 enodes
1.111 * * [simplify]: Extracting #0: cost 1 inf + 0
1.111 * * [simplify]: Extracting #1: cost 126 inf + 0
1.114 * * [simplify]: Extracting #2: cost 1587 inf + 1
1.119 * * [simplify]: Extracting #3: cost 2139 inf + 128
1.128 * * [simplify]: Extracting #4: cost 2273 inf + 2329
1.159 * * [simplify]: Extracting #5: cost 1683 inf + 209087
1.332 * * [simplify]: Extracting #6: cost 131 inf + 1062869
1.499 * * [simplify]: Extracting #7: cost 0 inf + 1169132
1.700 * [simplify]: Simplified to:
  (* (/ 1.0 (sqrt k)) (pow (* PI (* n 2.0)) (/ (- 1.0 k) 2.0)))
1.701 * * [progress]: iteration 1 / 4
1.701 * * * [progress]: picking best candidate
1.708 * * * * [pick]: Picked  #<alt (λ (k n) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))>
1.708 * * * [progress]: localizing error
1.750 * * * [progress]: generating rewritten candidates
1.750 * * * * [progress]: [ 1 / 4 ] rewriting at (2 1)
1.759 * * * * [progress]: [ 2 / 4 ] rewriting at (2 2 1)
1.783 * * * * [progress]: [ 3 / 4 ] rewriting at (2)
1.831 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2)
1.866 * * * [progress]: generating series expansions
1.866 * * * * [progress]: [ 1 / 4 ] generating series at (2 1)
1.867 * [backup-simplify]: Simplify (/ 1.0 (sqrt k)) into (* 1.0 (sqrt (/ 1 k)))
1.867 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in (k) around 0
1.867 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
1.867 * [taylor]: Taking taylor expansion of 1.0 in k
1.867 * [backup-simplify]: Simplify 1.0 into 1.0
1.867 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
1.867 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.867 * [taylor]: Taking taylor expansion of k in k
1.867 * [backup-simplify]: Simplify 0 into 0
1.867 * [backup-simplify]: Simplify 1 into 1
1.868 * [backup-simplify]: Simplify (/ 1 1) into 1
1.868 * [backup-simplify]: Simplify (sqrt 0) into 0
1.870 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
1.870 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt (/ 1 k))) in k
1.870 * [taylor]: Taking taylor expansion of 1.0 in k
1.870 * [backup-simplify]: Simplify 1.0 into 1.0
1.870 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
1.870 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.870 * [taylor]: Taking taylor expansion of k in k
1.870 * [backup-simplify]: Simplify 0 into 0
1.870 * [backup-simplify]: Simplify 1 into 1
1.871 * [backup-simplify]: Simplify (/ 1 1) into 1
1.871 * [backup-simplify]: Simplify (sqrt 0) into 0
1.872 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
1.873 * [backup-simplify]: Simplify (* 1.0 0) into 0
1.873 * [backup-simplify]: Simplify 0 into 0
1.875 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
1.875 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
1.877 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
1.881 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
1.883 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
1.883 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
1.885 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.889 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
1.892 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
1.892 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
1.894 * [backup-simplify]: Simplify (+ (* (- +nan.0) (pow k 2)) (+ (* (- +nan.0) k) (- +nan.0))) into (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
1.894 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 k))) into (* 1.0 (sqrt k))
1.894 * [approximate]: Taking taylor expansion of (* 1.0 (sqrt k)) in (k) around 0
1.894 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
1.894 * [taylor]: Taking taylor expansion of 1.0 in k
1.894 * [backup-simplify]: Simplify 1.0 into 1.0
1.894 * [taylor]: Taking taylor expansion of (sqrt k) in k
1.894 * [taylor]: Taking taylor expansion of k in k
1.894 * [backup-simplify]: Simplify 0 into 0
1.894 * [backup-simplify]: Simplify 1 into 1
1.895 * [backup-simplify]: Simplify (sqrt 0) into 0
1.896 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
1.896 * [taylor]: Taking taylor expansion of (* 1.0 (sqrt k)) in k
1.896 * [taylor]: Taking taylor expansion of 1.0 in k
1.896 * [backup-simplify]: Simplify 1.0 into 1.0
1.896 * [taylor]: Taking taylor expansion of (sqrt k) in k
1.896 * [taylor]: Taking taylor expansion of k in k
1.896 * [backup-simplify]: Simplify 0 into 0
1.896 * [backup-simplify]: Simplify 1 into 1
1.897 * [backup-simplify]: Simplify (sqrt 0) into 0
1.898 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
1.899 * [backup-simplify]: Simplify (* 1.0 0) into 0
1.899 * [backup-simplify]: Simplify 0 into 0
1.900 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (* 0 0)) into (- +nan.0)
1.901 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
1.903 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
1.907 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- +nan.0)
1.907 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
1.909 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
1.911 * [backup-simplify]: Simplify (+ (* 1.0 +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- +nan.0)
1.911 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
1.912 * [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))))))))
1.912 * [backup-simplify]: Simplify (/ 1.0 (sqrt (/ 1 (- k)))) into (/ 1.0 (sqrt (/ -1 k)))
1.912 * [approximate]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in (k) around 0
1.912 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
1.912 * [taylor]: Taking taylor expansion of 1.0 in k
1.912 * [backup-simplify]: Simplify 1.0 into 1.0
1.912 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
1.912 * [taylor]: Taking taylor expansion of (/ -1 k) in k
1.912 * [taylor]: Taking taylor expansion of -1 in k
1.912 * [backup-simplify]: Simplify -1 into -1
1.912 * [taylor]: Taking taylor expansion of k in k
1.912 * [backup-simplify]: Simplify 0 into 0
1.912 * [backup-simplify]: Simplify 1 into 1
1.913 * [backup-simplify]: Simplify (/ -1 1) into -1
1.913 * [backup-simplify]: Simplify (sqrt 0) into 0
1.914 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
1.914 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
1.914 * [taylor]: Taking taylor expansion of (/ 1.0 (sqrt (/ -1 k))) in k
1.914 * [taylor]: Taking taylor expansion of 1.0 in k
1.914 * [backup-simplify]: Simplify 1.0 into 1.0
1.914 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
1.914 * [taylor]: Taking taylor expansion of (/ -1 k) in k
1.914 * [taylor]: Taking taylor expansion of -1 in k
1.914 * [backup-simplify]: Simplify -1 into -1
1.914 * [taylor]: Taking taylor expansion of k in k
1.914 * [backup-simplify]: Simplify 0 into 0
1.914 * [backup-simplify]: Simplify 1 into 1
1.915 * [backup-simplify]: Simplify (/ -1 1) into -1
1.915 * [backup-simplify]: Simplify (sqrt 0) into 0
1.916 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
1.916 * [backup-simplify]: Simplify (/ 1.0 +nan.0) into +nan.0
1.916 * [backup-simplify]: Simplify +nan.0 into +nan.0
1.916 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
1.918 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
1.920 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)))) into (- +nan.0)
1.920 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
1.921 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.923 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
1.925 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* +nan.0 (/ +nan.0 +nan.0)) (* (- +nan.0) (/ +nan.0 +nan.0)))) into (- +nan.0)
1.926 * [backup-simplify]: Simplify (- +nan.0) into (- +nan.0)
1.926 * [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)))))
1.927 * * * * [progress]: [ 2 / 4 ] generating series at (2 2 1)
1.927 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
1.927 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
1.927 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
1.927 * [taylor]: Taking taylor expansion of 2.0 in n
1.927 * [backup-simplify]: Simplify 2.0 into 2.0
1.927 * [taylor]: Taking taylor expansion of (* n PI) in n
1.927 * [taylor]: Taking taylor expansion of n in n
1.927 * [backup-simplify]: Simplify 0 into 0
1.928 * [backup-simplify]: Simplify 1 into 1
1.928 * [taylor]: Taking taylor expansion of PI in n
1.928 * [backup-simplify]: Simplify PI into PI
1.928 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
1.928 * [taylor]: Taking taylor expansion of 2.0 in n
1.928 * [backup-simplify]: Simplify 2.0 into 2.0
1.928 * [taylor]: Taking taylor expansion of (* n PI) in n
1.928 * [taylor]: Taking taylor expansion of n in n
1.928 * [backup-simplify]: Simplify 0 into 0
1.928 * [backup-simplify]: Simplify 1 into 1
1.928 * [taylor]: Taking taylor expansion of PI in n
1.928 * [backup-simplify]: Simplify PI into PI
1.928 * [backup-simplify]: Simplify (* 0 PI) into 0
1.928 * [backup-simplify]: Simplify (* 2.0 0) into 0
1.928 * [backup-simplify]: Simplify 0 into 0
1.929 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.930 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
1.931 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
1.931 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
1.932 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
1.932 * [backup-simplify]: Simplify 0 into 0
1.933 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
1.934 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
1.934 * [backup-simplify]: Simplify 0 into 0
1.935 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
1.937 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
1.937 * [backup-simplify]: Simplify 0 into 0
1.939 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
1.940 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
1.941 * [backup-simplify]: Simplify 0 into 0
1.942 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
1.944 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
1.944 * [backup-simplify]: Simplify 0 into 0
1.947 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
1.949 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
1.949 * [backup-simplify]: Simplify 0 into 0
1.949 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
1.950 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
1.950 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
1.950 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
1.950 * [taylor]: Taking taylor expansion of 2.0 in n
1.950 * [backup-simplify]: Simplify 2.0 into 2.0
1.950 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.950 * [taylor]: Taking taylor expansion of PI in n
1.950 * [backup-simplify]: Simplify PI into PI
1.950 * [taylor]: Taking taylor expansion of n in n
1.950 * [backup-simplify]: Simplify 0 into 0
1.950 * [backup-simplify]: Simplify 1 into 1
1.951 * [backup-simplify]: Simplify (/ PI 1) into PI
1.951 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
1.951 * [taylor]: Taking taylor expansion of 2.0 in n
1.951 * [backup-simplify]: Simplify 2.0 into 2.0
1.951 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.951 * [taylor]: Taking taylor expansion of PI in n
1.951 * [backup-simplify]: Simplify PI into PI
1.951 * [taylor]: Taking taylor expansion of n in n
1.951 * [backup-simplify]: Simplify 0 into 0
1.951 * [backup-simplify]: Simplify 1 into 1
1.952 * [backup-simplify]: Simplify (/ PI 1) into PI
1.952 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
1.953 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
1.954 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.955 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
1.955 * [backup-simplify]: Simplify 0 into 0
1.956 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.957 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
1.957 * [backup-simplify]: Simplify 0 into 0
1.959 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.960 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.960 * [backup-simplify]: Simplify 0 into 0
1.961 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.963 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
1.963 * [backup-simplify]: Simplify 0 into 0
1.964 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.966 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
1.966 * [backup-simplify]: Simplify 0 into 0
1.967 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.969 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
1.969 * [backup-simplify]: Simplify 0 into 0
1.970 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
1.970 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
1.970 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
1.970 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
1.970 * [taylor]: Taking taylor expansion of -2.0 in n
1.970 * [backup-simplify]: Simplify -2.0 into -2.0
1.970 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.970 * [taylor]: Taking taylor expansion of PI in n
1.970 * [backup-simplify]: Simplify PI into PI
1.970 * [taylor]: Taking taylor expansion of n in n
1.970 * [backup-simplify]: Simplify 0 into 0
1.970 * [backup-simplify]: Simplify 1 into 1
1.971 * [backup-simplify]: Simplify (/ PI 1) into PI
1.971 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
1.971 * [taylor]: Taking taylor expansion of -2.0 in n
1.971 * [backup-simplify]: Simplify -2.0 into -2.0
1.971 * [taylor]: Taking taylor expansion of (/ PI n) in n
1.971 * [taylor]: Taking taylor expansion of PI in n
1.971 * [backup-simplify]: Simplify PI into PI
1.971 * [taylor]: Taking taylor expansion of n in n
1.971 * [backup-simplify]: Simplify 0 into 0
1.971 * [backup-simplify]: Simplify 1 into 1
1.972 * [backup-simplify]: Simplify (/ PI 1) into PI
1.972 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
1.973 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
1.974 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
1.975 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
1.975 * [backup-simplify]: Simplify 0 into 0
1.976 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.977 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
1.977 * [backup-simplify]: Simplify 0 into 0
1.978 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.980 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
1.980 * [backup-simplify]: Simplify 0 into 0
1.981 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.982 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
1.982 * [backup-simplify]: Simplify 0 into 0
1.984 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.985 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
1.985 * [backup-simplify]: Simplify 0 into 0
1.986 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
1.987 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
1.987 * [backup-simplify]: Simplify 0 into 0
1.987 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
1.987 * * * * [progress]: [ 3 / 4 ] generating series at (2)
1.988 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))))
1.988 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (k n) around 0
1.988 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
1.988 * [taylor]: Taking taylor expansion of 1.0 in n
1.988 * [backup-simplify]: Simplify 1.0 into 1.0
1.988 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
1.988 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
1.988 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
1.988 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
1.988 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
1.988 * [taylor]: Taking taylor expansion of 0.5 in n
1.988 * [backup-simplify]: Simplify 0.5 into 0.5
1.988 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
1.988 * [taylor]: Taking taylor expansion of 1.0 in n
1.988 * [backup-simplify]: Simplify 1.0 into 1.0
1.988 * [taylor]: Taking taylor expansion of k in n
1.988 * [backup-simplify]: Simplify k into k
1.988 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
1.988 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
1.988 * [taylor]: Taking taylor expansion of 2.0 in n
1.988 * [backup-simplify]: Simplify 2.0 into 2.0
1.988 * [taylor]: Taking taylor expansion of (* n PI) in n
1.988 * [taylor]: Taking taylor expansion of n in n
1.988 * [backup-simplify]: Simplify 0 into 0
1.988 * [backup-simplify]: Simplify 1 into 1
1.988 * [taylor]: Taking taylor expansion of PI in n
1.988 * [backup-simplify]: Simplify PI into PI
1.988 * [backup-simplify]: Simplify (* 0 PI) into 0
1.989 * [backup-simplify]: Simplify (* 2.0 0) into 0
1.990 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
1.991 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
1.991 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
1.991 * [backup-simplify]: Simplify (- k) into (- k)
1.991 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
1.991 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
1.992 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
1.993 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
1.994 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
1.994 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
1.994 * [taylor]: Taking taylor expansion of (/ 1 k) in n
1.994 * [taylor]: Taking taylor expansion of k in n
1.994 * [backup-simplify]: Simplify k into k
1.994 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
1.994 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
1.994 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
1.994 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
1.994 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
1.994 * [taylor]: Taking taylor expansion of 1.0 in k
1.994 * [backup-simplify]: Simplify 1.0 into 1.0
1.994 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
1.994 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
1.994 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
1.994 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
1.994 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
1.994 * [taylor]: Taking taylor expansion of 0.5 in k
1.994 * [backup-simplify]: Simplify 0.5 into 0.5
1.994 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
1.994 * [taylor]: Taking taylor expansion of 1.0 in k
1.994 * [backup-simplify]: Simplify 1.0 into 1.0
1.994 * [taylor]: Taking taylor expansion of k in k
1.994 * [backup-simplify]: Simplify 0 into 0
1.994 * [backup-simplify]: Simplify 1 into 1
1.994 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
1.994 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
1.994 * [taylor]: Taking taylor expansion of 2.0 in k
1.994 * [backup-simplify]: Simplify 2.0 into 2.0
1.994 * [taylor]: Taking taylor expansion of (* n PI) in k
1.994 * [taylor]: Taking taylor expansion of n in k
1.994 * [backup-simplify]: Simplify n into n
1.994 * [taylor]: Taking taylor expansion of PI in k
1.994 * [backup-simplify]: Simplify PI into PI
1.995 * [backup-simplify]: Simplify (* n PI) into (* n PI)
1.995 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
1.995 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
1.995 * [backup-simplify]: Simplify (- 0) into 0
1.995 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
1.995 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
1.996 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
1.996 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
1.996 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
1.996 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.996 * [taylor]: Taking taylor expansion of k in k
1.996 * [backup-simplify]: Simplify 0 into 0
1.996 * [backup-simplify]: Simplify 1 into 1
1.996 * [backup-simplify]: Simplify (/ 1 1) into 1
1.996 * [backup-simplify]: Simplify (sqrt 0) into 0
1.997 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
1.997 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
1.997 * [taylor]: Taking taylor expansion of 1.0 in k
1.997 * [backup-simplify]: Simplify 1.0 into 1.0
1.997 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
1.997 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
1.997 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
1.997 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
1.997 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
1.997 * [taylor]: Taking taylor expansion of 0.5 in k
1.997 * [backup-simplify]: Simplify 0.5 into 0.5
1.997 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
1.997 * [taylor]: Taking taylor expansion of 1.0 in k
1.997 * [backup-simplify]: Simplify 1.0 into 1.0
1.997 * [taylor]: Taking taylor expansion of k in k
1.997 * [backup-simplify]: Simplify 0 into 0
1.997 * [backup-simplify]: Simplify 1 into 1
1.997 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
1.997 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
1.997 * [taylor]: Taking taylor expansion of 2.0 in k
1.997 * [backup-simplify]: Simplify 2.0 into 2.0
1.997 * [taylor]: Taking taylor expansion of (* n PI) in k
1.997 * [taylor]: Taking taylor expansion of n in k
1.997 * [backup-simplify]: Simplify n into n
1.997 * [taylor]: Taking taylor expansion of PI in k
1.998 * [backup-simplify]: Simplify PI into PI
1.998 * [backup-simplify]: Simplify (* n PI) into (* n PI)
1.998 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
1.998 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
1.998 * [backup-simplify]: Simplify (- 0) into 0
1.998 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
1.999 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
1.999 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
1.999 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
1.999 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
1.999 * [taylor]: Taking taylor expansion of (/ 1 k) in k
1.999 * [taylor]: Taking taylor expansion of k in k
1.999 * [backup-simplify]: Simplify 0 into 0
1.999 * [backup-simplify]: Simplify 1 into 1
1.999 * [backup-simplify]: Simplify (/ 1 1) into 1
1.999 * [backup-simplify]: Simplify (sqrt 0) into 0
2.000 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.000 * [backup-simplify]: Simplify (* (pow (* 2.0 (* n PI)) 0.5) 0) into 0
2.001 * [backup-simplify]: Simplify (* 1.0 0) into 0
2.001 * [taylor]: Taking taylor expansion of 0 in n
2.001 * [backup-simplify]: Simplify 0 into 0
2.001 * [backup-simplify]: Simplify 0 into 0
2.001 * [backup-simplify]: Simplify (+ (* n 0) (* 0 PI)) into 0
2.001 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 (* n PI))) into 0
2.002 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 1) into 0
2.002 * [backup-simplify]: Simplify (- 1) into -1
2.002 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.003 * [backup-simplify]: Simplify (+ (* 0.5 -1) (* 0 1.0)) into (- 0.5)
2.004 * [backup-simplify]: Simplify (+ (* 0.5 0) (* (- 0.5) (log (* 2.0 (* n PI))))) into (- (* 0.5 (log (* 2.0 (* n PI)))))
2.004 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1)))) into (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))))
2.005 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) 0)) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))
2.006 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
2.006 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n
2.007 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n
2.007 * [taylor]: Taking taylor expansion of +nan.0 in n
2.007 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.007 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
2.007 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
2.007 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
2.007 * [taylor]: Taking taylor expansion of 0.5 in n
2.007 * [backup-simplify]: Simplify 0.5 into 0.5
2.007 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
2.007 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
2.007 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
2.007 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
2.007 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
2.007 * [taylor]: Taking taylor expansion of 1.0 in n
2.007 * [backup-simplify]: Simplify 1.0 into 1.0
2.007 * [taylor]: Taking taylor expansion of (log PI) in n
2.007 * [taylor]: Taking taylor expansion of PI in n
2.007 * [backup-simplify]: Simplify PI into PI
2.007 * [backup-simplify]: Simplify (log PI) into (log PI)
2.008 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
2.009 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
2.009 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
2.009 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
2.009 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
2.009 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
2.009 * [taylor]: Taking taylor expansion of 1.0 in n
2.009 * [backup-simplify]: Simplify 1.0 into 1.0
2.009 * [taylor]: Taking taylor expansion of (log n) in n
2.009 * [taylor]: Taking taylor expansion of n in n
2.009 * [backup-simplify]: Simplify 0 into 0
2.009 * [backup-simplify]: Simplify 1 into 1
2.009 * [backup-simplify]: Simplify (log 1) into 0
2.010 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
2.010 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
2.010 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
2.010 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
2.010 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
2.010 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
2.010 * [taylor]: Taking taylor expansion of 1.0 in n
2.010 * [backup-simplify]: Simplify 1.0 into 1.0
2.010 * [taylor]: Taking taylor expansion of (log 2.0) in n
2.010 * [taylor]: Taking taylor expansion of 2.0 in n
2.010 * [backup-simplify]: Simplify 2.0 into 2.0
2.010 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
2.011 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
2.012 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
2.012 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
2.013 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
2.014 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))
2.014 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))
2.015 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
2.016 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))
2.017 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))
2.018 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))
2.018 * [backup-simplify]: Simplify 0 into 0
2.019 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
2.023 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.023 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (* 0 PI))) into 0
2.024 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 (* n PI)))) into 0
2.025 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 2) into 0
2.025 * [backup-simplify]: Simplify (- 0) into 0
2.025 * [backup-simplify]: Simplify (+ 0 0) into 0
2.026 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 -1) (* 0 1.0))) into 0
2.027 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (* 0 (log (* 2.0 (* n PI)))))) into 0
2.028 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))
2.031 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) +nan.0) (* (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))
2.036 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))
2.036 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) in n
2.037 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))) in n
2.037 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n
2.037 * [taylor]: Taking taylor expansion of +nan.0 in n
2.037 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.037 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n
2.037 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
2.037 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
2.037 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
2.037 * [taylor]: Taking taylor expansion of 0.5 in n
2.037 * [backup-simplify]: Simplify 0.5 into 0.5
2.037 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
2.037 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
2.037 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
2.037 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
2.037 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
2.037 * [taylor]: Taking taylor expansion of 1.0 in n
2.037 * [backup-simplify]: Simplify 1.0 into 1.0
2.037 * [taylor]: Taking taylor expansion of (log PI) in n
2.037 * [taylor]: Taking taylor expansion of PI in n
2.037 * [backup-simplify]: Simplify PI into PI
2.038 * [backup-simplify]: Simplify (log PI) into (log PI)
2.039 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
2.040 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
2.040 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
2.040 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
2.040 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
2.040 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
2.040 * [taylor]: Taking taylor expansion of 1.0 in n
2.040 * [backup-simplify]: Simplify 1.0 into 1.0
2.040 * [taylor]: Taking taylor expansion of (log n) in n
2.040 * [taylor]: Taking taylor expansion of n in n
2.040 * [backup-simplify]: Simplify 0 into 0
2.041 * [backup-simplify]: Simplify 1 into 1
2.041 * [backup-simplify]: Simplify (log 1) into 0
2.041 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
2.041 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
2.042 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
2.042 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
2.042 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
2.042 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
2.042 * [taylor]: Taking taylor expansion of 1.0 in n
2.042 * [backup-simplify]: Simplify 1.0 into 1.0
2.042 * [taylor]: Taking taylor expansion of (log 2.0) in n
2.042 * [taylor]: Taking taylor expansion of 2.0 in n
2.042 * [backup-simplify]: Simplify 2.0 into 2.0
2.042 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
2.043 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
2.045 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
2.045 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
2.047 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
2.048 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))
2.049 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))
2.051 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
2.051 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
2.051 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
2.051 * [taylor]: Taking taylor expansion of 2.0 in n
2.051 * [backup-simplify]: Simplify 2.0 into 2.0
2.051 * [taylor]: Taking taylor expansion of (* n PI) in n
2.051 * [taylor]: Taking taylor expansion of n in n
2.051 * [backup-simplify]: Simplify 0 into 0
2.052 * [backup-simplify]: Simplify 1 into 1
2.052 * [taylor]: Taking taylor expansion of PI in n
2.052 * [backup-simplify]: Simplify PI into PI
2.052 * [backup-simplify]: Simplify (* 0 PI) into 0
2.052 * [backup-simplify]: Simplify (* 2.0 0) into 0
2.054 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.056 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
2.057 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.057 * [taylor]: Taking taylor expansion of (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) in n
2.057 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) in n
2.057 * [taylor]: Taking taylor expansion of +nan.0 in n
2.057 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.057 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
2.057 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
2.057 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
2.057 * [taylor]: Taking taylor expansion of 0.5 in n
2.057 * [backup-simplify]: Simplify 0.5 into 0.5
2.057 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
2.057 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
2.057 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
2.057 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
2.057 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
2.057 * [taylor]: Taking taylor expansion of 1.0 in n
2.057 * [backup-simplify]: Simplify 1.0 into 1.0
2.057 * [taylor]: Taking taylor expansion of (log PI) in n
2.057 * [taylor]: Taking taylor expansion of PI in n
2.057 * [backup-simplify]: Simplify PI into PI
2.058 * [backup-simplify]: Simplify (log PI) into (log PI)
2.059 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
2.061 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
2.061 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
2.061 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
2.061 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
2.061 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
2.061 * [taylor]: Taking taylor expansion of 1.0 in n
2.061 * [backup-simplify]: Simplify 1.0 into 1.0
2.061 * [taylor]: Taking taylor expansion of (log n) in n
2.061 * [taylor]: Taking taylor expansion of n in n
2.061 * [backup-simplify]: Simplify 0 into 0
2.061 * [backup-simplify]: Simplify 1 into 1
2.061 * [backup-simplify]: Simplify (log 1) into 0
2.062 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
2.062 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
2.062 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
2.062 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
2.062 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
2.062 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
2.062 * [taylor]: Taking taylor expansion of 1.0 in n
2.062 * [backup-simplify]: Simplify 1.0 into 1.0
2.062 * [taylor]: Taking taylor expansion of (log 2.0) in n
2.062 * [taylor]: Taking taylor expansion of 2.0 in n
2.062 * [backup-simplify]: Simplify 2.0 into 2.0
2.063 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
2.064 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
2.065 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
2.066 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
2.067 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
2.068 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))
2.070 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))
2.071 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
2.073 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.075 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))
2.078 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n))))
2.080 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))
2.081 * [backup-simplify]: Simplify (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))) into (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))
2.085 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))
2.091 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))))))))
2.097 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))
2.099 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 2.0 1)))) 1) into 0
2.100 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log 2.0))) into 0
2.101 * [backup-simplify]: Simplify (* (exp (* 1.0 (log 2.0))) (+ (* (/ (pow 0 1) 1)))) into 0
2.103 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow 1 1)))) 1) into 0
2.103 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
2.104 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log n))) into 0
2.105 * [backup-simplify]: Simplify (* (exp (* 1.0 (log n))) (+ (* (/ (pow 0 1) 1)))) into 0
2.105 * [backup-simplify]: Simplify (+ (* (pow n 1.0) 0) (* 0 (pow 2.0 1.0))) into 0
2.107 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow PI 1)))) 1) into 0
2.108 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (log PI))) into 0
2.110 * [backup-simplify]: Simplify (* (exp (* 1.0 (log PI))) (+ (* (/ (pow 0 1) 1)))) into 0
2.111 * [backup-simplify]: Simplify (+ (* (pow PI 1.0) 0) (* 0 (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0))) into 0
2.113 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1)))) 1) into 0
2.115 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0)))) into 0
2.117 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.119 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5))) into 0
2.120 * [backup-simplify]: Simplify (- 0) into 0
2.120 * [backup-simplify]: Simplify 0 into 0
2.120 * [backup-simplify]: Simplify 0 into 0
2.121 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.125 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.126 * [backup-simplify]: Simplify (+ (* n 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.127 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* n PI))))) into 0
2.131 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 (* n PI)) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 (* n PI)) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 (* n PI)) 1)))) 6) into 0
2.131 * [backup-simplify]: Simplify (- 0) into 0
2.131 * [backup-simplify]: Simplify (+ 0 0) into 0
2.133 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 -1) (* 0 1.0)))) into 0
2.134 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* (- 0.5) 0) (+ (* 0 0) (* 0 (log (* 2.0 (* n PI))))))) into 0
2.136 * [backup-simplify]: Simplify (* (exp (* 0.5 (log (* 2.0 (* n PI))))) (+ (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 3) 6)) (* (/ (pow (- (* 0.5 (log (* 2.0 (* n PI))))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 3)))
2.142 * [backup-simplify]: Simplify (+ (* (pow (* 2.0 (* n PI)) 0.5) +nan.0) (+ (* (* -0.5 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) +nan.0) (+ (* (* 0.125 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) +nan.0) (* (* -0.020833333333333332 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 3))) 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))
2.153 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))) (+ (* 0 (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))) (+ (* 0 (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))) (* 0 0)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))))
2.154 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))))) in n
2.154 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))))) in n
2.154 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI))))) in n
2.154 * [taylor]: Taking taylor expansion of +nan.0 in n
2.154 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.154 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 (* n PI)))) in n
2.154 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
2.154 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
2.154 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
2.154 * [taylor]: Taking taylor expansion of 0.5 in n
2.154 * [backup-simplify]: Simplify 0.5 into 0.5
2.154 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
2.154 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
2.154 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
2.154 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
2.154 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
2.154 * [taylor]: Taking taylor expansion of 1.0 in n
2.154 * [backup-simplify]: Simplify 1.0 into 1.0
2.154 * [taylor]: Taking taylor expansion of (log PI) in n
2.154 * [taylor]: Taking taylor expansion of PI in n
2.154 * [backup-simplify]: Simplify PI into PI
2.155 * [backup-simplify]: Simplify (log PI) into (log PI)
2.156 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
2.158 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
2.158 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
2.158 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
2.158 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
2.158 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
2.158 * [taylor]: Taking taylor expansion of 1.0 in n
2.158 * [backup-simplify]: Simplify 1.0 into 1.0
2.158 * [taylor]: Taking taylor expansion of (log n) in n
2.158 * [taylor]: Taking taylor expansion of n in n
2.158 * [backup-simplify]: Simplify 0 into 0
2.158 * [backup-simplify]: Simplify 1 into 1
2.158 * [backup-simplify]: Simplify (log 1) into 0
2.159 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
2.159 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
2.159 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
2.159 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
2.159 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
2.159 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
2.159 * [taylor]: Taking taylor expansion of 1.0 in n
2.159 * [backup-simplify]: Simplify 1.0 into 1.0
2.159 * [taylor]: Taking taylor expansion of (log 2.0) in n
2.159 * [taylor]: Taking taylor expansion of 2.0 in n
2.159 * [backup-simplify]: Simplify 2.0 into 2.0
2.160 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
2.161 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
2.162 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
2.163 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
2.165 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
2.166 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))
2.167 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))
2.169 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
2.169 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
2.169 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
2.169 * [taylor]: Taking taylor expansion of 2.0 in n
2.169 * [backup-simplify]: Simplify 2.0 into 2.0
2.169 * [taylor]: Taking taylor expansion of (* n PI) in n
2.169 * [taylor]: Taking taylor expansion of n in n
2.169 * [backup-simplify]: Simplify 0 into 0
2.169 * [backup-simplify]: Simplify 1 into 1
2.169 * [taylor]: Taking taylor expansion of PI in n
2.169 * [backup-simplify]: Simplify PI into PI
2.174 * [backup-simplify]: Simplify (* 0 PI) into 0
2.174 * [backup-simplify]: Simplify (* 2.0 0) into 0
2.176 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.178 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
2.179 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.179 * [taylor]: Taking taylor expansion of (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))))) in n
2.179 * [taylor]: Taking taylor expansion of (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))))) in n
2.179 * [taylor]: Taking taylor expansion of (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) in n
2.179 * [taylor]: Taking taylor expansion of +nan.0 in n
2.179 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.179 * [taylor]: Taking taylor expansion of (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) in n
2.179 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))))) in n
2.179 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))))) in n
2.179 * [taylor]: Taking taylor expansion of 0.5 in n
2.179 * [backup-simplify]: Simplify 0.5 into 0.5
2.179 * [taylor]: Taking taylor expansion of (log (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0)))) in n
2.179 * [taylor]: Taking taylor expansion of (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) in n
2.179 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
2.179 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
2.179 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
2.179 * [taylor]: Taking taylor expansion of 1.0 in n
2.179 * [backup-simplify]: Simplify 1.0 into 1.0
2.179 * [taylor]: Taking taylor expansion of (log 2.0) in n
2.179 * [taylor]: Taking taylor expansion of 2.0 in n
2.179 * [backup-simplify]: Simplify 2.0 into 2.0
2.180 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
2.181 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
2.182 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
2.182 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow PI 1.0)) in n
2.182 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
2.182 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
2.182 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
2.182 * [taylor]: Taking taylor expansion of 1.0 in n
2.182 * [backup-simplify]: Simplify 1.0 into 1.0
2.182 * [taylor]: Taking taylor expansion of (log n) in n
2.182 * [taylor]: Taking taylor expansion of n in n
2.182 * [backup-simplify]: Simplify 0 into 0
2.182 * [backup-simplify]: Simplify 1 into 1
2.182 * [backup-simplify]: Simplify (log 1) into 0
2.182 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
2.182 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
2.182 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
2.182 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
2.183 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
2.183 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
2.183 * [taylor]: Taking taylor expansion of 1.0 in n
2.183 * [backup-simplify]: Simplify 1.0 into 1.0
2.183 * [taylor]: Taking taylor expansion of (log PI) in n
2.183 * [taylor]: Taking taylor expansion of PI in n
2.183 * [backup-simplify]: Simplify PI into PI
2.183 * [backup-simplify]: Simplify (log PI) into (log PI)
2.183 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
2.185 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
2.185 * [backup-simplify]: Simplify (* (pow n 1.0) (pow PI 1.0)) into (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)
2.186 * [backup-simplify]: Simplify (* (pow 2.0 1.0) (pow (* (pow n 1.0) (pow PI 1.0)) 1.0)) into (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)
2.187 * [backup-simplify]: Simplify (log (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0)) into (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))
2.188 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))
2.189 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
2.189 * [taylor]: Taking taylor expansion of (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)))) in n
2.189 * [taylor]: Taking taylor expansion of (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2))) in n
2.189 * [taylor]: Taking taylor expansion of +nan.0 in n
2.189 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.189 * [taylor]: Taking taylor expansion of (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 (* n PI))) 2)) in n
2.189 * [taylor]: Taking taylor expansion of (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) in n
2.189 * [taylor]: Taking taylor expansion of (exp (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))))) in n
2.189 * [taylor]: Taking taylor expansion of (* 0.5 (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))))) in n
2.189 * [taylor]: Taking taylor expansion of 0.5 in n
2.189 * [backup-simplify]: Simplify 0.5 into 0.5
2.189 * [taylor]: Taking taylor expansion of (log (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0)))) in n
2.189 * [taylor]: Taking taylor expansion of (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) in n
2.189 * [taylor]: Taking taylor expansion of (pow PI 1.0) in n
2.189 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log PI))) in n
2.189 * [taylor]: Taking taylor expansion of (* 1.0 (log PI)) in n
2.189 * [taylor]: Taking taylor expansion of 1.0 in n
2.189 * [backup-simplify]: Simplify 1.0 into 1.0
2.189 * [taylor]: Taking taylor expansion of (log PI) in n
2.189 * [taylor]: Taking taylor expansion of PI in n
2.189 * [backup-simplify]: Simplify PI into PI
2.189 * [backup-simplify]: Simplify (log PI) into (log PI)
2.190 * [backup-simplify]: Simplify (* 1.0 (log PI)) into (* 1.0 (log PI))
2.191 * [backup-simplify]: Simplify (exp (* 1.0 (log PI))) into (pow PI 1.0)
2.191 * [taylor]: Taking taylor expansion of (* (pow n 1.0) (pow 2.0 1.0)) in n
2.191 * [taylor]: Taking taylor expansion of (pow n 1.0) in n
2.191 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log n))) in n
2.191 * [taylor]: Taking taylor expansion of (* 1.0 (log n)) in n
2.191 * [taylor]: Taking taylor expansion of 1.0 in n
2.191 * [backup-simplify]: Simplify 1.0 into 1.0
2.191 * [taylor]: Taking taylor expansion of (log n) in n
2.191 * [taylor]: Taking taylor expansion of n in n
2.191 * [backup-simplify]: Simplify 0 into 0
2.191 * [backup-simplify]: Simplify 1 into 1
2.191 * [backup-simplify]: Simplify (log 1) into 0
2.192 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) 0) into (log n)
2.192 * [backup-simplify]: Simplify (* 1.0 (log n)) into (* 1.0 (log n))
2.192 * [backup-simplify]: Simplify (exp (* 1.0 (log n))) into (pow n 1.0)
2.192 * [taylor]: Taking taylor expansion of (pow 2.0 1.0) in n
2.192 * [taylor]: Taking taylor expansion of (exp (* 1.0 (log 2.0))) in n
2.192 * [taylor]: Taking taylor expansion of (* 1.0 (log 2.0)) in n
2.192 * [taylor]: Taking taylor expansion of 1.0 in n
2.192 * [backup-simplify]: Simplify 1.0 into 1.0
2.192 * [taylor]: Taking taylor expansion of (log 2.0) in n
2.192 * [taylor]: Taking taylor expansion of 2.0 in n
2.192 * [backup-simplify]: Simplify 2.0 into 2.0
2.192 * [backup-simplify]: Simplify (log 2.0) into (log 2.0)
2.193 * [backup-simplify]: Simplify (* 1.0 (log 2.0)) into (* 1.0 (log 2.0))
2.194 * [backup-simplify]: Simplify (exp (* 1.0 (log 2.0))) into (pow 2.0 1.0)
2.194 * [backup-simplify]: Simplify (* (pow n 1.0) (pow 2.0 1.0)) into (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)
2.195 * [backup-simplify]: Simplify (* (pow PI 1.0) (pow (* (pow n 1.0) (pow 2.0 1.0)) 1.0)) into (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)
2.196 * [backup-simplify]: Simplify (log (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0)) into (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))
2.196 * [backup-simplify]: Simplify (* 0.5 (log (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0))) into (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))
2.197 * [backup-simplify]: Simplify (exp (* 0.5 (log (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0)))) into (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)
2.197 * [taylor]: Taking taylor expansion of (pow (log (* 2.0 (* n PI))) 2) in n
2.197 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
2.197 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
2.197 * [taylor]: Taking taylor expansion of 2.0 in n
2.197 * [backup-simplify]: Simplify 2.0 into 2.0
2.197 * [taylor]: Taking taylor expansion of (* n PI) in n
2.197 * [taylor]: Taking taylor expansion of n in n
2.197 * [backup-simplify]: Simplify 0 into 0
2.197 * [backup-simplify]: Simplify 1 into 1
2.197 * [taylor]: Taking taylor expansion of PI in n
2.198 * [backup-simplify]: Simplify PI into PI
2.198 * [backup-simplify]: Simplify (* 0 PI) into 0
2.198 * [backup-simplify]: Simplify (* 2.0 0) into 0
2.199 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.200 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
2.201 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.201 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.203 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.204 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (+ (log (* 2.0 PI)) (log n))) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))
2.206 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n))))
2.207 * [backup-simplify]: Simplify (* +nan.0 (pow (pow (pow (pow (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5)) into (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))
2.208 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.209 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.211 * [backup-simplify]: Simplify (* (+ (log (* 2.0 PI)) (log n)) (+ (log (* 2.0 PI)) (log n))) into (pow (+ (log (* 2.0 PI)) (log n)) 2)
2.214 * [backup-simplify]: Simplify (* (pow (pow (pow (pow (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 1.0) 1.0) 1.0) 1.0) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)) into (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2))
2.217 * [backup-simplify]: Simplify (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2))) into (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)))
2.220 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (+ (log (* 2.0 PI)) (log n)) 2)))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))
2.228 * [backup-simplify]: Simplify (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))
2.234 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)))))))))) into (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))))
2.242 * [backup-simplify]: Simplify (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (+ (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))
2.252 * [backup-simplify]: Simplify (- (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)))))))))))))
2.268 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (pow (log n) 2))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))))))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n)))))))))))))))
2.291 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log n) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow (log (* 2.0 PI)) 2))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5)) (- (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (log n))))))))))))))) (pow (* 1 k) 2)) (+ (* (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log (* 2.0 PI)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (log n))) (- (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5))))))) (* 1 k)) (- (* +nan.0 (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5))))) into (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow k 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log n) 2) (pow k 2)))))))))))))))))))))))
2.292 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 k))) (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) into (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)))
2.292 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (k n) around 0
2.292 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
2.292 * [taylor]: Taking taylor expansion of 1.0 in n
2.292 * [backup-simplify]: Simplify 1.0 into 1.0
2.292 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
2.292 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
2.292 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
2.292 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
2.292 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
2.292 * [taylor]: Taking taylor expansion of 0.5 in n
2.292 * [backup-simplify]: Simplify 0.5 into 0.5
2.292 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
2.292 * [taylor]: Taking taylor expansion of 1.0 in n
2.292 * [backup-simplify]: Simplify 1.0 into 1.0
2.292 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.292 * [taylor]: Taking taylor expansion of k in n
2.292 * [backup-simplify]: Simplify k into k
2.293 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.293 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
2.293 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
2.293 * [taylor]: Taking taylor expansion of 2.0 in n
2.293 * [backup-simplify]: Simplify 2.0 into 2.0
2.293 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.293 * [taylor]: Taking taylor expansion of PI in n
2.293 * [backup-simplify]: Simplify PI into PI
2.293 * [taylor]: Taking taylor expansion of n in n
2.293 * [backup-simplify]: Simplify 0 into 0
2.293 * [backup-simplify]: Simplify 1 into 1
2.293 * [backup-simplify]: Simplify (/ PI 1) into PI
2.293 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.294 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.294 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
2.294 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
2.294 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
2.295 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.296 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
2.296 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
2.297 * [taylor]: Taking taylor expansion of (sqrt k) in n
2.297 * [taylor]: Taking taylor expansion of k in n
2.297 * [backup-simplify]: Simplify k into k
2.297 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
2.297 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
2.297 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k
2.297 * [taylor]: Taking taylor expansion of 1.0 in k
2.297 * [backup-simplify]: Simplify 1.0 into 1.0
2.297 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k
2.297 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
2.297 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
2.297 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
2.297 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
2.297 * [taylor]: Taking taylor expansion of 0.5 in k
2.297 * [backup-simplify]: Simplify 0.5 into 0.5
2.297 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
2.297 * [taylor]: Taking taylor expansion of 1.0 in k
2.297 * [backup-simplify]: Simplify 1.0 into 1.0
2.297 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.297 * [taylor]: Taking taylor expansion of k in k
2.297 * [backup-simplify]: Simplify 0 into 0
2.297 * [backup-simplify]: Simplify 1 into 1
2.297 * [backup-simplify]: Simplify (/ 1 1) into 1
2.297 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
2.297 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
2.297 * [taylor]: Taking taylor expansion of 2.0 in k
2.297 * [backup-simplify]: Simplify 2.0 into 2.0
2.297 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.297 * [taylor]: Taking taylor expansion of PI in k
2.297 * [backup-simplify]: Simplify PI into PI
2.297 * [taylor]: Taking taylor expansion of n in k
2.297 * [backup-simplify]: Simplify n into n
2.297 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.297 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
2.298 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
2.298 * [backup-simplify]: Simplify (- 1) into -1
2.298 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.298 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
2.298 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
2.299 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
2.299 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.299 * [taylor]: Taking taylor expansion of k in k
2.299 * [backup-simplify]: Simplify 0 into 0
2.299 * [backup-simplify]: Simplify 1 into 1
2.299 * [backup-simplify]: Simplify (sqrt 0) into 0
2.300 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.300 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k
2.300 * [taylor]: Taking taylor expansion of 1.0 in k
2.300 * [backup-simplify]: Simplify 1.0 into 1.0
2.300 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k
2.300 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
2.300 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
2.300 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
2.300 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
2.300 * [taylor]: Taking taylor expansion of 0.5 in k
2.300 * [backup-simplify]: Simplify 0.5 into 0.5
2.300 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
2.300 * [taylor]: Taking taylor expansion of 1.0 in k
2.300 * [backup-simplify]: Simplify 1.0 into 1.0
2.300 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.300 * [taylor]: Taking taylor expansion of k in k
2.300 * [backup-simplify]: Simplify 0 into 0
2.300 * [backup-simplify]: Simplify 1 into 1
2.300 * [backup-simplify]: Simplify (/ 1 1) into 1
2.300 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
2.300 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
2.300 * [taylor]: Taking taylor expansion of 2.0 in k
2.300 * [backup-simplify]: Simplify 2.0 into 2.0
2.300 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.300 * [taylor]: Taking taylor expansion of PI in k
2.300 * [backup-simplify]: Simplify PI into PI
2.300 * [taylor]: Taking taylor expansion of n in k
2.300 * [backup-simplify]: Simplify n into n
2.301 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.301 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
2.301 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
2.301 * [backup-simplify]: Simplify (- 1) into -1
2.301 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.301 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
2.302 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
2.302 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
2.302 * [taylor]: Taking taylor expansion of (sqrt k) in k
2.302 * [taylor]: Taking taylor expansion of k in k
2.302 * [backup-simplify]: Simplify 0 into 0
2.302 * [backup-simplify]: Simplify 1 into 1
2.302 * [backup-simplify]: Simplify (sqrt 0) into 0
2.303 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
2.303 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) 0) into 0
2.303 * [backup-simplify]: Simplify (* 1.0 0) into 0
2.303 * [taylor]: Taking taylor expansion of 0 in n
2.303 * [backup-simplify]: Simplify 0 into 0
2.303 * [backup-simplify]: Simplify 0 into 0
2.304 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))
2.304 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))
2.304 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n
2.304 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n
2.304 * [taylor]: Taking taylor expansion of +nan.0 in n
2.304 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.304 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n
2.304 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n
2.304 * [taylor]: Taking taylor expansion of 0.5 in n
2.304 * [backup-simplify]: Simplify 0.5 into 0.5
2.304 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n
2.304 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
2.304 * [taylor]: Taking taylor expansion of 1.0 in n
2.304 * [backup-simplify]: Simplify 1.0 into 1.0
2.304 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.304 * [taylor]: Taking taylor expansion of k in n
2.305 * [backup-simplify]: Simplify k into k
2.305 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.305 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
2.305 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
2.305 * [taylor]: Taking taylor expansion of 2.0 in n
2.305 * [backup-simplify]: Simplify 2.0 into 2.0
2.305 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.305 * [taylor]: Taking taylor expansion of PI in n
2.305 * [backup-simplify]: Simplify PI into PI
2.305 * [taylor]: Taking taylor expansion of n in n
2.305 * [backup-simplify]: Simplify 0 into 0
2.305 * [backup-simplify]: Simplify 1 into 1
2.305 * [backup-simplify]: Simplify (/ PI 1) into PI
2.305 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.306 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.306 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
2.306 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
2.307 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.308 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))
2.308 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
2.309 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
2.310 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))
2.311 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
2.312 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
2.312 * [backup-simplify]: Simplify 0 into 0
2.314 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.314 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))
2.315 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))
2.315 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n
2.315 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n
2.315 * [taylor]: Taking taylor expansion of +nan.0 in n
2.315 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.315 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n
2.315 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n
2.315 * [taylor]: Taking taylor expansion of 0.5 in n
2.315 * [backup-simplify]: Simplify 0.5 into 0.5
2.315 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n
2.315 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
2.315 * [taylor]: Taking taylor expansion of 1.0 in n
2.315 * [backup-simplify]: Simplify 1.0 into 1.0
2.315 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.315 * [taylor]: Taking taylor expansion of k in n
2.315 * [backup-simplify]: Simplify k into k
2.315 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.315 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
2.315 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
2.315 * [taylor]: Taking taylor expansion of 2.0 in n
2.315 * [backup-simplify]: Simplify 2.0 into 2.0
2.315 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.315 * [taylor]: Taking taylor expansion of PI in n
2.315 * [backup-simplify]: Simplify PI into PI
2.315 * [taylor]: Taking taylor expansion of n in n
2.315 * [backup-simplify]: Simplify 0 into 0
2.315 * [backup-simplify]: Simplify 1 into 1
2.316 * [backup-simplify]: Simplify (/ PI 1) into PI
2.316 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.317 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.317 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
2.317 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
2.318 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.320 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))
2.321 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
2.322 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
2.323 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))
2.325 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
2.326 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
2.327 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.328 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
2.330 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
2.330 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.330 * [backup-simplify]: Simplify (- 0) into 0
2.331 * [backup-simplify]: Simplify (+ 0 0) into 0
2.332 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.333 * [backup-simplify]: Simplify (+ (* (- 1.0 (/ 1 k)) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
2.335 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into 0
2.337 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.339 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0
2.339 * [backup-simplify]: Simplify (- 0) into 0
2.339 * [backup-simplify]: Simplify 0 into 0
2.339 * [backup-simplify]: Simplify 0 into 0
2.342 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.343 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))
2.344 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))))
2.344 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))))) in n
2.344 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))) in n
2.344 * [taylor]: Taking taylor expansion of +nan.0 in n
2.344 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.344 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))))) in n
2.344 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))) in n
2.344 * [taylor]: Taking taylor expansion of 0.5 in n
2.344 * [backup-simplify]: Simplify 0.5 into 0.5
2.344 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n)))) in n
2.344 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
2.344 * [taylor]: Taking taylor expansion of 1.0 in n
2.344 * [backup-simplify]: Simplify 1.0 into 1.0
2.344 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.344 * [taylor]: Taking taylor expansion of k in n
2.344 * [backup-simplify]: Simplify k into k
2.344 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.344 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
2.344 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
2.344 * [taylor]: Taking taylor expansion of 2.0 in n
2.344 * [backup-simplify]: Simplify 2.0 into 2.0
2.344 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.344 * [taylor]: Taking taylor expansion of PI in n
2.344 * [backup-simplify]: Simplify PI into PI
2.344 * [taylor]: Taking taylor expansion of n in n
2.344 * [backup-simplify]: Simplify 0 into 0
2.344 * [backup-simplify]: Simplify 1 into 1
2.344 * [backup-simplify]: Simplify (/ PI 1) into PI
2.345 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.345 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.345 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
2.345 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
2.346 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.347 * [backup-simplify]: Simplify (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) into (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))
2.348 * [backup-simplify]: Simplify (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
2.348 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
2.349 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))
2.350 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
2.351 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
2.354 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* 1 (/ 1 k)) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (* 1 (/ 1 k))))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
2.354 * [backup-simplify]: Simplify (* (/ 1.0 (sqrt (/ 1 (- k)))) (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))))
2.354 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (k n) around 0
2.354 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
2.354 * [taylor]: Taking taylor expansion of 1.0 in n
2.354 * [backup-simplify]: Simplify 1.0 into 1.0
2.354 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
2.354 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
2.354 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
2.354 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
2.354 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
2.354 * [taylor]: Taking taylor expansion of 0.5 in n
2.354 * [backup-simplify]: Simplify 0.5 into 0.5
2.354 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
2.354 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.354 * [taylor]: Taking taylor expansion of k in n
2.354 * [backup-simplify]: Simplify k into k
2.355 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.355 * [taylor]: Taking taylor expansion of 1.0 in n
2.355 * [backup-simplify]: Simplify 1.0 into 1.0
2.355 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
2.355 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
2.355 * [taylor]: Taking taylor expansion of -2.0 in n
2.355 * [backup-simplify]: Simplify -2.0 into -2.0
2.355 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.355 * [taylor]: Taking taylor expansion of PI in n
2.355 * [backup-simplify]: Simplify PI into PI
2.355 * [taylor]: Taking taylor expansion of n in n
2.355 * [backup-simplify]: Simplify 0 into 0
2.355 * [backup-simplify]: Simplify 1 into 1
2.355 * [backup-simplify]: Simplify (/ PI 1) into PI
2.355 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
2.356 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
2.356 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
2.356 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
2.357 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.358 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
2.358 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
2.358 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
2.358 * [taylor]: Taking taylor expansion of (/ -1 k) in n
2.359 * [taylor]: Taking taylor expansion of -1 in n
2.359 * [backup-simplify]: Simplify -1 into -1
2.359 * [taylor]: Taking taylor expansion of k in n
2.359 * [backup-simplify]: Simplify k into k
2.359 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
2.359 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
2.359 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
2.359 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
2.360 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
2.360 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
2.360 * [taylor]: Taking taylor expansion of 1.0 in k
2.360 * [backup-simplify]: Simplify 1.0 into 1.0
2.360 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
2.360 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
2.360 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
2.360 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
2.360 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
2.360 * [taylor]: Taking taylor expansion of 0.5 in k
2.360 * [backup-simplify]: Simplify 0.5 into 0.5
2.360 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
2.360 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.360 * [taylor]: Taking taylor expansion of k in k
2.360 * [backup-simplify]: Simplify 0 into 0
2.360 * [backup-simplify]: Simplify 1 into 1
2.360 * [backup-simplify]: Simplify (/ 1 1) into 1
2.360 * [taylor]: Taking taylor expansion of 1.0 in k
2.360 * [backup-simplify]: Simplify 1.0 into 1.0
2.360 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
2.360 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
2.360 * [taylor]: Taking taylor expansion of -2.0 in k
2.360 * [backup-simplify]: Simplify -2.0 into -2.0
2.360 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.360 * [taylor]: Taking taylor expansion of PI in k
2.360 * [backup-simplify]: Simplify PI into PI
2.361 * [taylor]: Taking taylor expansion of n in k
2.361 * [backup-simplify]: Simplify n into n
2.361 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.361 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
2.361 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
2.361 * [backup-simplify]: Simplify (+ 1 0) into 1
2.361 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
2.361 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
2.361 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
2.362 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.362 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.362 * [taylor]: Taking taylor expansion of -1 in k
2.362 * [backup-simplify]: Simplify -1 into -1
2.362 * [taylor]: Taking taylor expansion of k in k
2.362 * [backup-simplify]: Simplify 0 into 0
2.362 * [backup-simplify]: Simplify 1 into 1
2.362 * [backup-simplify]: Simplify (/ -1 1) into -1
2.362 * [backup-simplify]: Simplify (sqrt 0) into 0
2.363 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.363 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
2.363 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
2.363 * [taylor]: Taking taylor expansion of 1.0 in k
2.363 * [backup-simplify]: Simplify 1.0 into 1.0
2.363 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
2.363 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
2.363 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
2.363 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
2.363 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
2.363 * [taylor]: Taking taylor expansion of 0.5 in k
2.363 * [backup-simplify]: Simplify 0.5 into 0.5
2.363 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
2.363 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.363 * [taylor]: Taking taylor expansion of k in k
2.363 * [backup-simplify]: Simplify 0 into 0
2.363 * [backup-simplify]: Simplify 1 into 1
2.364 * [backup-simplify]: Simplify (/ 1 1) into 1
2.364 * [taylor]: Taking taylor expansion of 1.0 in k
2.364 * [backup-simplify]: Simplify 1.0 into 1.0
2.364 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
2.364 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
2.364 * [taylor]: Taking taylor expansion of -2.0 in k
2.364 * [backup-simplify]: Simplify -2.0 into -2.0
2.364 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.364 * [taylor]: Taking taylor expansion of PI in k
2.364 * [backup-simplify]: Simplify PI into PI
2.364 * [taylor]: Taking taylor expansion of n in k
2.364 * [backup-simplify]: Simplify n into n
2.364 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.364 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
2.364 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
2.364 * [backup-simplify]: Simplify (+ 1 0) into 1
2.365 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
2.365 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
2.365 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
2.365 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
2.365 * [taylor]: Taking taylor expansion of (/ -1 k) in k
2.365 * [taylor]: Taking taylor expansion of -1 in k
2.365 * [backup-simplify]: Simplify -1 into -1
2.365 * [taylor]: Taking taylor expansion of k in k
2.365 * [backup-simplify]: Simplify 0 into 0
2.365 * [backup-simplify]: Simplify 1 into 1
2.365 * [backup-simplify]: Simplify (/ -1 1) into -1
2.365 * [backup-simplify]: Simplify (sqrt 0) into 0
2.366 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
2.366 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
2.367 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
2.367 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n
2.367 * [taylor]: Taking taylor expansion of +nan.0 in n
2.367 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.367 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n
2.367 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n
2.367 * [taylor]: Taking taylor expansion of 0.5 in n
2.367 * [backup-simplify]: Simplify 0.5 into 0.5
2.367 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n
2.367 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
2.367 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
2.367 * [taylor]: Taking taylor expansion of -2.0 in n
2.367 * [backup-simplify]: Simplify -2.0 into -2.0
2.367 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.367 * [taylor]: Taking taylor expansion of PI in n
2.367 * [backup-simplify]: Simplify PI into PI
2.367 * [taylor]: Taking taylor expansion of n in n
2.367 * [backup-simplify]: Simplify 0 into 0
2.367 * [backup-simplify]: Simplify 1 into 1
2.367 * [backup-simplify]: Simplify (/ PI 1) into PI
2.368 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
2.368 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
2.368 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
2.368 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.368 * [taylor]: Taking taylor expansion of k in n
2.368 * [backup-simplify]: Simplify k into k
2.368 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.368 * [taylor]: Taking taylor expansion of 1.0 in n
2.368 * [backup-simplify]: Simplify 1.0 into 1.0
2.369 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.369 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
2.370 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))
2.371 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
2.371 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
2.372 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
2.373 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
2.374 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
2.377 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
2.378 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))
2.379 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))
2.379 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n
2.379 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n
2.379 * [taylor]: Taking taylor expansion of +nan.0 in n
2.379 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.379 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n
2.379 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n
2.379 * [taylor]: Taking taylor expansion of 0.5 in n
2.379 * [backup-simplify]: Simplify 0.5 into 0.5
2.379 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n
2.379 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
2.379 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
2.379 * [taylor]: Taking taylor expansion of -2.0 in n
2.379 * [backup-simplify]: Simplify -2.0 into -2.0
2.379 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.379 * [taylor]: Taking taylor expansion of PI in n
2.379 * [backup-simplify]: Simplify PI into PI
2.379 * [taylor]: Taking taylor expansion of n in n
2.379 * [backup-simplify]: Simplify 0 into 0
2.379 * [backup-simplify]: Simplify 1 into 1
2.380 * [backup-simplify]: Simplify (/ PI 1) into PI
2.380 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
2.381 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
2.381 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
2.381 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.381 * [taylor]: Taking taylor expansion of k in n
2.381 * [backup-simplify]: Simplify k into k
2.381 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.381 * [taylor]: Taking taylor expansion of 1.0 in n
2.381 * [backup-simplify]: Simplify 1.0 into 1.0
2.383 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.383 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
2.384 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))
2.385 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
2.386 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
2.387 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
2.388 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
2.390 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
2.391 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.391 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.392 * [backup-simplify]: Simplify (+ 0 0) into 0
2.393 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.395 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
2.397 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
2.397 * [backup-simplify]: Simplify (+ (* (- (log (* -2.0 PI)) (log n)) 0) (* 0 (+ (/ 1 k) 1.0))) into 0
2.398 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into 0
2.399 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.400 * [backup-simplify]: Simplify (+ (* +nan.0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0
2.401 * [backup-simplify]: Simplify 0 into 0
2.401 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.403 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
2.405 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))
2.405 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))
2.405 * [taylor]: Taking taylor expansion of (- (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))) in n
2.405 * [taylor]: Taking taylor expansion of (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) in n
2.405 * [taylor]: Taking taylor expansion of +nan.0 in n
2.405 * [backup-simplify]: Simplify +nan.0 into +nan.0
2.405 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) in n
2.405 * [taylor]: Taking taylor expansion of (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))) in n
2.405 * [taylor]: Taking taylor expansion of 0.5 in n
2.405 * [backup-simplify]: Simplify 0.5 into 0.5
2.405 * [taylor]: Taking taylor expansion of (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)) in n
2.405 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
2.405 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
2.405 * [taylor]: Taking taylor expansion of -2.0 in n
2.405 * [backup-simplify]: Simplify -2.0 into -2.0
2.405 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.405 * [taylor]: Taking taylor expansion of PI in n
2.405 * [backup-simplify]: Simplify PI into PI
2.405 * [taylor]: Taking taylor expansion of n in n
2.405 * [backup-simplify]: Simplify 0 into 0
2.405 * [backup-simplify]: Simplify 1 into 1
2.406 * [backup-simplify]: Simplify (/ PI 1) into PI
2.406 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
2.407 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
2.407 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
2.407 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.407 * [taylor]: Taking taylor expansion of k in n
2.407 * [backup-simplify]: Simplify k into k
2.407 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.407 * [taylor]: Taking taylor expansion of 1.0 in n
2.407 * [backup-simplify]: Simplify 1.0 into 1.0
2.408 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.408 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
2.409 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) into (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))
2.409 * [backup-simplify]: Simplify (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
2.410 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
2.411 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
2.412 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
2.413 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
2.415 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (* 1 (/ 1 (- k))) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (* 1 (/ 1 (- k)))) (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))))))))
2.415 * * * * [progress]: [ 4 / 4 ] generating series at (2 2)
2.416 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
2.416 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
2.416 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
2.416 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
2.416 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
2.416 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
2.416 * [taylor]: Taking taylor expansion of 0.5 in k
2.416 * [backup-simplify]: Simplify 0.5 into 0.5
2.416 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
2.416 * [taylor]: Taking taylor expansion of 1.0 in k
2.416 * [backup-simplify]: Simplify 1.0 into 1.0
2.416 * [taylor]: Taking taylor expansion of k in k
2.416 * [backup-simplify]: Simplify 0 into 0
2.416 * [backup-simplify]: Simplify 1 into 1
2.416 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
2.416 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
2.416 * [taylor]: Taking taylor expansion of 2.0 in k
2.416 * [backup-simplify]: Simplify 2.0 into 2.0
2.416 * [taylor]: Taking taylor expansion of (* n PI) in k
2.416 * [taylor]: Taking taylor expansion of n in k
2.416 * [backup-simplify]: Simplify n into n
2.416 * [taylor]: Taking taylor expansion of PI in k
2.416 * [backup-simplify]: Simplify PI into PI
2.416 * [backup-simplify]: Simplify (* n PI) into (* n PI)
2.416 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
2.416 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
2.417 * [backup-simplify]: Simplify (- 0) into 0
2.417 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
2.417 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
2.417 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
2.417 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
2.417 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
2.417 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
2.418 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
2.418 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
2.418 * [taylor]: Taking taylor expansion of 0.5 in n
2.418 * [backup-simplify]: Simplify 0.5 into 0.5
2.418 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
2.418 * [taylor]: Taking taylor expansion of 1.0 in n
2.418 * [backup-simplify]: Simplify 1.0 into 1.0
2.418 * [taylor]: Taking taylor expansion of k in n
2.418 * [backup-simplify]: Simplify k into k
2.418 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
2.418 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
2.418 * [taylor]: Taking taylor expansion of 2.0 in n
2.418 * [backup-simplify]: Simplify 2.0 into 2.0
2.418 * [taylor]: Taking taylor expansion of (* n PI) in n
2.418 * [taylor]: Taking taylor expansion of n in n
2.418 * [backup-simplify]: Simplify 0 into 0
2.418 * [backup-simplify]: Simplify 1 into 1
2.418 * [taylor]: Taking taylor expansion of PI in n
2.418 * [backup-simplify]: Simplify PI into PI
2.418 * [backup-simplify]: Simplify (* 0 PI) into 0
2.418 * [backup-simplify]: Simplify (* 2.0 0) into 0
2.419 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.420 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
2.421 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.421 * [backup-simplify]: Simplify (- k) into (- k)
2.421 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
2.421 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
2.422 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.423 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
2.423 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
2.423 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
2.423 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
2.423 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
2.423 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
2.423 * [taylor]: Taking taylor expansion of 0.5 in n
2.423 * [backup-simplify]: Simplify 0.5 into 0.5
2.423 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
2.423 * [taylor]: Taking taylor expansion of 1.0 in n
2.423 * [backup-simplify]: Simplify 1.0 into 1.0
2.423 * [taylor]: Taking taylor expansion of k in n
2.423 * [backup-simplify]: Simplify k into k
2.424 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
2.424 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
2.424 * [taylor]: Taking taylor expansion of 2.0 in n
2.424 * [backup-simplify]: Simplify 2.0 into 2.0
2.424 * [taylor]: Taking taylor expansion of (* n PI) in n
2.424 * [taylor]: Taking taylor expansion of n in n
2.424 * [backup-simplify]: Simplify 0 into 0
2.424 * [backup-simplify]: Simplify 1 into 1
2.424 * [taylor]: Taking taylor expansion of PI in n
2.424 * [backup-simplify]: Simplify PI into PI
2.424 * [backup-simplify]: Simplify (* 0 PI) into 0
2.424 * [backup-simplify]: Simplify (* 2.0 0) into 0
2.425 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
2.426 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
2.427 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.427 * [backup-simplify]: Simplify (- k) into (- k)
2.427 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
2.427 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
2.428 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.428 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
2.429 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
2.429 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
2.429 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
2.429 * [taylor]: Taking taylor expansion of 0.5 in k
2.429 * [backup-simplify]: Simplify 0.5 into 0.5
2.429 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
2.429 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
2.429 * [taylor]: Taking taylor expansion of 1.0 in k
2.429 * [backup-simplify]: Simplify 1.0 into 1.0
2.429 * [taylor]: Taking taylor expansion of k in k
2.429 * [backup-simplify]: Simplify 0 into 0
2.429 * [backup-simplify]: Simplify 1 into 1
2.430 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
2.430 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
2.430 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
2.430 * [taylor]: Taking taylor expansion of 2.0 in k
2.430 * [backup-simplify]: Simplify 2.0 into 2.0
2.430 * [taylor]: Taking taylor expansion of PI in k
2.430 * [backup-simplify]: Simplify PI into PI
2.430 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.431 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.431 * [taylor]: Taking taylor expansion of (log n) in k
2.431 * [taylor]: Taking taylor expansion of n in k
2.431 * [backup-simplify]: Simplify n into n
2.431 * [backup-simplify]: Simplify (log n) into (log n)
2.431 * [backup-simplify]: Simplify (- 0) into 0
2.431 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
2.432 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
2.433 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
2.433 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
2.434 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
2.435 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
2.435 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
2.436 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
2.437 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
2.437 * [backup-simplify]: Simplify (- 0) into 0
2.437 * [backup-simplify]: Simplify (+ 0 0) into 0
2.438 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
2.439 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.439 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
2.440 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.441 * [taylor]: Taking taylor expansion of 0 in k
2.441 * [backup-simplify]: Simplify 0 into 0
2.441 * [backup-simplify]: Simplify 0 into 0
2.441 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
2.443 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
2.444 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
2.444 * [backup-simplify]: Simplify (+ 0 0) into 0
2.445 * [backup-simplify]: Simplify (- 1) into -1
2.445 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.446 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
2.448 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
2.451 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
2.454 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
2.454 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
2.455 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
2.457 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
2.457 * [backup-simplify]: Simplify (- 0) into 0
2.458 * [backup-simplify]: Simplify (+ 0 0) into 0
2.458 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
2.459 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
2.460 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
2.462 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.462 * [taylor]: Taking taylor expansion of 0 in k
2.462 * [backup-simplify]: Simplify 0 into 0
2.462 * [backup-simplify]: Simplify 0 into 0
2.462 * [backup-simplify]: Simplify 0 into 0
2.462 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
2.464 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
2.466 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
2.466 * [backup-simplify]: Simplify (+ 0 0) into 0
2.466 * [backup-simplify]: Simplify (- 0) into 0
2.466 * [backup-simplify]: Simplify (+ 0 0) into 0
2.467 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
2.469 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
2.472 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
2.475 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
2.481 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))
2.482 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))
2.482 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
2.482 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
2.482 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
2.482 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
2.482 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
2.482 * [taylor]: Taking taylor expansion of 0.5 in k
2.482 * [backup-simplify]: Simplify 0.5 into 0.5
2.482 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
2.482 * [taylor]: Taking taylor expansion of 1.0 in k
2.482 * [backup-simplify]: Simplify 1.0 into 1.0
2.482 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.482 * [taylor]: Taking taylor expansion of k in k
2.482 * [backup-simplify]: Simplify 0 into 0
2.482 * [backup-simplify]: Simplify 1 into 1
2.483 * [backup-simplify]: Simplify (/ 1 1) into 1
2.483 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
2.483 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
2.483 * [taylor]: Taking taylor expansion of 2.0 in k
2.483 * [backup-simplify]: Simplify 2.0 into 2.0
2.483 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.483 * [taylor]: Taking taylor expansion of PI in k
2.483 * [backup-simplify]: Simplify PI into PI
2.483 * [taylor]: Taking taylor expansion of n in k
2.483 * [backup-simplify]: Simplify n into n
2.483 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.483 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
2.483 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
2.483 * [backup-simplify]: Simplify (- 1) into -1
2.483 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.484 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
2.484 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
2.484 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
2.484 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
2.484 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
2.484 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
2.484 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
2.484 * [taylor]: Taking taylor expansion of 0.5 in n
2.484 * [backup-simplify]: Simplify 0.5 into 0.5
2.484 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
2.484 * [taylor]: Taking taylor expansion of 1.0 in n
2.484 * [backup-simplify]: Simplify 1.0 into 1.0
2.484 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.484 * [taylor]: Taking taylor expansion of k in n
2.484 * [backup-simplify]: Simplify k into k
2.484 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.484 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
2.484 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
2.484 * [taylor]: Taking taylor expansion of 2.0 in n
2.484 * [backup-simplify]: Simplify 2.0 into 2.0
2.484 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.484 * [taylor]: Taking taylor expansion of PI in n
2.484 * [backup-simplify]: Simplify PI into PI
2.484 * [taylor]: Taking taylor expansion of n in n
2.484 * [backup-simplify]: Simplify 0 into 0
2.484 * [backup-simplify]: Simplify 1 into 1
2.485 * [backup-simplify]: Simplify (/ PI 1) into PI
2.485 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.486 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.486 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
2.486 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
2.487 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
2.488 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.493 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
2.494 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
2.494 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
2.494 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
2.494 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
2.494 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
2.494 * [taylor]: Taking taylor expansion of 0.5 in n
2.494 * [backup-simplify]: Simplify 0.5 into 0.5
2.494 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
2.495 * [taylor]: Taking taylor expansion of 1.0 in n
2.495 * [backup-simplify]: Simplify 1.0 into 1.0
2.495 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.495 * [taylor]: Taking taylor expansion of k in n
2.495 * [backup-simplify]: Simplify k into k
2.495 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.495 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
2.495 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
2.495 * [taylor]: Taking taylor expansion of 2.0 in n
2.495 * [backup-simplify]: Simplify 2.0 into 2.0
2.495 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.495 * [taylor]: Taking taylor expansion of PI in n
2.495 * [backup-simplify]: Simplify PI into PI
2.495 * [taylor]: Taking taylor expansion of n in n
2.495 * [backup-simplify]: Simplify 0 into 0
2.495 * [backup-simplify]: Simplify 1 into 1
2.496 * [backup-simplify]: Simplify (/ PI 1) into PI
2.496 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.497 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.497 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
2.497 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
2.497 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
2.498 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.499 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
2.499 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
2.500 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
2.500 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
2.500 * [taylor]: Taking taylor expansion of 0.5 in k
2.500 * [backup-simplify]: Simplify 0.5 into 0.5
2.500 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
2.500 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
2.500 * [taylor]: Taking taylor expansion of 1.0 in k
2.500 * [backup-simplify]: Simplify 1.0 into 1.0
2.500 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.500 * [taylor]: Taking taylor expansion of k in k
2.500 * [backup-simplify]: Simplify 0 into 0
2.500 * [backup-simplify]: Simplify 1 into 1
2.500 * [backup-simplify]: Simplify (/ 1 1) into 1
2.500 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
2.500 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
2.500 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
2.500 * [taylor]: Taking taylor expansion of 2.0 in k
2.500 * [backup-simplify]: Simplify 2.0 into 2.0
2.500 * [taylor]: Taking taylor expansion of PI in k
2.500 * [backup-simplify]: Simplify PI into PI
2.500 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
2.501 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
2.501 * [taylor]: Taking taylor expansion of (log n) in k
2.501 * [taylor]: Taking taylor expansion of n in k
2.501 * [backup-simplify]: Simplify n into n
2.501 * [backup-simplify]: Simplify (log n) into (log n)
2.501 * [backup-simplify]: Simplify (- 1) into -1
2.502 * [backup-simplify]: Simplify (+ 0 -1) into -1
2.502 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.502 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
2.503 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
2.504 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
2.505 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
2.505 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
2.506 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.506 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
2.508 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
2.508 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.508 * [backup-simplify]: Simplify (- 0) into 0
2.508 * [backup-simplify]: Simplify (+ 0 0) into 0
2.509 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
2.510 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.510 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
2.512 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
2.512 * [taylor]: Taking taylor expansion of 0 in k
2.512 * [backup-simplify]: Simplify 0 into 0
2.512 * [backup-simplify]: Simplify 0 into 0
2.512 * [backup-simplify]: Simplify 0 into 0
2.513 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.513 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
2.515 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
2.516 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.516 * [backup-simplify]: Simplify (- 0) into 0
2.516 * [backup-simplify]: Simplify (+ 0 0) into 0
2.517 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
2.518 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.519 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
2.521 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.521 * [taylor]: Taking taylor expansion of 0 in k
2.521 * [backup-simplify]: Simplify 0 into 0
2.521 * [backup-simplify]: Simplify 0 into 0
2.521 * [backup-simplify]: Simplify 0 into 0
2.521 * [backup-simplify]: Simplify 0 into 0
2.522 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.522 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.526 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
2.526 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.527 * [backup-simplify]: Simplify (- 0) into 0
2.527 * [backup-simplify]: Simplify (+ 0 0) into 0
2.528 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
2.529 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
2.530 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
2.531 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.531 * [taylor]: Taking taylor expansion of 0 in k
2.531 * [backup-simplify]: Simplify 0 into 0
2.531 * [backup-simplify]: Simplify 0 into 0
2.532 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n))))))
2.533 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))
2.533 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
2.533 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
2.533 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
2.533 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
2.533 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
2.533 * [taylor]: Taking taylor expansion of 0.5 in k
2.533 * [backup-simplify]: Simplify 0.5 into 0.5
2.533 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
2.533 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.533 * [taylor]: Taking taylor expansion of k in k
2.533 * [backup-simplify]: Simplify 0 into 0
2.533 * [backup-simplify]: Simplify 1 into 1
2.533 * [backup-simplify]: Simplify (/ 1 1) into 1
2.533 * [taylor]: Taking taylor expansion of 1.0 in k
2.533 * [backup-simplify]: Simplify 1.0 into 1.0
2.533 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
2.533 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
2.533 * [taylor]: Taking taylor expansion of -2.0 in k
2.533 * [backup-simplify]: Simplify -2.0 into -2.0
2.533 * [taylor]: Taking taylor expansion of (/ PI n) in k
2.534 * [taylor]: Taking taylor expansion of PI in k
2.534 * [backup-simplify]: Simplify PI into PI
2.534 * [taylor]: Taking taylor expansion of n in k
2.534 * [backup-simplify]: Simplify n into n
2.534 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
2.534 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
2.534 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
2.534 * [backup-simplify]: Simplify (+ 1 0) into 1
2.534 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
2.534 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
2.534 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
2.535 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
2.535 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
2.535 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
2.535 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
2.535 * [taylor]: Taking taylor expansion of 0.5 in n
2.535 * [backup-simplify]: Simplify 0.5 into 0.5
2.535 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
2.535 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.535 * [taylor]: Taking taylor expansion of k in n
2.535 * [backup-simplify]: Simplify k into k
2.535 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.535 * [taylor]: Taking taylor expansion of 1.0 in n
2.535 * [backup-simplify]: Simplify 1.0 into 1.0
2.535 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
2.535 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
2.535 * [taylor]: Taking taylor expansion of -2.0 in n
2.535 * [backup-simplify]: Simplify -2.0 into -2.0
2.535 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.535 * [taylor]: Taking taylor expansion of PI in n
2.535 * [backup-simplify]: Simplify PI into PI
2.535 * [taylor]: Taking taylor expansion of n in n
2.535 * [backup-simplify]: Simplify 0 into 0
2.535 * [backup-simplify]: Simplify 1 into 1
2.535 * [backup-simplify]: Simplify (/ PI 1) into PI
2.536 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
2.536 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
2.536 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
2.536 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
2.537 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.538 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
2.539 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
2.539 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
2.539 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
2.539 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
2.539 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
2.539 * [taylor]: Taking taylor expansion of 0.5 in n
2.539 * [backup-simplify]: Simplify 0.5 into 0.5
2.539 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
2.539 * [taylor]: Taking taylor expansion of (/ 1 k) in n
2.539 * [taylor]: Taking taylor expansion of k in n
2.539 * [backup-simplify]: Simplify k into k
2.539 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
2.539 * [taylor]: Taking taylor expansion of 1.0 in n
2.539 * [backup-simplify]: Simplify 1.0 into 1.0
2.539 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
2.539 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
2.539 * [taylor]: Taking taylor expansion of -2.0 in n
2.539 * [backup-simplify]: Simplify -2.0 into -2.0
2.539 * [taylor]: Taking taylor expansion of (/ PI n) in n
2.539 * [taylor]: Taking taylor expansion of PI in n
2.539 * [backup-simplify]: Simplify PI into PI
2.539 * [taylor]: Taking taylor expansion of n in n
2.539 * [backup-simplify]: Simplify 0 into 0
2.539 * [backup-simplify]: Simplify 1 into 1
2.540 * [backup-simplify]: Simplify (/ PI 1) into PI
2.540 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
2.541 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
2.541 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
2.541 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
2.542 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.544 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
2.545 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
2.545 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
2.545 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
2.545 * [taylor]: Taking taylor expansion of 0.5 in k
2.545 * [backup-simplify]: Simplify 0.5 into 0.5
2.545 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
2.545 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
2.545 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
2.545 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
2.545 * [taylor]: Taking taylor expansion of -2.0 in k
2.545 * [backup-simplify]: Simplify -2.0 into -2.0
2.545 * [taylor]: Taking taylor expansion of PI in k
2.546 * [backup-simplify]: Simplify PI into PI
2.546 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
2.547 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
2.547 * [taylor]: Taking taylor expansion of (log n) in k
2.547 * [taylor]: Taking taylor expansion of n in k
2.547 * [backup-simplify]: Simplify n into n
2.547 * [backup-simplify]: Simplify (log n) into (log n)
2.547 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
2.547 * [taylor]: Taking taylor expansion of (/ 1 k) in k
2.548 * [taylor]: Taking taylor expansion of k in k
2.548 * [backup-simplify]: Simplify 0 into 0
2.548 * [backup-simplify]: Simplify 1 into 1
2.548 * [backup-simplify]: Simplify (/ 1 1) into 1
2.548 * [taylor]: Taking taylor expansion of 1.0 in k
2.548 * [backup-simplify]: Simplify 1.0 into 1.0
2.548 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
2.549 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
2.550 * [backup-simplify]: Simplify (+ 1 0) into 1
2.551 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
2.552 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
2.554 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
2.555 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
2.556 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
2.556 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
2.558 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
2.558 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
2.559 * [backup-simplify]: Simplify (+ 0 0) into 0
2.559 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
2.561 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.562 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
2.564 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
2.564 * [taylor]: Taking taylor expansion of 0 in k
2.564 * [backup-simplify]: Simplify 0 into 0
2.564 * [backup-simplify]: Simplify 0 into 0
2.564 * [backup-simplify]: Simplify 0 into 0
2.565 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.566 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
2.569 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
2.570 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.570 * [backup-simplify]: Simplify (+ 0 0) into 0
2.571 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
2.572 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.574 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
2.576 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
2.576 * [taylor]: Taking taylor expansion of 0 in k
2.576 * [backup-simplify]: Simplify 0 into 0
2.576 * [backup-simplify]: Simplify 0 into 0
2.576 * [backup-simplify]: Simplify 0 into 0
2.576 * [backup-simplify]: Simplify 0 into 0
2.577 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
2.578 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
2.584 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0
2.584 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
2.585 * [backup-simplify]: Simplify (+ 0 0) into 0
2.585 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
2.586 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
2.587 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
2.589 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
2.589 * [taylor]: Taking taylor expansion of 0 in k
2.589 * [backup-simplify]: Simplify 0 into 0
2.589 * [backup-simplify]: Simplify 0 into 0
2.590 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
2.590 * * * [progress]: simplifying candidates
2.592 * [simplify]: Simplifying:
  (expm1 (/ 1.0 (sqrt k)))
  (log1p (/ 1.0 (sqrt k)))
  (- (log 1.0) (log (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (- 1.0)
  (- (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (cbrt 1.0) (cbrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (* (cbrt k) (cbrt k))))
  (/ (cbrt 1.0) (sqrt (cbrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 1))
  (/ (cbrt 1.0) (sqrt k))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (sqrt k)))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) 1)
  (/ (cbrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (sqrt 1.0) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (* (cbrt k) (cbrt k))))
  (/ (sqrt 1.0) (sqrt (cbrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt 1))
  (/ (sqrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) 1)
  (/ (sqrt 1.0) (sqrt k))
  (/ 1 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (cbrt (sqrt k)))
  (/ 1 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1.0 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 (sqrt 1))
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1 1)
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1.0)
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1.0 (sqrt 1))
  (/ 1.0 (sqrt (sqrt k)))
  (/ 1.0 1)
  (/ (sqrt k) (cbrt 1.0))
  (/ (sqrt k) (sqrt 1.0))
  (/ (sqrt k) 1.0)
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (expm1 (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (log1p (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (+ (- (log 1.0) (log (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (- (log 1.0) (log (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (+ (log (/ 1.0 (sqrt k))) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0)))
  (+ (log (/ 1.0 (sqrt k))) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (log (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (exp (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (* (* 1.0 1.0) 1.0) (* (* (sqrt k) (sqrt k)) (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k))) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (cbrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
  (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (/ 1.0 (sqrt k)) (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (/ 1.0 (sqrt k)) 1)
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
  (* (cbrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (sqrt (/ 1.0 (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (cbrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))
  (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (pow (* (* 2.0 PI) n) (/ 1.0 2.0))
  (pow (* (* 2.0 PI) n) (/ k 2.0))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) 1)
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (- (+ (* +nan.0 (pow k 2)) (- (+ +nan.0 (- (* +nan.0 k))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- (* +nan.0 (/ 1 (pow k 3))))))))
  (- (+ (* +nan.0 (/ 1 (pow k 2))) (- (+ (* +nan.0 (/ 1 k)) (- +nan.0)))))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) k)) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (pow k 2))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5)) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log (* 2.0 PI)) 2) (pow k 2)))) (- (+ (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (log (* 2.0 PI)) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log n) k))) (- (+ (* +nan.0 (* (pow (* (pow 2.0 1.0) (* (pow n 1.0) (pow PI 1.0))) 0.5) (* (log (* 2.0 PI)) (pow k 2)))) (- (* +nan.0 (* (pow (* (pow PI 1.0) (* (pow n 1.0) (pow 2.0 1.0))) 0.5) (* (pow (log n) 2) (pow k 2)))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))))))))
  (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n))))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
2.596 * * [simplify]: iteration 0: 361 enodes
2.676 * * [simplify]: iteration 1: 1013 enodes
3.327 * * [simplify]: iteration 2: 4865 enodes
4.454 * * [simplify]: iteration complete: 5000 enodes
4.455 * * [simplify]: Extracting #0: cost 128 inf + 0
4.458 * * [simplify]: Extracting #1: cost 741 inf + 84
4.466 * * [simplify]: Extracting #2: cost 1359 inf + 2611
4.491 * * [simplify]: Extracting #3: cost 1253 inf + 61292
4.535 * * [simplify]: Extracting #4: cost 698 inf + 222924
4.617 * * [simplify]: Extracting #5: cost 382 inf + 410391
4.739 * * [simplify]: Extracting #6: cost 334 inf + 486091
4.880 * * [simplify]: Extracting #7: cost 110 inf + 660372
5.042 * * [simplify]: Extracting #8: cost 25 inf + 745631
5.203 * * [simplify]: Extracting #9: cost 2 inf + 785086
5.366 * * [simplify]: Extracting #10: cost 0 inf + 787165
5.528 * * [simplify]: Extracting #11: cost 0 inf + 786495
5.683 * * [simplify]: Extracting #12: cost 0 inf + 786365
5.877 * [simplify]: Simplified to:
  (expm1 (/ 1.0 (sqrt k)))
  (log1p (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (log (/ 1.0 (sqrt k)))
  (exp (/ 1.0 (sqrt k)))
  (* (/ (* 1.0 1.0) (sqrt k)) (/ 1.0 k))
  (* (cbrt (/ 1.0 (sqrt k))) (cbrt (/ 1.0 (sqrt k))))
  (cbrt (/ 1.0 (sqrt k)))
  (* (* (/ 1.0 (sqrt k)) (/ 1.0 (sqrt k))) (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (sqrt (/ 1.0 (sqrt k)))
  (- 1.0)
  (- (sqrt k))
  (* (/ (cbrt 1.0) (cbrt (sqrt k))) (/ (cbrt 1.0) (cbrt (sqrt k))))
  (/ (cbrt 1.0) (cbrt (sqrt k)))
  (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt k)))
  (/ (cbrt 1.0) (sqrt (cbrt k)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt (sqrt k)))
  (* (cbrt 1.0) (cbrt 1.0))
  (/ (cbrt 1.0) (sqrt k))
  (/ (/ (sqrt 1.0) (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (cbrt (sqrt k)))
  (/ (sqrt 1.0) (fabs (cbrt k)))
  (/ (sqrt 1.0) (sqrt (cbrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt k))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (/ (sqrt 1.0) (sqrt (sqrt k)))
  (sqrt 1.0)
  (/ (sqrt 1.0) (sqrt k))
  (/ (/ 1 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ 1.0 (cbrt (sqrt k)))
  (/ 1 (fabs (cbrt k)))
  (/ 1.0 (sqrt (cbrt k)))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1
  (/ 1.0 (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) 1.0)
  (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ 1.0 (fabs (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  1.0
  (/ 1.0 (sqrt (sqrt k)))
  1.0
  (/ (sqrt k) (cbrt 1.0))
  (/ (sqrt k) (sqrt 1.0))
  (/ (sqrt k) 1.0)
  (expm1 (* PI (* 2.0 n)))
  (log1p (* PI (* 2.0 n)))
  (* PI (* 2.0 n))
  (* PI (* 2.0 n))
  (log (* PI (* 2.0 n)))
  (log (* PI (* 2.0 n)))
  (log (* PI (* 2.0 n)))
  (exp (* PI (* 2.0 n)))
  (* (* (* (* PI 2.0) (* (* PI 2.0) (* PI 2.0))) n) (* n n))
  (* (* (* (* PI 2.0) (* (* PI 2.0) (* PI 2.0))) n) (* n n))
  (* (cbrt (* PI (* 2.0 n))) (cbrt (* PI (* 2.0 n))))
  (cbrt (* PI (* 2.0 n)))
  (* (* (* PI (* 2.0 n)) (* PI (* 2.0 n))) (* PI (* 2.0 n)))
  (sqrt (* PI (* 2.0 n)))
  (sqrt (* PI (* 2.0 n)))
  (* PI (* 2.0 (* (cbrt n) (cbrt n))))
  (* 2.0 (* PI (sqrt n)))
  (* PI 2.0)
  (* n PI)
  (expm1 (* (/ 1.0 (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))))
  (log1p (* (/ 1.0 (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))))
  (fma (log (* PI (* 2.0 n))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* PI (* 2.0 n))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* PI (* 2.0 n))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* PI (* 2.0 n))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* PI (* 2.0 n))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* PI (* 2.0 n))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* PI (* 2.0 n))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* PI (* 2.0 n))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* PI (* 2.0 n))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* PI (* 2.0 n))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (fma (log (* PI (* 2.0 n))) (/ (- 1.0 k) 2.0) (log (/ 1.0 (sqrt k))))
  (exp (* (/ 1.0 (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))))
  (* (* (* (/ (* 1.0 1.0) (sqrt k)) (/ 1.0 k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))) (* (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))))
  (* (* (/ 1.0 (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))) (* (* (/ 1.0 (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))))
  (* (cbrt (* (/ 1.0 (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))) (cbrt (* (/ 1.0 (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))))
  (cbrt (* (/ 1.0 (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))))
  (* (* (/ 1.0 (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))) (* (* (/ 1.0 (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))) (* (/ 1.0 (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))))
  (sqrt (* (/ 1.0 (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))))
  (* (pow (* PI (* 2.0 n)) (/ 1.0 2.0)) 1.0)
  (* (sqrt k) (pow (* PI (* 2.0 n)) (/ k 2.0)))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))))
  (* (sqrt (/ 1.0 (sqrt k))) (sqrt (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))))
  (* (pow (* PI (* 2.0 n)) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (/ 1.0 (sqrt k))))
  (* (pow (* PI (* 2.0 n)) (/ (/ (- 1.0 k) 2.0) 2)) (sqrt (/ 1.0 (sqrt k))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))))
  (* (pow (* PI (* 2.0 n)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (* (pow (* PI (* 2.0 n)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))))
  (* (/ (sqrt 1.0) (sqrt (sqrt k))) (sqrt (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))))
  (* (pow (* PI (* 2.0 n)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (* (pow (* PI (* 2.0 n)) (/ (/ (- 1.0 k) 2.0) 2)) (/ (sqrt 1.0) (sqrt (sqrt k))))
  (/ (* 1.0 (pow (* PI 2.0) (/ (- 1.0 k) 2.0))) (sqrt k))
  (* (* (cbrt (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))) (/ 1.0 (sqrt k)))
  (* (/ 1.0 (sqrt k)) (sqrt (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (sqrt k))
  (/ (* (pow (* PI (* 2.0 n)) (/ (/ (- 1.0 k) 2.0) 2)) 1.0) (sqrt k))
  (* (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)) (cbrt (/ 1.0 (sqrt k))))
  (* (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)) (sqrt (/ 1.0 (sqrt k))))
  (* (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)) (/ (cbrt 1.0) (cbrt (sqrt k))))
  (/ (* (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)) (cbrt 1.0)) (sqrt (cbrt k)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt (sqrt k))) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (* (/ (cbrt 1.0) (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (* (/ (sqrt 1.0) (cbrt (sqrt k))) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (* (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)) (/ (sqrt 1.0) (sqrt (cbrt k))))
  (/ (* (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (sqrt k)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (/ (* (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)) (sqrt 1.0)) (sqrt (sqrt k)))
  (* (/ (sqrt 1.0) (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (/ (* 1.0 (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))) (cbrt (sqrt k)))
  (* (/ 1.0 (sqrt (cbrt k))) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (/ (* 1.0 (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (* (/ 1.0 (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (/ (* 1.0 (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (* (/ 1.0 (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt k)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (/ (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ (* 1.0 (pow (* PI (* 2.0 n)) (/ 1.0 2.0))) (sqrt k))
  (* 1.0 (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (expm1 (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (/ (* (- 1.0 k) (log (* PI (* 2.0 n)))) 2.0)
  (/ (* (- 1.0 k) (log (* PI (* 2.0 n)))) 2.0)
  (/ (* (- 1.0 k) (log (* PI (* 2.0 n)))) 2.0)
  (/ (* (- 1.0 k) (log (* PI (* 2.0 n)))) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (pow (* PI (* 2.0 n)) (/ 1.0 2.0))
  (pow (* PI (* 2.0 n)) (/ k 2.0))
  (pow (* PI (* 2.0 n)) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* PI (* 2.0 n)) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* PI (* 2.0 n)) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0))))
  (pow (* PI (* 2.0 n)) (* (/ (cbrt (- 1.0 k)) (sqrt 2.0)) (cbrt (- 1.0 k))))
  (pow (* PI (* 2.0 n)) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* PI (* 2.0 n)) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* PI (* 2.0 n)) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* PI (* 2.0 n)) (sqrt (- 1.0 k)))
  (pow (* PI (* 2.0 n)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0)))
  (pow (* PI (* 2.0 n)) (/ 1 (sqrt 2.0)))
  (* PI (* 2.0 n))
  (pow (* PI (* 2.0 n)) (/ (/ (+ (sqrt 1.0) (sqrt k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* PI (* 2.0 n)) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* PI (* 2.0 n)) (+ (sqrt 1.0) (sqrt k)))
  (pow (* PI (* 2.0 n)) (/ (/ 1 (cbrt 2.0)) (cbrt 2.0)))
  (pow (* PI (* 2.0 n)) (/ 1 (sqrt 2.0)))
  (* PI (* 2.0 n))
  (* PI (* 2.0 n))
  (pow (* PI (* 2.0 n)) (- 1.0 k))
  (pow (* PI 2.0) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (/ (* (- 1.0 k) (log (* PI (* 2.0 n)))) 2.0)
  (exp (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))) (cbrt (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0))) (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* PI (* 2.0 n)) (/ (- 1.0 k) 2.0)))
  (pow (* PI (* 2.0 n)) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* PI (* 2.0 n)) (/ (/ (- 1.0 k) 2.0) 2))
  (+ (- (* +nan.0 (* k k))) (- +nan.0 (* k +nan.0)))
  (+ (- (/ +nan.0 k) (/ (/ +nan.0 (* k k)) k)) (- (/ +nan.0 (* k k))))
  (+ (- (/ +nan.0 (* k k))) (- (/ +nan.0 k) +nan.0))
  (* PI (* 2.0 n))
  (* PI (* 2.0 n))
  (* PI (* 2.0 n))
  (- (fma k (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0) (fma (- (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0)) (* k k) (fma (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0) (* (* k k) (log n)) (+ (fma (* (* k (log (* PI 2.0))) (* k (log (* PI 2.0)))) (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0) (+ (fma (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0) (* k (log (* PI 2.0))) (- (fma (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0) (* (log n) k) (- (- (* (* (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0) (log (* PI 2.0))) (* k k)) (* (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0) (* (* (log n) k) (* (log n) k)))))))) (* (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0) (- (* (* (* k k) (log n)) (log (* PI 2.0))))))) (- (* (pow (* (pow 2.0 1.0) (* (pow PI 1.0) (pow n 1.0))) 0.5) +nan.0)))))))
  (- (fma +nan.0 (/ (exp (* (* (log (* PI (* 2.0 n))) (- 1.0 k)) 0.5)) (* k k)) (fma (- +nan.0) (/ (exp (* (* (log (* PI (* 2.0 n))) (- 1.0 k)) 0.5)) k) (* (/ +nan.0 k) (/ (exp (* (* (log (* PI (* 2.0 n))) (- 1.0 k)) 0.5)) (* k k))))))
  (- (* (exp (* (* (- 1.0 k) 0.5) (- (log (* PI -2.0)) (log (/ -1 n))))) (- +nan.0)) (- (/ (* (exp (* (* (- 1.0 k) 0.5) (- (log (* PI -2.0)) (log (/ -1 n))))) (- +nan.0)) k) (/ (* (exp (* (* (- 1.0 k) 0.5) (- (log (* PI -2.0)) (log (/ -1 n))))) (- +nan.0)) (* k k))))
  (fma (* (* (exp (* 0.5 (log (* PI (* 2.0 n))))) (log n)) (* (log (* PI 2.0)) (* k k))) 0.25 (- (fma (* (exp (* 0.5 (log (* PI (* 2.0 n))))) 0.125) (* (* (log n) k) (* (log n) k)) (fma (* (* (* (log (* PI 2.0)) (log (* PI 2.0))) (* k k)) (exp (* 0.5 (log (* PI (* 2.0 n)))))) 0.125 (exp (* 0.5 (log (* PI (* 2.0 n))))))) (* 0.5 (fma (* (log n) k) (exp (* 0.5 (log (* PI (* 2.0 n))))) (* (* (log (* PI 2.0)) k) (exp (* 0.5 (log (* PI (* 2.0 n))))))))))
  (exp (* (* (log (* PI (* 2.0 n))) (- 1.0 k)) 0.5))
  (exp (* (* (- 1.0 k) 0.5) (- (log (* PI -2.0)) (log (/ -1 n)))))
5.888 * * * [progress]: adding candidates to table
6.769 * * [progress]: iteration 2 / 4
6.769 * * * [progress]: picking best candidate
6.866 * * * * [pick]: Picked  #<alt (λ (k n) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))>
6.866 * * * [progress]: localizing error
6.898 * * * [progress]: generating rewritten candidates
6.898 * * * * [progress]: [ 1 / 3 ] rewriting at (2 1 2 1)
6.912 * * * * [progress]: [ 2 / 3 ] rewriting at (2)
6.932 * * * * [progress]: [ 3 / 3 ] rewriting at (2 1 2)
6.952 * * * [progress]: generating series expansions
6.952 * * * * [progress]: [ 1 / 3 ] generating series at (2 1 2 1)
6.953 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
6.953 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
6.953 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
6.953 * [taylor]: Taking taylor expansion of 2.0 in n
6.953 * [backup-simplify]: Simplify 2.0 into 2.0
6.953 * [taylor]: Taking taylor expansion of (* n PI) in n
6.953 * [taylor]: Taking taylor expansion of n in n
6.953 * [backup-simplify]: Simplify 0 into 0
6.953 * [backup-simplify]: Simplify 1 into 1
6.953 * [taylor]: Taking taylor expansion of PI in n
6.953 * [backup-simplify]: Simplify PI into PI
6.953 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
6.953 * [taylor]: Taking taylor expansion of 2.0 in n
6.953 * [backup-simplify]: Simplify 2.0 into 2.0
6.953 * [taylor]: Taking taylor expansion of (* n PI) in n
6.953 * [taylor]: Taking taylor expansion of n in n
6.953 * [backup-simplify]: Simplify 0 into 0
6.953 * [backup-simplify]: Simplify 1 into 1
6.953 * [taylor]: Taking taylor expansion of PI in n
6.953 * [backup-simplify]: Simplify PI into PI
6.954 * [backup-simplify]: Simplify (* 0 PI) into 0
6.954 * [backup-simplify]: Simplify (* 2.0 0) into 0
6.954 * [backup-simplify]: Simplify 0 into 0
6.955 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.956 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
6.956 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
6.957 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
6.957 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
6.958 * [backup-simplify]: Simplify 0 into 0
6.958 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
6.959 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
6.959 * [backup-simplify]: Simplify 0 into 0
6.960 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
6.960 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
6.960 * [backup-simplify]: Simplify 0 into 0
6.961 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
6.962 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
6.962 * [backup-simplify]: Simplify 0 into 0
6.963 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
6.964 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
6.964 * [backup-simplify]: Simplify 0 into 0
6.965 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
6.966 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
6.966 * [backup-simplify]: Simplify 0 into 0
6.967 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
6.967 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
6.967 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
6.967 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
6.967 * [taylor]: Taking taylor expansion of 2.0 in n
6.967 * [backup-simplify]: Simplify 2.0 into 2.0
6.967 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.967 * [taylor]: Taking taylor expansion of PI in n
6.967 * [backup-simplify]: Simplify PI into PI
6.967 * [taylor]: Taking taylor expansion of n in n
6.967 * [backup-simplify]: Simplify 0 into 0
6.967 * [backup-simplify]: Simplify 1 into 1
6.967 * [backup-simplify]: Simplify (/ PI 1) into PI
6.967 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
6.967 * [taylor]: Taking taylor expansion of 2.0 in n
6.967 * [backup-simplify]: Simplify 2.0 into 2.0
6.967 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.968 * [taylor]: Taking taylor expansion of PI in n
6.968 * [backup-simplify]: Simplify PI into PI
6.968 * [taylor]: Taking taylor expansion of n in n
6.968 * [backup-simplify]: Simplify 0 into 0
6.968 * [backup-simplify]: Simplify 1 into 1
6.968 * [backup-simplify]: Simplify (/ PI 1) into PI
6.968 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
6.969 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
6.969 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.970 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
6.970 * [backup-simplify]: Simplify 0 into 0
6.970 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.971 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
6.971 * [backup-simplify]: Simplify 0 into 0
6.971 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.972 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
6.972 * [backup-simplify]: Simplify 0 into 0
6.973 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.973 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
6.974 * [backup-simplify]: Simplify 0 into 0
6.974 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.975 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
6.975 * [backup-simplify]: Simplify 0 into 0
6.976 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.977 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
6.977 * [backup-simplify]: Simplify 0 into 0
6.977 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
6.977 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
6.977 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
6.977 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
6.977 * [taylor]: Taking taylor expansion of -2.0 in n
6.977 * [backup-simplify]: Simplify -2.0 into -2.0
6.978 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.978 * [taylor]: Taking taylor expansion of PI in n
6.978 * [backup-simplify]: Simplify PI into PI
6.978 * [taylor]: Taking taylor expansion of n in n
6.978 * [backup-simplify]: Simplify 0 into 0
6.978 * [backup-simplify]: Simplify 1 into 1
6.978 * [backup-simplify]: Simplify (/ PI 1) into PI
6.978 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
6.978 * [taylor]: Taking taylor expansion of -2.0 in n
6.978 * [backup-simplify]: Simplify -2.0 into -2.0
6.978 * [taylor]: Taking taylor expansion of (/ PI n) in n
6.978 * [taylor]: Taking taylor expansion of PI in n
6.978 * [backup-simplify]: Simplify PI into PI
6.978 * [taylor]: Taking taylor expansion of n in n
6.978 * [backup-simplify]: Simplify 0 into 0
6.978 * [backup-simplify]: Simplify 1 into 1
6.978 * [backup-simplify]: Simplify (/ PI 1) into PI
6.979 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
6.979 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
6.980 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
6.980 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
6.980 * [backup-simplify]: Simplify 0 into 0
6.981 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.981 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
6.981 * [backup-simplify]: Simplify 0 into 0
6.982 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.982 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
6.982 * [backup-simplify]: Simplify 0 into 0
6.983 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.984 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
6.984 * [backup-simplify]: Simplify 0 into 0
6.985 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.985 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
6.985 * [backup-simplify]: Simplify 0 into 0
6.986 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
6.987 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
6.987 * [backup-simplify]: Simplify 0 into 0
6.988 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
6.988 * * * * [progress]: [ 2 / 3 ] generating series at (2)
6.988 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))))
6.988 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (n k) around 0
6.988 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
6.988 * [taylor]: Taking taylor expansion of 1.0 in k
6.988 * [backup-simplify]: Simplify 1.0 into 1.0
6.988 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
6.988 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
6.988 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
6.988 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
6.988 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
6.988 * [taylor]: Taking taylor expansion of 0.5 in k
6.988 * [backup-simplify]: Simplify 0.5 into 0.5
6.988 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
6.988 * [taylor]: Taking taylor expansion of 1.0 in k
6.988 * [backup-simplify]: Simplify 1.0 into 1.0
6.988 * [taylor]: Taking taylor expansion of k in k
6.988 * [backup-simplify]: Simplify 0 into 0
6.988 * [backup-simplify]: Simplify 1 into 1
6.988 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
6.989 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
6.989 * [taylor]: Taking taylor expansion of 2.0 in k
6.989 * [backup-simplify]: Simplify 2.0 into 2.0
6.989 * [taylor]: Taking taylor expansion of (* n PI) in k
6.989 * [taylor]: Taking taylor expansion of n in k
6.989 * [backup-simplify]: Simplify n into n
6.989 * [taylor]: Taking taylor expansion of PI in k
6.989 * [backup-simplify]: Simplify PI into PI
6.989 * [backup-simplify]: Simplify (* n PI) into (* n PI)
6.989 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
6.989 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
6.989 * [backup-simplify]: Simplify (- 0) into 0
6.989 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
6.990 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
6.990 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
6.990 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
6.990 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
6.990 * [taylor]: Taking taylor expansion of (/ 1 k) in k
6.990 * [taylor]: Taking taylor expansion of k in k
6.990 * [backup-simplify]: Simplify 0 into 0
6.990 * [backup-simplify]: Simplify 1 into 1
6.990 * [backup-simplify]: Simplify (/ 1 1) into 1
6.990 * [backup-simplify]: Simplify (sqrt 0) into 0
6.991 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
6.991 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
6.991 * [taylor]: Taking taylor expansion of 1.0 in n
6.991 * [backup-simplify]: Simplify 1.0 into 1.0
6.991 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
6.991 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
6.991 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
6.991 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
6.991 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
6.991 * [taylor]: Taking taylor expansion of 0.5 in n
6.991 * [backup-simplify]: Simplify 0.5 into 0.5
6.991 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
6.991 * [taylor]: Taking taylor expansion of 1.0 in n
6.991 * [backup-simplify]: Simplify 1.0 into 1.0
6.991 * [taylor]: Taking taylor expansion of k in n
6.991 * [backup-simplify]: Simplify k into k
6.991 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
6.991 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
6.991 * [taylor]: Taking taylor expansion of 2.0 in n
6.991 * [backup-simplify]: Simplify 2.0 into 2.0
6.991 * [taylor]: Taking taylor expansion of (* n PI) in n
6.991 * [taylor]: Taking taylor expansion of n in n
6.992 * [backup-simplify]: Simplify 0 into 0
6.992 * [backup-simplify]: Simplify 1 into 1
6.992 * [taylor]: Taking taylor expansion of PI in n
6.992 * [backup-simplify]: Simplify PI into PI
6.992 * [backup-simplify]: Simplify (* 0 PI) into 0
6.992 * [backup-simplify]: Simplify (* 2.0 0) into 0
6.993 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
6.994 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
6.995 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
6.995 * [backup-simplify]: Simplify (- k) into (- k)
6.995 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
6.995 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
6.996 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
6.996 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
6.997 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
6.997 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
6.997 * [taylor]: Taking taylor expansion of (/ 1 k) in n
6.997 * [taylor]: Taking taylor expansion of k in n
6.997 * [backup-simplify]: Simplify k into k
6.997 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
6.997 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
6.997 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
6.997 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
6.997 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
6.997 * [taylor]: Taking taylor expansion of 1.0 in n
6.997 * [backup-simplify]: Simplify 1.0 into 1.0
6.997 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
6.997 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
6.997 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
6.997 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
6.997 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
6.997 * [taylor]: Taking taylor expansion of 0.5 in n
6.997 * [backup-simplify]: Simplify 0.5 into 0.5
6.997 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
6.998 * [taylor]: Taking taylor expansion of 1.0 in n
6.998 * [backup-simplify]: Simplify 1.0 into 1.0
6.998 * [taylor]: Taking taylor expansion of k in n
6.998 * [backup-simplify]: Simplify k into k
6.998 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
6.998 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
6.998 * [taylor]: Taking taylor expansion of 2.0 in n
6.998 * [backup-simplify]: Simplify 2.0 into 2.0
6.998 * [taylor]: Taking taylor expansion of (* n PI) in n
6.998 * [taylor]: Taking taylor expansion of n in n
6.998 * [backup-simplify]: Simplify 0 into 0
6.998 * [backup-simplify]: Simplify 1 into 1
6.998 * [taylor]: Taking taylor expansion of PI in n
6.998 * [backup-simplify]: Simplify PI into PI
6.998 * [backup-simplify]: Simplify (* 0 PI) into 0
6.998 * [backup-simplify]: Simplify (* 2.0 0) into 0
6.999 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.000 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
7.001 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.001 * [backup-simplify]: Simplify (- k) into (- k)
7.001 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
7.001 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
7.002 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.002 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
7.003 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
7.003 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
7.003 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.003 * [taylor]: Taking taylor expansion of k in n
7.003 * [backup-simplify]: Simplify k into k
7.003 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.003 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
7.003 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.003 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
7.004 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))
7.005 * [backup-simplify]: Simplify (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) into (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))
7.005 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) in k
7.005 * [taylor]: Taking taylor expansion of 1.0 in k
7.005 * [backup-simplify]: Simplify 1.0 into 1.0
7.005 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) in k
7.005 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
7.005 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
7.005 * [taylor]: Taking taylor expansion of 0.5 in k
7.005 * [backup-simplify]: Simplify 0.5 into 0.5
7.005 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
7.005 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
7.005 * [taylor]: Taking taylor expansion of 1.0 in k
7.005 * [backup-simplify]: Simplify 1.0 into 1.0
7.005 * [taylor]: Taking taylor expansion of k in k
7.005 * [backup-simplify]: Simplify 0 into 0
7.005 * [backup-simplify]: Simplify 1 into 1
7.005 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
7.005 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
7.005 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
7.005 * [taylor]: Taking taylor expansion of 2.0 in k
7.005 * [backup-simplify]: Simplify 2.0 into 2.0
7.005 * [taylor]: Taking taylor expansion of PI in k
7.006 * [backup-simplify]: Simplify PI into PI
7.006 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.007 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.007 * [taylor]: Taking taylor expansion of (log n) in k
7.007 * [taylor]: Taking taylor expansion of n in k
7.007 * [backup-simplify]: Simplify n into n
7.007 * [backup-simplify]: Simplify (log n) into (log n)
7.007 * [backup-simplify]: Simplify (- 0) into 0
7.007 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
7.008 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
7.009 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
7.010 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
7.016 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
7.016 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
7.016 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.016 * [taylor]: Taking taylor expansion of k in k
7.016 * [backup-simplify]: Simplify 0 into 0
7.016 * [backup-simplify]: Simplify 1 into 1
7.017 * [backup-simplify]: Simplify (/ 1 1) into 1
7.017 * [backup-simplify]: Simplify (sqrt 0) into 0
7.018 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.020 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0) into 0
7.020 * [backup-simplify]: Simplify (* 1.0 0) into 0
7.020 * [backup-simplify]: Simplify 0 into 0
7.021 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
7.022 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
7.024 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
7.024 * [backup-simplify]: Simplify (- 0) into 0
7.025 * [backup-simplify]: Simplify (+ 0 0) into 0
7.025 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
7.027 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.028 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
7.030 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.031 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
7.033 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))) into 0
7.033 * [taylor]: Taking taylor expansion of 0 in k
7.033 * [backup-simplify]: Simplify 0 into 0
7.034 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
7.035 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
7.036 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
7.037 * [backup-simplify]: Simplify (+ 0 0) into 0
7.037 * [backup-simplify]: Simplify (- 1) into -1
7.037 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.038 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
7.040 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
7.042 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
7.044 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
7.045 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
7.046 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
7.046 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.046 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
7.047 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
7.048 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
7.050 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
7.050 * [backup-simplify]: Simplify (- 0) into 0
7.050 * [backup-simplify]: Simplify (+ 0 0) into 0
7.051 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
7.052 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.053 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
7.054 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.055 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
7.056 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))))) into 0
7.056 * [taylor]: Taking taylor expansion of 0 in k
7.056 * [backup-simplify]: Simplify 0 into 0
7.056 * [backup-simplify]: Simplify 0 into 0
7.057 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
7.059 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
7.059 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.062 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
7.063 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
7.063 * [backup-simplify]: Simplify (+ 0 0) into 0
7.063 * [backup-simplify]: Simplify (- 0) into 0
7.064 * [backup-simplify]: Simplify (+ 0 0) into 0
7.065 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
7.066 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
7.069 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
7.079 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) +nan.0) (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 0))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
7.086 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
7.091 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
7.092 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.093 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
7.094 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
7.095 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
7.101 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
7.102 * [backup-simplify]: Simplify (- 0) into 0
7.102 * [backup-simplify]: Simplify (+ 0 0) into 0
7.104 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
7.105 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.107 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
7.110 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
7.112 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
7.115 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))))) into 0
7.115 * [taylor]: Taking taylor expansion of 0 in k
7.115 * [backup-simplify]: Simplify 0 into 0
7.115 * [backup-simplify]: Simplify 0 into 0
7.115 * [backup-simplify]: Simplify 0 into 0
7.116 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.120 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
7.121 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.124 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
7.126 * [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
7.126 * [backup-simplify]: Simplify (+ 0 0) into 0
7.126 * [backup-simplify]: Simplify (- 0) into 0
7.126 * [backup-simplify]: Simplify (+ 0 0) into 0
7.128 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
7.134 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))))) into 0
7.138 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
7.149 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) +nan.0) (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) +nan.0) (* (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
7.166 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))) (+ (* 0 (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
7.175 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
7.187 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) (* k 1)) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))))))))))))))))))
7.188 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) (sqrt (/ 1 k))) into (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)))
7.188 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (n k) around 0
7.188 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k
7.188 * [taylor]: Taking taylor expansion of 1.0 in k
7.188 * [backup-simplify]: Simplify 1.0 into 1.0
7.188 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k
7.188 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
7.188 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
7.188 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
7.188 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
7.188 * [taylor]: Taking taylor expansion of 0.5 in k
7.188 * [backup-simplify]: Simplify 0.5 into 0.5
7.188 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
7.188 * [taylor]: Taking taylor expansion of 1.0 in k
7.188 * [backup-simplify]: Simplify 1.0 into 1.0
7.188 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.188 * [taylor]: Taking taylor expansion of k in k
7.188 * [backup-simplify]: Simplify 0 into 0
7.188 * [backup-simplify]: Simplify 1 into 1
7.188 * [backup-simplify]: Simplify (/ 1 1) into 1
7.188 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
7.188 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
7.188 * [taylor]: Taking taylor expansion of 2.0 in k
7.188 * [backup-simplify]: Simplify 2.0 into 2.0
7.188 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.188 * [taylor]: Taking taylor expansion of PI in k
7.188 * [backup-simplify]: Simplify PI into PI
7.188 * [taylor]: Taking taylor expansion of n in k
7.188 * [backup-simplify]: Simplify n into n
7.188 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.189 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
7.189 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
7.189 * [backup-simplify]: Simplify (- 1) into -1
7.189 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.189 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
7.189 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
7.190 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
7.190 * [taylor]: Taking taylor expansion of (sqrt k) in k
7.190 * [taylor]: Taking taylor expansion of k in k
7.190 * [backup-simplify]: Simplify 0 into 0
7.190 * [backup-simplify]: Simplify 1 into 1
7.190 * [backup-simplify]: Simplify (sqrt 0) into 0
7.191 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.191 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
7.191 * [taylor]: Taking taylor expansion of 1.0 in n
7.191 * [backup-simplify]: Simplify 1.0 into 1.0
7.191 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
7.191 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
7.191 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
7.191 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
7.191 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
7.191 * [taylor]: Taking taylor expansion of 0.5 in n
7.191 * [backup-simplify]: Simplify 0.5 into 0.5
7.191 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
7.191 * [taylor]: Taking taylor expansion of 1.0 in n
7.191 * [backup-simplify]: Simplify 1.0 into 1.0
7.191 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.191 * [taylor]: Taking taylor expansion of k in n
7.191 * [backup-simplify]: Simplify k into k
7.191 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.191 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
7.191 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
7.191 * [taylor]: Taking taylor expansion of 2.0 in n
7.191 * [backup-simplify]: Simplify 2.0 into 2.0
7.191 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.191 * [taylor]: Taking taylor expansion of PI in n
7.191 * [backup-simplify]: Simplify PI into PI
7.191 * [taylor]: Taking taylor expansion of n in n
7.191 * [backup-simplify]: Simplify 0 into 0
7.191 * [backup-simplify]: Simplify 1 into 1
7.192 * [backup-simplify]: Simplify (/ PI 1) into PI
7.192 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.193 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.193 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
7.193 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
7.193 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
7.194 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.194 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
7.195 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
7.195 * [taylor]: Taking taylor expansion of (sqrt k) in n
7.195 * [taylor]: Taking taylor expansion of k in n
7.195 * [backup-simplify]: Simplify k into k
7.196 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
7.196 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
7.196 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
7.196 * [taylor]: Taking taylor expansion of 1.0 in n
7.196 * [backup-simplify]: Simplify 1.0 into 1.0
7.196 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
7.196 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
7.196 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
7.196 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
7.196 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
7.196 * [taylor]: Taking taylor expansion of 0.5 in n
7.196 * [backup-simplify]: Simplify 0.5 into 0.5
7.196 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
7.196 * [taylor]: Taking taylor expansion of 1.0 in n
7.196 * [backup-simplify]: Simplify 1.0 into 1.0
7.196 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.196 * [taylor]: Taking taylor expansion of k in n
7.196 * [backup-simplify]: Simplify k into k
7.196 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.196 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
7.196 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
7.196 * [taylor]: Taking taylor expansion of 2.0 in n
7.196 * [backup-simplify]: Simplify 2.0 into 2.0
7.196 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.196 * [taylor]: Taking taylor expansion of PI in n
7.196 * [backup-simplify]: Simplify PI into PI
7.196 * [taylor]: Taking taylor expansion of n in n
7.196 * [backup-simplify]: Simplify 0 into 0
7.196 * [backup-simplify]: Simplify 1 into 1
7.196 * [backup-simplify]: Simplify (/ PI 1) into PI
7.197 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.197 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.197 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
7.198 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
7.198 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
7.199 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.199 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
7.200 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
7.200 * [taylor]: Taking taylor expansion of (sqrt k) in n
7.200 * [taylor]: Taking taylor expansion of k in n
7.200 * [backup-simplify]: Simplify k into k
7.200 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
7.200 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
7.201 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) into (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))
7.202 * [backup-simplify]: Simplify (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) into (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))
7.202 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) in k
7.202 * [taylor]: Taking taylor expansion of 1.0 in k
7.202 * [backup-simplify]: Simplify 1.0 into 1.0
7.202 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) in k
7.202 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
7.202 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
7.202 * [taylor]: Taking taylor expansion of 0.5 in k
7.202 * [backup-simplify]: Simplify 0.5 into 0.5
7.202 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
7.202 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
7.202 * [taylor]: Taking taylor expansion of 1.0 in k
7.202 * [backup-simplify]: Simplify 1.0 into 1.0
7.202 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.202 * [taylor]: Taking taylor expansion of k in k
7.202 * [backup-simplify]: Simplify 0 into 0
7.202 * [backup-simplify]: Simplify 1 into 1
7.202 * [backup-simplify]: Simplify (/ 1 1) into 1
7.202 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
7.202 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
7.203 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
7.203 * [taylor]: Taking taylor expansion of 2.0 in k
7.203 * [backup-simplify]: Simplify 2.0 into 2.0
7.203 * [taylor]: Taking taylor expansion of PI in k
7.203 * [backup-simplify]: Simplify PI into PI
7.203 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.203 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.204 * [taylor]: Taking taylor expansion of (log n) in k
7.204 * [taylor]: Taking taylor expansion of n in k
7.204 * [backup-simplify]: Simplify n into n
7.204 * [backup-simplify]: Simplify (log n) into (log n)
7.204 * [backup-simplify]: Simplify (- 1) into -1
7.204 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.204 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.205 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
7.206 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
7.206 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
7.207 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
7.207 * [taylor]: Taking taylor expansion of (sqrt k) in k
7.207 * [taylor]: Taking taylor expansion of k in k
7.207 * [backup-simplify]: Simplify 0 into 0
7.207 * [backup-simplify]: Simplify 1 into 1
7.207 * [backup-simplify]: Simplify (sqrt 0) into 0
7.208 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
7.209 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) into 0
7.209 * [backup-simplify]: Simplify (* 1.0 0) into 0
7.209 * [backup-simplify]: Simplify 0 into 0
7.210 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.210 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
7.211 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
7.212 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.212 * [backup-simplify]: Simplify (- 0) into 0
7.212 * [backup-simplify]: Simplify (+ 0 0) into 0
7.212 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
7.213 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.214 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
7.215 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.216 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
7.217 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))) into 0
7.217 * [taylor]: Taking taylor expansion of 0 in k
7.217 * [backup-simplify]: Simplify 0 into 0
7.217 * [backup-simplify]: Simplify 0 into 0
7.219 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
7.220 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
7.221 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
7.221 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
7.222 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.223 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.225 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
7.225 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.225 * [backup-simplify]: Simplify (- 0) into 0
7.229 * [backup-simplify]: Simplify (+ 0 0) into 0
7.230 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
7.231 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.232 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
7.234 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.235 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
7.236 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))))) into 0
7.236 * [taylor]: Taking taylor expansion of 0 in k
7.236 * [backup-simplify]: Simplify 0 into 0
7.236 * [backup-simplify]: Simplify 0 into 0
7.236 * [backup-simplify]: Simplify 0 into 0
7.238 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
7.239 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
7.241 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
7.242 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
7.242 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
7.243 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.244 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.249 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
7.250 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.250 * [backup-simplify]: Simplify (- 0) into 0
7.250 * [backup-simplify]: Simplify (+ 0 0) into 0
7.252 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
7.253 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.255 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
7.258 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
7.260 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
7.263 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))))) into 0
7.263 * [taylor]: Taking taylor expansion of 0 in k
7.263 * [backup-simplify]: Simplify 0 into 0
7.263 * [backup-simplify]: Simplify 0 into 0
7.263 * [backup-simplify]: Simplify 0 into 0
7.263 * [backup-simplify]: Simplify 0 into 0
7.267 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
7.269 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
7.272 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
7.272 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
7.275 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
7.276 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) (sqrt (/ 1 (- k)))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))))
7.276 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (n k) around 0
7.276 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
7.276 * [taylor]: Taking taylor expansion of 1.0 in k
7.276 * [backup-simplify]: Simplify 1.0 into 1.0
7.276 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
7.276 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
7.276 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
7.276 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
7.276 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
7.276 * [taylor]: Taking taylor expansion of 0.5 in k
7.276 * [backup-simplify]: Simplify 0.5 into 0.5
7.276 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
7.276 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.276 * [taylor]: Taking taylor expansion of k in k
7.276 * [backup-simplify]: Simplify 0 into 0
7.276 * [backup-simplify]: Simplify 1 into 1
7.276 * [backup-simplify]: Simplify (/ 1 1) into 1
7.276 * [taylor]: Taking taylor expansion of 1.0 in k
7.276 * [backup-simplify]: Simplify 1.0 into 1.0
7.276 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
7.276 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
7.276 * [taylor]: Taking taylor expansion of -2.0 in k
7.277 * [backup-simplify]: Simplify -2.0 into -2.0
7.277 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.277 * [taylor]: Taking taylor expansion of PI in k
7.277 * [backup-simplify]: Simplify PI into PI
7.277 * [taylor]: Taking taylor expansion of n in k
7.277 * [backup-simplify]: Simplify n into n
7.277 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.277 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
7.277 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
7.277 * [backup-simplify]: Simplify (+ 1 0) into 1
7.277 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
7.277 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
7.278 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
7.278 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
7.278 * [taylor]: Taking taylor expansion of (/ -1 k) in k
7.278 * [taylor]: Taking taylor expansion of -1 in k
7.278 * [backup-simplify]: Simplify -1 into -1
7.278 * [taylor]: Taking taylor expansion of k in k
7.278 * [backup-simplify]: Simplify 0 into 0
7.278 * [backup-simplify]: Simplify 1 into 1
7.278 * [backup-simplify]: Simplify (/ -1 1) into -1
7.278 * [backup-simplify]: Simplify (sqrt 0) into 0
7.279 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
7.279 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
7.279 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
7.279 * [taylor]: Taking taylor expansion of 1.0 in n
7.279 * [backup-simplify]: Simplify 1.0 into 1.0
7.279 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
7.279 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
7.279 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
7.279 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
7.279 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
7.279 * [taylor]: Taking taylor expansion of 0.5 in n
7.279 * [backup-simplify]: Simplify 0.5 into 0.5
7.279 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
7.279 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.279 * [taylor]: Taking taylor expansion of k in n
7.279 * [backup-simplify]: Simplify k into k
7.279 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.279 * [taylor]: Taking taylor expansion of 1.0 in n
7.279 * [backup-simplify]: Simplify 1.0 into 1.0
7.279 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
7.279 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
7.280 * [taylor]: Taking taylor expansion of -2.0 in n
7.280 * [backup-simplify]: Simplify -2.0 into -2.0
7.280 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.280 * [taylor]: Taking taylor expansion of PI in n
7.280 * [backup-simplify]: Simplify PI into PI
7.280 * [taylor]: Taking taylor expansion of n in n
7.280 * [backup-simplify]: Simplify 0 into 0
7.280 * [backup-simplify]: Simplify 1 into 1
7.280 * [backup-simplify]: Simplify (/ PI 1) into PI
7.280 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.281 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
7.281 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
7.281 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
7.282 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.283 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
7.283 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
7.283 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
7.283 * [taylor]: Taking taylor expansion of (/ -1 k) in n
7.283 * [taylor]: Taking taylor expansion of -1 in n
7.284 * [backup-simplify]: Simplify -1 into -1
7.284 * [taylor]: Taking taylor expansion of k in n
7.284 * [backup-simplify]: Simplify k into k
7.284 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
7.284 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
7.284 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
7.284 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
7.285 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
7.285 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
7.285 * [taylor]: Taking taylor expansion of 1.0 in n
7.285 * [backup-simplify]: Simplify 1.0 into 1.0
7.285 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
7.285 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
7.285 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
7.285 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
7.285 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
7.285 * [taylor]: Taking taylor expansion of 0.5 in n
7.285 * [backup-simplify]: Simplify 0.5 into 0.5
7.285 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
7.285 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.285 * [taylor]: Taking taylor expansion of k in n
7.285 * [backup-simplify]: Simplify k into k
7.285 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.285 * [taylor]: Taking taylor expansion of 1.0 in n
7.285 * [backup-simplify]: Simplify 1.0 into 1.0
7.285 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
7.285 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
7.285 * [taylor]: Taking taylor expansion of -2.0 in n
7.285 * [backup-simplify]: Simplify -2.0 into -2.0
7.285 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.285 * [taylor]: Taking taylor expansion of PI in n
7.285 * [backup-simplify]: Simplify PI into PI
7.285 * [taylor]: Taking taylor expansion of n in n
7.285 * [backup-simplify]: Simplify 0 into 0
7.285 * [backup-simplify]: Simplify 1 into 1
7.285 * [backup-simplify]: Simplify (/ PI 1) into PI
7.286 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.286 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
7.286 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
7.286 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
7.287 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.288 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
7.289 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
7.289 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
7.289 * [taylor]: Taking taylor expansion of (/ -1 k) in n
7.289 * [taylor]: Taking taylor expansion of -1 in n
7.289 * [backup-simplify]: Simplify -1 into -1
7.289 * [taylor]: Taking taylor expansion of k in n
7.289 * [backup-simplify]: Simplify k into k
7.289 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
7.289 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
7.289 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
7.289 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
7.290 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
7.291 * [backup-simplify]: Simplify (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) into (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))))
7.291 * [taylor]: Taking taylor expansion of (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) in k
7.291 * [taylor]: Taking taylor expansion of 1.0 in k
7.291 * [backup-simplify]: Simplify 1.0 into 1.0
7.291 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in k
7.291 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
7.291 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
7.291 * [taylor]: Taking taylor expansion of 0.5 in k
7.291 * [backup-simplify]: Simplify 0.5 into 0.5
7.291 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
7.291 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
7.291 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
7.291 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
7.291 * [taylor]: Taking taylor expansion of -2.0 in k
7.291 * [backup-simplify]: Simplify -2.0 into -2.0
7.291 * [taylor]: Taking taylor expansion of PI in k
7.291 * [backup-simplify]: Simplify PI into PI
7.291 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.292 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
7.292 * [taylor]: Taking taylor expansion of (log n) in k
7.292 * [taylor]: Taking taylor expansion of n in k
7.292 * [backup-simplify]: Simplify n into n
7.292 * [backup-simplify]: Simplify (log n) into (log n)
7.292 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
7.292 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.292 * [taylor]: Taking taylor expansion of k in k
7.292 * [backup-simplify]: Simplify 0 into 0
7.292 * [backup-simplify]: Simplify 1 into 1
7.292 * [backup-simplify]: Simplify (/ 1 1) into 1
7.293 * [taylor]: Taking taylor expansion of 1.0 in k
7.293 * [backup-simplify]: Simplify 1.0 into 1.0
7.293 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.293 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
7.293 * [backup-simplify]: Simplify (+ 1 0) into 1
7.294 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
7.295 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
7.296 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
7.296 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
7.296 * [taylor]: Taking taylor expansion of (/ -1 k) in k
7.296 * [taylor]: Taking taylor expansion of -1 in k
7.296 * [backup-simplify]: Simplify -1 into -1
7.296 * [taylor]: Taking taylor expansion of k in k
7.296 * [backup-simplify]: Simplify 0 into 0
7.296 * [backup-simplify]: Simplify 1 into 1
7.296 * [backup-simplify]: Simplify (/ -1 1) into -1
7.296 * [backup-simplify]: Simplify (sqrt 0) into 0
7.297 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
7.298 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
7.299 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
7.299 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
7.300 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.300 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
7.301 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
7.301 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.302 * [backup-simplify]: Simplify (+ 0 0) into 0
7.302 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
7.303 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.304 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
7.305 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
7.306 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
7.307 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))))) into 0
7.307 * [taylor]: Taking taylor expansion of 0 in k
7.307 * [backup-simplify]: Simplify 0 into 0
7.307 * [backup-simplify]: Simplify 0 into 0
7.308 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
7.310 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
7.311 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
7.312 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
7.313 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
7.314 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.314 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.316 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
7.316 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.317 * [backup-simplify]: Simplify (+ 0 0) into 0
7.317 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
7.318 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.319 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
7.321 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.321 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.321 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
7.322 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
7.323 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))))) into 0
7.323 * [taylor]: Taking taylor expansion of 0 in k
7.323 * [backup-simplify]: Simplify 0 into 0
7.323 * [backup-simplify]: Simplify 0 into 0
7.323 * [backup-simplify]: Simplify 0 into 0
7.324 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.330 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
7.333 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
7.335 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
7.336 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
7.339 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))))))))
7.339 * * * * [progress]: [ 3 / 3 ] generating series at (2 1 2)
7.339 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) into (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k)))
7.339 * [approximate]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in (n k) around 0
7.339 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
7.339 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
7.339 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
7.339 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
7.339 * [taylor]: Taking taylor expansion of 0.5 in k
7.339 * [backup-simplify]: Simplify 0.5 into 0.5
7.339 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
7.339 * [taylor]: Taking taylor expansion of 1.0 in k
7.339 * [backup-simplify]: Simplify 1.0 into 1.0
7.339 * [taylor]: Taking taylor expansion of k in k
7.339 * [backup-simplify]: Simplify 0 into 0
7.339 * [backup-simplify]: Simplify 1 into 1
7.339 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
7.339 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
7.339 * [taylor]: Taking taylor expansion of 2.0 in k
7.339 * [backup-simplify]: Simplify 2.0 into 2.0
7.339 * [taylor]: Taking taylor expansion of (* n PI) in k
7.339 * [taylor]: Taking taylor expansion of n in k
7.339 * [backup-simplify]: Simplify n into n
7.339 * [taylor]: Taking taylor expansion of PI in k
7.340 * [backup-simplify]: Simplify PI into PI
7.340 * [backup-simplify]: Simplify (* n PI) into (* n PI)
7.340 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
7.340 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
7.340 * [backup-simplify]: Simplify (- 0) into 0
7.340 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
7.340 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
7.341 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
7.341 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
7.341 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
7.341 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
7.341 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
7.341 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
7.341 * [taylor]: Taking taylor expansion of 0.5 in n
7.341 * [backup-simplify]: Simplify 0.5 into 0.5
7.341 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
7.341 * [taylor]: Taking taylor expansion of 1.0 in n
7.341 * [backup-simplify]: Simplify 1.0 into 1.0
7.341 * [taylor]: Taking taylor expansion of k in n
7.341 * [backup-simplify]: Simplify k into k
7.341 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
7.341 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
7.341 * [taylor]: Taking taylor expansion of 2.0 in n
7.341 * [backup-simplify]: Simplify 2.0 into 2.0
7.341 * [taylor]: Taking taylor expansion of (* n PI) in n
7.341 * [taylor]: Taking taylor expansion of n in n
7.341 * [backup-simplify]: Simplify 0 into 0
7.341 * [backup-simplify]: Simplify 1 into 1
7.341 * [taylor]: Taking taylor expansion of PI in n
7.341 * [backup-simplify]: Simplify PI into PI
7.341 * [backup-simplify]: Simplify (* 0 PI) into 0
7.342 * [backup-simplify]: Simplify (* 2.0 0) into 0
7.343 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.343 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
7.344 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.344 * [backup-simplify]: Simplify (- k) into (- k)
7.344 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
7.344 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
7.345 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.346 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
7.347 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
7.347 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
7.347 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
7.347 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
7.347 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
7.347 * [taylor]: Taking taylor expansion of 0.5 in n
7.347 * [backup-simplify]: Simplify 0.5 into 0.5
7.347 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
7.347 * [taylor]: Taking taylor expansion of 1.0 in n
7.347 * [backup-simplify]: Simplify 1.0 into 1.0
7.347 * [taylor]: Taking taylor expansion of k in n
7.347 * [backup-simplify]: Simplify k into k
7.347 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
7.347 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
7.347 * [taylor]: Taking taylor expansion of 2.0 in n
7.347 * [backup-simplify]: Simplify 2.0 into 2.0
7.347 * [taylor]: Taking taylor expansion of (* n PI) in n
7.347 * [taylor]: Taking taylor expansion of n in n
7.347 * [backup-simplify]: Simplify 0 into 0
7.347 * [backup-simplify]: Simplify 1 into 1
7.347 * [taylor]: Taking taylor expansion of PI in n
7.347 * [backup-simplify]: Simplify PI into PI
7.348 * [backup-simplify]: Simplify (* 0 PI) into 0
7.348 * [backup-simplify]: Simplify (* 2.0 0) into 0
7.349 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
7.350 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
7.351 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.351 * [backup-simplify]: Simplify (- k) into (- k)
7.351 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
7.351 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
7.352 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.352 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
7.353 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
7.353 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
7.353 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
7.353 * [taylor]: Taking taylor expansion of 0.5 in k
7.353 * [backup-simplify]: Simplify 0.5 into 0.5
7.353 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
7.353 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
7.353 * [taylor]: Taking taylor expansion of 1.0 in k
7.353 * [backup-simplify]: Simplify 1.0 into 1.0
7.353 * [taylor]: Taking taylor expansion of k in k
7.353 * [backup-simplify]: Simplify 0 into 0
7.353 * [backup-simplify]: Simplify 1 into 1
7.353 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
7.353 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
7.354 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
7.354 * [taylor]: Taking taylor expansion of 2.0 in k
7.354 * [backup-simplify]: Simplify 2.0 into 2.0
7.354 * [taylor]: Taking taylor expansion of PI in k
7.354 * [backup-simplify]: Simplify PI into PI
7.354 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.355 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.355 * [taylor]: Taking taylor expansion of (log n) in k
7.355 * [taylor]: Taking taylor expansion of n in k
7.355 * [backup-simplify]: Simplify n into n
7.355 * [backup-simplify]: Simplify (log n) into (log n)
7.355 * [backup-simplify]: Simplify (- 0) into 0
7.355 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
7.356 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
7.356 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
7.357 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
7.358 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
7.359 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
7.359 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
7.360 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
7.361 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
7.361 * [backup-simplify]: Simplify (- 0) into 0
7.362 * [backup-simplify]: Simplify (+ 0 0) into 0
7.362 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
7.363 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.363 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
7.365 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.365 * [taylor]: Taking taylor expansion of 0 in k
7.365 * [backup-simplify]: Simplify 0 into 0
7.365 * [backup-simplify]: Simplify 0 into 0
7.365 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
7.367 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
7.367 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
7.367 * [backup-simplify]: Simplify (+ 0 0) into 0
7.368 * [backup-simplify]: Simplify (- 1) into -1
7.368 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.369 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
7.371 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
7.373 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
7.376 * [backup-simplify]: Simplify (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
7.376 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
7.377 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
7.379 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
7.379 * [backup-simplify]: Simplify (- 0) into 0
7.379 * [backup-simplify]: Simplify (+ 0 0) into 0
7.380 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
7.381 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
7.383 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
7.385 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.385 * [taylor]: Taking taylor expansion of 0 in k
7.385 * [backup-simplify]: Simplify 0 into 0
7.385 * [backup-simplify]: Simplify 0 into 0
7.386 * [backup-simplify]: Simplify 0 into 0
7.387 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.390 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
7.392 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
7.392 * [backup-simplify]: Simplify (+ 0 0) into 0
7.393 * [backup-simplify]: Simplify (- 0) into 0
7.393 * [backup-simplify]: Simplify (+ 0 0) into 0
7.395 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
7.398 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
7.402 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
7.408 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
7.419 * [backup-simplify]: Simplify (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) (pow (* k 1) 2)) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (* k 1)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))
7.420 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0)) into (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))
7.420 * [approximate]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in (n k) around 0
7.420 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
7.420 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
7.420 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
7.420 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
7.420 * [taylor]: Taking taylor expansion of 0.5 in k
7.420 * [backup-simplify]: Simplify 0.5 into 0.5
7.420 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
7.420 * [taylor]: Taking taylor expansion of 1.0 in k
7.420 * [backup-simplify]: Simplify 1.0 into 1.0
7.420 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.420 * [taylor]: Taking taylor expansion of k in k
7.420 * [backup-simplify]: Simplify 0 into 0
7.420 * [backup-simplify]: Simplify 1 into 1
7.421 * [backup-simplify]: Simplify (/ 1 1) into 1
7.421 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
7.421 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
7.421 * [taylor]: Taking taylor expansion of 2.0 in k
7.421 * [backup-simplify]: Simplify 2.0 into 2.0
7.421 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.421 * [taylor]: Taking taylor expansion of PI in k
7.421 * [backup-simplify]: Simplify PI into PI
7.421 * [taylor]: Taking taylor expansion of n in k
7.421 * [backup-simplify]: Simplify n into n
7.421 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.421 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
7.421 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
7.422 * [backup-simplify]: Simplify (- 1) into -1
7.422 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.422 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
7.423 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
7.423 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
7.423 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
7.423 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
7.423 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
7.423 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
7.423 * [taylor]: Taking taylor expansion of 0.5 in n
7.423 * [backup-simplify]: Simplify 0.5 into 0.5
7.423 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
7.423 * [taylor]: Taking taylor expansion of 1.0 in n
7.423 * [backup-simplify]: Simplify 1.0 into 1.0
7.423 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.423 * [taylor]: Taking taylor expansion of k in n
7.423 * [backup-simplify]: Simplify k into k
7.423 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.423 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
7.423 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
7.423 * [taylor]: Taking taylor expansion of 2.0 in n
7.423 * [backup-simplify]: Simplify 2.0 into 2.0
7.423 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.423 * [taylor]: Taking taylor expansion of PI in n
7.423 * [backup-simplify]: Simplify PI into PI
7.423 * [taylor]: Taking taylor expansion of n in n
7.423 * [backup-simplify]: Simplify 0 into 0
7.423 * [backup-simplify]: Simplify 1 into 1
7.424 * [backup-simplify]: Simplify (/ PI 1) into PI
7.424 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.426 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.426 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
7.426 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
7.426 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
7.427 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.428 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
7.429 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
7.429 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
7.429 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
7.429 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
7.429 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
7.429 * [taylor]: Taking taylor expansion of 0.5 in n
7.429 * [backup-simplify]: Simplify 0.5 into 0.5
7.429 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
7.429 * [taylor]: Taking taylor expansion of 1.0 in n
7.429 * [backup-simplify]: Simplify 1.0 into 1.0
7.429 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.430 * [taylor]: Taking taylor expansion of k in n
7.430 * [backup-simplify]: Simplify k into k
7.430 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.430 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
7.430 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
7.430 * [taylor]: Taking taylor expansion of 2.0 in n
7.430 * [backup-simplify]: Simplify 2.0 into 2.0
7.430 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.430 * [taylor]: Taking taylor expansion of PI in n
7.430 * [backup-simplify]: Simplify PI into PI
7.430 * [taylor]: Taking taylor expansion of n in n
7.430 * [backup-simplify]: Simplify 0 into 0
7.430 * [backup-simplify]: Simplify 1 into 1
7.430 * [backup-simplify]: Simplify (/ PI 1) into PI
7.430 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.431 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.431 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
7.431 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
7.431 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
7.432 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.433 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
7.434 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
7.434 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
7.434 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
7.434 * [taylor]: Taking taylor expansion of 0.5 in k
7.434 * [backup-simplify]: Simplify 0.5 into 0.5
7.434 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
7.434 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
7.434 * [taylor]: Taking taylor expansion of 1.0 in k
7.434 * [backup-simplify]: Simplify 1.0 into 1.0
7.434 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.434 * [taylor]: Taking taylor expansion of k in k
7.434 * [backup-simplify]: Simplify 0 into 0
7.434 * [backup-simplify]: Simplify 1 into 1
7.434 * [backup-simplify]: Simplify (/ 1 1) into 1
7.434 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
7.434 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
7.434 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
7.434 * [taylor]: Taking taylor expansion of 2.0 in k
7.434 * [backup-simplify]: Simplify 2.0 into 2.0
7.434 * [taylor]: Taking taylor expansion of PI in k
7.434 * [backup-simplify]: Simplify PI into PI
7.435 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
7.435 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
7.435 * [taylor]: Taking taylor expansion of (log n) in k
7.435 * [taylor]: Taking taylor expansion of n in k
7.435 * [backup-simplify]: Simplify n into n
7.435 * [backup-simplify]: Simplify (log n) into (log n)
7.436 * [backup-simplify]: Simplify (- 1) into -1
7.436 * [backup-simplify]: Simplify (+ 0 -1) into -1
7.436 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.437 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
7.437 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
7.438 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
7.439 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
7.440 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
7.440 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.441 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
7.446 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
7.446 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.447 * [backup-simplify]: Simplify (- 0) into 0
7.447 * [backup-simplify]: Simplify (+ 0 0) into 0
7.447 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
7.448 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.450 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
7.452 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
7.452 * [taylor]: Taking taylor expansion of 0 in k
7.452 * [backup-simplify]: Simplify 0 into 0
7.452 * [backup-simplify]: Simplify 0 into 0
7.452 * [backup-simplify]: Simplify 0 into 0
7.453 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.454 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.457 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
7.458 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.458 * [backup-simplify]: Simplify (- 0) into 0
7.458 * [backup-simplify]: Simplify (+ 0 0) into 0
7.460 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
7.461 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.463 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
7.465 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.466 * [taylor]: Taking taylor expansion of 0 in k
7.466 * [backup-simplify]: Simplify 0 into 0
7.466 * [backup-simplify]: Simplify 0 into 0
7.466 * [backup-simplify]: Simplify 0 into 0
7.466 * [backup-simplify]: Simplify 0 into 0
7.467 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.468 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.474 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
7.474 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.475 * [backup-simplify]: Simplify (- 0) into 0
7.475 * [backup-simplify]: Simplify (+ 0 0) into 0
7.477 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
7.478 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
7.480 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
7.483 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
7.484 * [taylor]: Taking taylor expansion of 0 in k
7.484 * [backup-simplify]: Simplify 0 into 0
7.484 * [backup-simplify]: Simplify 0 into 0
7.485 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n))))))
7.486 * [backup-simplify]: Simplify (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0)) into (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))
7.486 * [approximate]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in (n k) around 0
7.486 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
7.486 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
7.486 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
7.486 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
7.486 * [taylor]: Taking taylor expansion of 0.5 in k
7.486 * [backup-simplify]: Simplify 0.5 into 0.5
7.486 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
7.486 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.486 * [taylor]: Taking taylor expansion of k in k
7.486 * [backup-simplify]: Simplify 0 into 0
7.486 * [backup-simplify]: Simplify 1 into 1
7.487 * [backup-simplify]: Simplify (/ 1 1) into 1
7.487 * [taylor]: Taking taylor expansion of 1.0 in k
7.487 * [backup-simplify]: Simplify 1.0 into 1.0
7.487 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
7.487 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
7.487 * [taylor]: Taking taylor expansion of -2.0 in k
7.487 * [backup-simplify]: Simplify -2.0 into -2.0
7.487 * [taylor]: Taking taylor expansion of (/ PI n) in k
7.487 * [taylor]: Taking taylor expansion of PI in k
7.487 * [backup-simplify]: Simplify PI into PI
7.487 * [taylor]: Taking taylor expansion of n in k
7.487 * [backup-simplify]: Simplify n into n
7.487 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
7.487 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
7.487 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
7.488 * [backup-simplify]: Simplify (+ 1 0) into 1
7.488 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
7.488 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
7.489 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
7.489 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
7.489 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
7.489 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
7.489 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
7.489 * [taylor]: Taking taylor expansion of 0.5 in n
7.489 * [backup-simplify]: Simplify 0.5 into 0.5
7.489 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
7.489 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.489 * [taylor]: Taking taylor expansion of k in n
7.489 * [backup-simplify]: Simplify k into k
7.489 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.489 * [taylor]: Taking taylor expansion of 1.0 in n
7.489 * [backup-simplify]: Simplify 1.0 into 1.0
7.489 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
7.489 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
7.489 * [taylor]: Taking taylor expansion of -2.0 in n
7.489 * [backup-simplify]: Simplify -2.0 into -2.0
7.489 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.489 * [taylor]: Taking taylor expansion of PI in n
7.489 * [backup-simplify]: Simplify PI into PI
7.489 * [taylor]: Taking taylor expansion of n in n
7.489 * [backup-simplify]: Simplify 0 into 0
7.489 * [backup-simplify]: Simplify 1 into 1
7.490 * [backup-simplify]: Simplify (/ PI 1) into PI
7.490 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.492 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
7.492 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
7.492 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
7.493 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.494 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
7.496 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
7.496 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
7.496 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
7.496 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
7.496 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
7.496 * [taylor]: Taking taylor expansion of 0.5 in n
7.496 * [backup-simplify]: Simplify 0.5 into 0.5
7.496 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
7.496 * [taylor]: Taking taylor expansion of (/ 1 k) in n
7.496 * [taylor]: Taking taylor expansion of k in n
7.496 * [backup-simplify]: Simplify k into k
7.496 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
7.496 * [taylor]: Taking taylor expansion of 1.0 in n
7.496 * [backup-simplify]: Simplify 1.0 into 1.0
7.497 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
7.497 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
7.497 * [taylor]: Taking taylor expansion of -2.0 in n
7.497 * [backup-simplify]: Simplify -2.0 into -2.0
7.497 * [taylor]: Taking taylor expansion of (/ PI n) in n
7.497 * [taylor]: Taking taylor expansion of PI in n
7.497 * [backup-simplify]: Simplify PI into PI
7.497 * [taylor]: Taking taylor expansion of n in n
7.497 * [backup-simplify]: Simplify 0 into 0
7.497 * [backup-simplify]: Simplify 1 into 1
7.497 * [backup-simplify]: Simplify (/ PI 1) into PI
7.498 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.499 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
7.499 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
7.499 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
7.501 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.502 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
7.503 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
7.503 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
7.503 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
7.503 * [taylor]: Taking taylor expansion of 0.5 in k
7.503 * [backup-simplify]: Simplify 0.5 into 0.5
7.503 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
7.503 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
7.504 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
7.504 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
7.504 * [taylor]: Taking taylor expansion of -2.0 in k
7.504 * [backup-simplify]: Simplify -2.0 into -2.0
7.504 * [taylor]: Taking taylor expansion of PI in k
7.504 * [backup-simplify]: Simplify PI into PI
7.504 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
7.505 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
7.505 * [taylor]: Taking taylor expansion of (log n) in k
7.505 * [taylor]: Taking taylor expansion of n in k
7.505 * [backup-simplify]: Simplify n into n
7.505 * [backup-simplify]: Simplify (log n) into (log n)
7.505 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
7.506 * [taylor]: Taking taylor expansion of (/ 1 k) in k
7.506 * [taylor]: Taking taylor expansion of k in k
7.506 * [backup-simplify]: Simplify 0 into 0
7.506 * [backup-simplify]: Simplify 1 into 1
7.506 * [backup-simplify]: Simplify (/ 1 1) into 1
7.506 * [taylor]: Taking taylor expansion of 1.0 in k
7.506 * [backup-simplify]: Simplify 1.0 into 1.0
7.506 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
7.507 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
7.508 * [backup-simplify]: Simplify (+ 1 0) into 1
7.509 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
7.510 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
7.511 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
7.513 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
7.514 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
7.514 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
7.516 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
7.516 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
7.517 * [backup-simplify]: Simplify (+ 0 0) into 0
7.517 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
7.519 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.520 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
7.522 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
7.522 * [taylor]: Taking taylor expansion of 0 in k
7.523 * [backup-simplify]: Simplify 0 into 0
7.523 * [backup-simplify]: Simplify 0 into 0
7.523 * [backup-simplify]: Simplify 0 into 0
7.524 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.525 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
7.528 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
7.529 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.529 * [backup-simplify]: Simplify (+ 0 0) into 0
7.529 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
7.530 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.531 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
7.533 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
7.533 * [taylor]: Taking taylor expansion of 0 in k
7.533 * [backup-simplify]: Simplify 0 into 0
7.533 * [backup-simplify]: Simplify 0 into 0
7.533 * [backup-simplify]: Simplify 0 into 0
7.533 * [backup-simplify]: Simplify 0 into 0
7.533 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
7.534 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
7.537 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* -2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* -2.0 PI) 1)))) 6) into 0
7.537 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
7.538 * [backup-simplify]: Simplify (+ 0 0) into 0
7.538 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0))))) into 0
7.539 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
7.541 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n)))))) into 0
7.542 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
7.542 * [taylor]: Taking taylor expansion of 0 in k
7.543 * [backup-simplify]: Simplify 0 into 0
7.543 * [backup-simplify]: Simplify 0 into 0
7.544 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))) into (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
7.544 * * * [progress]: simplifying candidates
7.545 * [simplify]: Simplifying:
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (expm1 (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (log1p (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (- (+ (log 1.0) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k)))
  (- (log (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k)))
  (log (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (exp (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (/ (* (* (* 1.0 1.0) 1.0) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (/ (* (* (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (* (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (- (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- (sqrt k))
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 (sqrt 1))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 1)
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt 1))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1)
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (expm1 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (* 1 (/ (- 1.0 k) 2.0))
  (pow (* (* 2.0 PI) n) (/ 1.0 2.0))
  (pow (* (* 2.0 PI) n) (/ k 2.0))
  (pow (* (* 2.0 PI) n) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* 2.0 PI) n) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))) 1))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (sqrt (- 1.0 k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ (+ (sqrt 1.0) (sqrt k)) 1))
  (pow (* (* 2.0 PI) n) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* 2.0 PI) n) (/ 1 (sqrt 2.0)))
  (pow (* (* 2.0 PI) n) (/ 1 1))
  (pow (* (* 2.0 PI) n) 1)
  (pow (* (* 2.0 PI) n) (- 1.0 k))
  (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (exp (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))))))))
  (- (+ (* 0.25 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (+ (* 0.125 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (+ (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))))) (+ (* 0.5 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (* 0.5 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n))))))
  (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))
7.547 * * [simplify]: iteration 0: 268 enodes
7.634 * * [simplify]: iteration 1: 765 enodes
8.025 * * [simplify]: iteration 2: 3588 enodes
9.304 * * [simplify]: iteration complete: 5002 enodes
9.305 * * [simplify]: Extracting #0: cost 74 inf + 0
9.306 * * [simplify]: Extracting #1: cost 667 inf + 1
9.311 * * [simplify]: Extracting #2: cost 1302 inf + 8115
9.350 * * [simplify]: Extracting #3: cost 956 inf + 83898
9.418 * * [simplify]: Extracting #4: cost 445 inf + 274523
9.517 * * [simplify]: Extracting #5: cost 163 inf + 415694
9.648 * * [simplify]: Extracting #6: cost 82 inf + 460974
9.805 * * [simplify]: Extracting #7: cost 12 inf + 506670
10.024 * * [simplify]: Extracting #8: cost 0 inf + 511988
10.218 * * [simplify]: Extracting #9: cost 0 inf + 508743
10.362 * * [simplify]: Extracting #10: cost 0 inf + 507343
10.554 * * [simplify]: Extracting #11: cost 0 inf + 507218
10.757 * [simplify]: Simplified to:
  (expm1 (* (* n 2.0) PI))
  (log1p (* (* n 2.0) PI))
  (* (* n 2.0) PI)
  (* (* n 2.0) PI)
  (log (* (* n 2.0) PI))
  (log (* (* n 2.0) PI))
  (log (* (* n 2.0) PI))
  (exp (* (* n 2.0) PI))
  (* (* (* n 2.0) PI) (* (* (* n 2.0) PI) (* (* n 2.0) PI)))
  (* (* (* n 2.0) PI) (* (* (* n 2.0) PI) (* (* n 2.0) PI)))
  (* (cbrt (* (* n 2.0) PI)) (cbrt (* (* n 2.0) PI)))
  (cbrt (* (* n 2.0) PI))
  (* (* (* n 2.0) PI) (* (* (* n 2.0) PI) (* (* n 2.0) PI)))
  (sqrt (* (* n 2.0) PI))
  (sqrt (* (* n 2.0) PI))
  (* (* (* (cbrt n) (cbrt n)) 2.0) PI)
  (* (sqrt n) (* PI 2.0))
  (* PI 2.0)
  (* n PI)
  (expm1 (/ (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (log1p (/ (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (- (/ (* (log (* (* n 2.0) PI)) (- 1.0 k)) 2.0) (log (/ (sqrt k) 1.0)))
  (- (/ (* (log (* (* n 2.0) PI)) (- 1.0 k)) 2.0) (log (/ (sqrt k) 1.0)))
  (- (/ (* (log (* (* n 2.0) PI)) (- 1.0 k)) 2.0) (log (/ (sqrt k) 1.0)))
  (- (/ (* (log (* (* n 2.0) PI)) (- 1.0 k)) 2.0) (log (/ (sqrt k) 1.0)))
  (- (/ (* (log (* (* n 2.0) PI)) (- 1.0 k)) 2.0) (log (/ (sqrt k) 1.0)))
  (- (/ (* (log (* (* n 2.0) PI)) (- 1.0 k)) 2.0) (log (/ (sqrt k) 1.0)))
  (- (/ (* (log (* (* n 2.0) PI)) (- 1.0 k)) 2.0) (log (/ (sqrt k) 1.0)))
  (exp (/ (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (/ (* 1.0 (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (/ (* (sqrt k) k) (* (* 1.0 (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))))))
  (/ (* 1.0 (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (/ (* (sqrt k) k) (* (* 1.0 (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))))))
  (* (cbrt (/ (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (cbrt (/ (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (cbrt (/ (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (* (/ (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (* (/ (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (/ (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (sqrt (/ (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (* (- 1.0) (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))
  (- (sqrt k))
  (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (fabs (cbrt k)))
  (/ (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (* 1.0 (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))))
  (* (/ (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k))) (/ 1.0 (cbrt (sqrt k))))
  (/ (* 1.0 (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (fabs (cbrt k)))
  (/ (* 1.0 (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (* 1.0 (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))
  (/ (* 1.0 (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (* 1.0 (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))
  (/ (sqrt k) (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))
  (* (pow (* (* n 2.0) PI) (/ k 2.0)) (sqrt k))
  (expm1 (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))
  (log1p (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))
  (/ (* (log (* (* n 2.0) PI)) (- 1.0 k)) 2.0)
  (/ (* (log (* (* n 2.0) PI)) (- 1.0 k)) 2.0)
  (/ (* (log (* (* n 2.0) PI)) (- 1.0 k)) 2.0)
  (/ (* (log (* (* n 2.0) PI)) (- 1.0 k)) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (/ (- 1.0 k) 2.0)
  (pow (* (* n 2.0) PI) (/ 1.0 2.0))
  (pow (* (* n 2.0) PI) (/ k 2.0))
  (pow (* (* n 2.0) PI) (* (cbrt (/ (- 1.0 k) 2.0)) (cbrt (/ (- 1.0 k) 2.0))))
  (pow (* (* n 2.0) PI) (sqrt (/ (- 1.0 k) 2.0)))
  (pow (* (* n 2.0) PI) (* (/ (cbrt (- 1.0 k)) (cbrt 2.0)) (/ (cbrt (- 1.0 k)) (cbrt 2.0))))
  (pow (* (* n 2.0) PI) (* (/ (cbrt (- 1.0 k)) (sqrt 2.0)) (cbrt (- 1.0 k))))
  (pow (* (* n 2.0) PI) (* (cbrt (- 1.0 k)) (cbrt (- 1.0 k))))
  (pow (* (* n 2.0) PI) (/ (/ (sqrt (- 1.0 k)) (cbrt 2.0)) (cbrt 2.0)))
  (pow (* (* n 2.0) PI) (/ (sqrt (- 1.0 k)) (sqrt 2.0)))
  (pow (* (* n 2.0) PI) (sqrt (- 1.0 k)))
  (pow (* (* n 2.0) PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* n 2.0) PI) (/ 1 (sqrt 2.0)))
  (* (* n 2.0) PI)
  (pow (* (* n 2.0) PI) (/ (+ (sqrt k) (sqrt 1.0)) (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* n 2.0) PI) (/ (+ (sqrt k) (sqrt 1.0)) (sqrt 2.0)))
  (pow (* (* n 2.0) PI) (+ (sqrt k) (sqrt 1.0)))
  (pow (* (* n 2.0) PI) (/ 1 (* (cbrt 2.0) (cbrt 2.0))))
  (pow (* (* n 2.0) PI) (/ 1 (sqrt 2.0)))
  (* (* n 2.0) PI)
  (* (* n 2.0) PI)
  (exp (* (- 1.0 k) (log (* (* n 2.0) PI))))
  (pow (* PI 2.0) (/ (- 1.0 k) 2.0))
  (pow n (/ (- 1.0 k) 2.0))
  (/ (* (log (* (* n 2.0) PI)) (- 1.0 k)) 2.0)
  (exp (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))
  (* (cbrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (cbrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))))
  (cbrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))
  (* (* (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)) (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0))) (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))
  (sqrt (pow (* (* n 2.0) PI) (/ (- 1.0 k) 2.0)))
  (pow (* (* n 2.0) PI) (* (/ (- 1.0 k) 2.0) 1/2))
  (pow (* (* n 2.0) PI) (* (/ (- 1.0 k) 2.0) 1/2))
  (* (* n 2.0) PI)
  (* (* n 2.0) PI)
  (* (* n 2.0) PI)
  (- (fma (* +nan.0 (log (* PI 2.0))) (* (log n) (* (exp (* (log (* (* n 2.0) PI)) 0.5)) (* k k))) (+ (* (- +nan.0) (exp (* (log (* (* n 2.0) PI)) 0.5))) (- (fma (* (log (* PI 2.0)) (log (* PI 2.0))) (* (* +nan.0 (* k k)) (exp (* (log (* (* n 2.0) PI)) 0.5))) (fma (* (* +nan.0 (* k k)) (exp (* (log (* (* n 2.0) PI)) 0.5))) (* (log n) (log n)) (fma (* (log n) (* (exp (* (log (* (* n 2.0) PI)) 0.5)) (* k k))) (- +nan.0) (fma (* +nan.0 (log (* PI 2.0))) (* (exp (* (log (* (* n 2.0) PI)) 0.5)) (* k k)) (fma (* (exp (* (log (* (* n 2.0) PI)) 0.5)) k) (+ (- +nan.0) (* +nan.0 (log (* PI 2.0)))) (* (* (- +nan.0) (exp (* (log (* (* n 2.0) PI)) 0.5))) (* k (log n)))))))) (* (* +nan.0 (* k k)) (exp (* (log (* (* n 2.0) PI)) 0.5)))))))
  (fma +nan.0 (- (/ (exp (* (* (- 1.0 k) (log (* (* n 2.0) PI))) 0.5)) k) (/ (exp (* (* (- 1.0 k) (log (* (* n 2.0) PI))) 0.5)) (* (* k k) k))) (/ (- (* (exp (* (* (- 1.0 k) (log (* (* n 2.0) PI))) 0.5)) +nan.0)) (* k k)))
  (fma +nan.0 (- (exp (* (* 0.5 (- (log (* -2.0 PI)) (log (/ -1 n)))) (- 1.0 k)))) (* +nan.0 (- (/ (exp (* (* 0.5 (- (log (* -2.0 PI)) (log (/ -1 n)))) (- 1.0 k))) k) (/ (/ (exp (* (* 0.5 (- (log (* -2.0 PI)) (log (/ -1 n)))) (- 1.0 k))) k) k))))
  (- (fma (* (log n) (* (exp (* (log (* (* n 2.0) PI)) 0.5)) (* k k))) (* 0.25 (log (* PI 2.0))) (fma (exp (* (log (* (* n 2.0) PI)) 0.5)) (* (* (* (log n) k) (* (log n) k)) 0.125) (fma (* (log (* PI 2.0)) (* (* (exp (* (log (* (* n 2.0) PI)) 0.5)) (* k k)) (log (* PI 2.0)))) 0.125 (exp (* (log (* (* n 2.0) PI)) 0.5))))) (* 0.5 (* k (fma (exp (* (log (* (* n 2.0) PI)) 0.5)) (log n) (* (log (* PI 2.0)) (exp (* (log (* (* n 2.0) PI)) 0.5)))))))
  (exp (* (* (- 1.0 k) (log (* (* n 2.0) PI))) 0.5))
  (exp (* (* 0.5 (- (log (* -2.0 PI)) (log (/ -1 n)))) (- 1.0 k)))
10.770 * * * [progress]: adding candidates to table
11.419 * * [progress]: iteration 3 / 4
11.419 * * * [progress]: picking best candidate
11.498 * * * * [pick]: Picked  #<alt (λ (k n) (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))>
11.498 * * * [progress]: localizing error
11.543 * * * [progress]: generating rewritten candidates
11.543 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1 2 1)
11.558 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1 2 1)
11.578 * * * * [progress]: [ 3 / 4 ] rewriting at (2)
11.634 * * * * [progress]: [ 4 / 4 ] rewriting at (2 2 1)
11.667 * * * [progress]: generating series expansions
11.667 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1 2 1)
11.668 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
11.668 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
11.668 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.668 * [taylor]: Taking taylor expansion of 2.0 in n
11.668 * [backup-simplify]: Simplify 2.0 into 2.0
11.668 * [taylor]: Taking taylor expansion of (* n PI) in n
11.668 * [taylor]: Taking taylor expansion of n in n
11.668 * [backup-simplify]: Simplify 0 into 0
11.668 * [backup-simplify]: Simplify 1 into 1
11.668 * [taylor]: Taking taylor expansion of PI in n
11.668 * [backup-simplify]: Simplify PI into PI
11.668 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.668 * [taylor]: Taking taylor expansion of 2.0 in n
11.668 * [backup-simplify]: Simplify 2.0 into 2.0
11.668 * [taylor]: Taking taylor expansion of (* n PI) in n
11.668 * [taylor]: Taking taylor expansion of n in n
11.668 * [backup-simplify]: Simplify 0 into 0
11.668 * [backup-simplify]: Simplify 1 into 1
11.668 * [taylor]: Taking taylor expansion of PI in n
11.668 * [backup-simplify]: Simplify PI into PI
11.669 * [backup-simplify]: Simplify (* 0 PI) into 0
11.669 * [backup-simplify]: Simplify (* 2.0 0) into 0
11.669 * [backup-simplify]: Simplify 0 into 0
11.670 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.671 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
11.671 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.672 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.673 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
11.673 * [backup-simplify]: Simplify 0 into 0
11.673 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
11.674 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
11.674 * [backup-simplify]: Simplify 0 into 0
11.675 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.676 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
11.676 * [backup-simplify]: Simplify 0 into 0
11.677 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.677 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
11.678 * [backup-simplify]: Simplify 0 into 0
11.679 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.679 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
11.680 * [backup-simplify]: Simplify 0 into 0
11.681 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
11.682 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
11.682 * [backup-simplify]: Simplify 0 into 0
11.682 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
11.683 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
11.683 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
11.683 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
11.683 * [taylor]: Taking taylor expansion of 2.0 in n
11.683 * [backup-simplify]: Simplify 2.0 into 2.0
11.683 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.683 * [taylor]: Taking taylor expansion of PI in n
11.683 * [backup-simplify]: Simplify PI into PI
11.683 * [taylor]: Taking taylor expansion of n in n
11.683 * [backup-simplify]: Simplify 0 into 0
11.683 * [backup-simplify]: Simplify 1 into 1
11.683 * [backup-simplify]: Simplify (/ PI 1) into PI
11.683 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
11.683 * [taylor]: Taking taylor expansion of 2.0 in n
11.683 * [backup-simplify]: Simplify 2.0 into 2.0
11.683 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.683 * [taylor]: Taking taylor expansion of PI in n
11.683 * [backup-simplify]: Simplify PI into PI
11.683 * [taylor]: Taking taylor expansion of n in n
11.683 * [backup-simplify]: Simplify 0 into 0
11.683 * [backup-simplify]: Simplify 1 into 1
11.684 * [backup-simplify]: Simplify (/ PI 1) into PI
11.684 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.684 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.685 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.685 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
11.685 * [backup-simplify]: Simplify 0 into 0
11.686 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.687 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
11.687 * [backup-simplify]: Simplify 0 into 0
11.687 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.688 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.688 * [backup-simplify]: Simplify 0 into 0
11.689 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.689 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.689 * [backup-simplify]: Simplify 0 into 0
11.690 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.691 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.691 * [backup-simplify]: Simplify 0 into 0
11.692 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.692 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.693 * [backup-simplify]: Simplify 0 into 0
11.693 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
11.693 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
11.693 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
11.693 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
11.693 * [taylor]: Taking taylor expansion of -2.0 in n
11.693 * [backup-simplify]: Simplify -2.0 into -2.0
11.693 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.693 * [taylor]: Taking taylor expansion of PI in n
11.693 * [backup-simplify]: Simplify PI into PI
11.693 * [taylor]: Taking taylor expansion of n in n
11.693 * [backup-simplify]: Simplify 0 into 0
11.693 * [backup-simplify]: Simplify 1 into 1
11.694 * [backup-simplify]: Simplify (/ PI 1) into PI
11.694 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
11.694 * [taylor]: Taking taylor expansion of -2.0 in n
11.694 * [backup-simplify]: Simplify -2.0 into -2.0
11.694 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.694 * [taylor]: Taking taylor expansion of PI in n
11.694 * [backup-simplify]: Simplify PI into PI
11.694 * [taylor]: Taking taylor expansion of n in n
11.694 * [backup-simplify]: Simplify 0 into 0
11.694 * [backup-simplify]: Simplify 1 into 1
11.694 * [backup-simplify]: Simplify (/ PI 1) into PI
11.695 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
11.695 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
11.695 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.696 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
11.696 * [backup-simplify]: Simplify 0 into 0
11.697 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.697 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
11.697 * [backup-simplify]: Simplify 0 into 0
11.698 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.698 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.699 * [backup-simplify]: Simplify 0 into 0
11.699 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.700 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.700 * [backup-simplify]: Simplify 0 into 0
11.701 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.702 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.702 * [backup-simplify]: Simplify 0 into 0
11.703 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.703 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.704 * [backup-simplify]: Simplify 0 into 0
11.704 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
11.704 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1 2 1)
11.704 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
11.704 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
11.704 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.704 * [taylor]: Taking taylor expansion of 2.0 in n
11.704 * [backup-simplify]: Simplify 2.0 into 2.0
11.704 * [taylor]: Taking taylor expansion of (* n PI) in n
11.704 * [taylor]: Taking taylor expansion of n in n
11.704 * [backup-simplify]: Simplify 0 into 0
11.704 * [backup-simplify]: Simplify 1 into 1
11.704 * [taylor]: Taking taylor expansion of PI in n
11.704 * [backup-simplify]: Simplify PI into PI
11.705 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.705 * [taylor]: Taking taylor expansion of 2.0 in n
11.705 * [backup-simplify]: Simplify 2.0 into 2.0
11.705 * [taylor]: Taking taylor expansion of (* n PI) in n
11.705 * [taylor]: Taking taylor expansion of n in n
11.705 * [backup-simplify]: Simplify 0 into 0
11.705 * [backup-simplify]: Simplify 1 into 1
11.705 * [taylor]: Taking taylor expansion of PI in n
11.705 * [backup-simplify]: Simplify PI into PI
11.705 * [backup-simplify]: Simplify (* 0 PI) into 0
11.705 * [backup-simplify]: Simplify (* 2.0 0) into 0
11.705 * [backup-simplify]: Simplify 0 into 0
11.706 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.707 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
11.707 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.708 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.709 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
11.709 * [backup-simplify]: Simplify 0 into 0
11.710 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
11.711 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
11.711 * [backup-simplify]: Simplify 0 into 0
11.713 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.714 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
11.715 * [backup-simplify]: Simplify 0 into 0
11.716 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.718 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
11.718 * [backup-simplify]: Simplify 0 into 0
11.720 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.721 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
11.721 * [backup-simplify]: Simplify 0 into 0
11.723 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
11.726 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
11.726 * [backup-simplify]: Simplify 0 into 0
11.726 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
11.727 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
11.727 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
11.727 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
11.727 * [taylor]: Taking taylor expansion of 2.0 in n
11.727 * [backup-simplify]: Simplify 2.0 into 2.0
11.727 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.727 * [taylor]: Taking taylor expansion of PI in n
11.727 * [backup-simplify]: Simplify PI into PI
11.727 * [taylor]: Taking taylor expansion of n in n
11.727 * [backup-simplify]: Simplify 0 into 0
11.727 * [backup-simplify]: Simplify 1 into 1
11.728 * [backup-simplify]: Simplify (/ PI 1) into PI
11.728 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
11.728 * [taylor]: Taking taylor expansion of 2.0 in n
11.728 * [backup-simplify]: Simplify 2.0 into 2.0
11.728 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.728 * [taylor]: Taking taylor expansion of PI in n
11.728 * [backup-simplify]: Simplify PI into PI
11.728 * [taylor]: Taking taylor expansion of n in n
11.728 * [backup-simplify]: Simplify 0 into 0
11.728 * [backup-simplify]: Simplify 1 into 1
11.728 * [backup-simplify]: Simplify (/ PI 1) into PI
11.729 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.730 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.731 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.731 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
11.731 * [backup-simplify]: Simplify 0 into 0
11.733 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.734 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
11.734 * [backup-simplify]: Simplify 0 into 0
11.735 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.737 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.737 * [backup-simplify]: Simplify 0 into 0
11.738 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.740 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.740 * [backup-simplify]: Simplify 0 into 0
11.741 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.745 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.745 * [backup-simplify]: Simplify 0 into 0
11.747 * [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
11.749 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.749 * [backup-simplify]: Simplify 0 into 0
11.749 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
11.750 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
11.750 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
11.750 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
11.750 * [taylor]: Taking taylor expansion of -2.0 in n
11.750 * [backup-simplify]: Simplify -2.0 into -2.0
11.750 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.750 * [taylor]: Taking taylor expansion of PI in n
11.750 * [backup-simplify]: Simplify PI into PI
11.750 * [taylor]: Taking taylor expansion of n in n
11.750 * [backup-simplify]: Simplify 0 into 0
11.750 * [backup-simplify]: Simplify 1 into 1
11.751 * [backup-simplify]: Simplify (/ PI 1) into PI
11.751 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
11.751 * [taylor]: Taking taylor expansion of -2.0 in n
11.751 * [backup-simplify]: Simplify -2.0 into -2.0
11.751 * [taylor]: Taking taylor expansion of (/ PI n) in n
11.751 * [taylor]: Taking taylor expansion of PI in n
11.751 * [backup-simplify]: Simplify PI into PI
11.751 * [taylor]: Taking taylor expansion of n in n
11.751 * [backup-simplify]: Simplify 0 into 0
11.751 * [backup-simplify]: Simplify 1 into 1
11.751 * [backup-simplify]: Simplify (/ PI 1) into PI
11.752 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
11.753 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
11.754 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
11.754 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
11.754 * [backup-simplify]: Simplify 0 into 0
11.755 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.756 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
11.756 * [backup-simplify]: Simplify 0 into 0
11.757 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.759 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.759 * [backup-simplify]: Simplify 0 into 0
11.760 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.761 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.761 * [backup-simplify]: Simplify 0 into 0
11.762 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.764 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
11.764 * [backup-simplify]: Simplify 0 into 0
11.765 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.767 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
11.767 * [backup-simplify]: Simplify 0 into 0
11.768 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
11.768 * * * * [progress]: [ 3 / 4 ] generating series at (2)
11.769 * [backup-simplify]: Simplify (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) into (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k)))
11.769 * [approximate]: Taking taylor expansion of (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k))) in (n k) around 0
11.770 * [taylor]: Taking taylor expansion of (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k))) in k
11.770 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in k
11.770 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
11.770 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
11.770 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
11.770 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
11.770 * [taylor]: Taking taylor expansion of 0.5 in k
11.770 * [backup-simplify]: Simplify 0.5 into 0.5
11.770 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
11.770 * [taylor]: Taking taylor expansion of 1.0 in k
11.770 * [backup-simplify]: Simplify 1.0 into 1.0
11.770 * [taylor]: Taking taylor expansion of k in k
11.770 * [backup-simplify]: Simplify 0 into 0
11.770 * [backup-simplify]: Simplify 1 into 1
11.770 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
11.770 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
11.770 * [taylor]: Taking taylor expansion of 2.0 in k
11.770 * [backup-simplify]: Simplify 2.0 into 2.0
11.770 * [taylor]: Taking taylor expansion of (* n PI) in k
11.770 * [taylor]: Taking taylor expansion of n in k
11.770 * [backup-simplify]: Simplify n into n
11.770 * [taylor]: Taking taylor expansion of PI in k
11.770 * [backup-simplify]: Simplify PI into PI
11.770 * [backup-simplify]: Simplify (* n PI) into (* n PI)
11.770 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
11.770 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
11.771 * [backup-simplify]: Simplify (- 0) into 0
11.771 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
11.772 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
11.772 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
11.772 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
11.772 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
11.772 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
11.773 * [taylor]: Taking taylor expansion of 1.0 in k
11.773 * [backup-simplify]: Simplify 1.0 into 1.0
11.773 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
11.774 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
11.774 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
11.774 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.774 * [taylor]: Taking taylor expansion of k in k
11.774 * [backup-simplify]: Simplify 0 into 0
11.774 * [backup-simplify]: Simplify 1 into 1
11.774 * [backup-simplify]: Simplify (/ 1 1) into 1
11.774 * [backup-simplify]: Simplify (sqrt 0) into 0
11.776 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
11.776 * [taylor]: Taking taylor expansion of (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k))) in n
11.776 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in n
11.776 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
11.776 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
11.776 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
11.776 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
11.776 * [taylor]: Taking taylor expansion of 0.5 in n
11.776 * [backup-simplify]: Simplify 0.5 into 0.5
11.776 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
11.776 * [taylor]: Taking taylor expansion of 1.0 in n
11.776 * [backup-simplify]: Simplify 1.0 into 1.0
11.776 * [taylor]: Taking taylor expansion of k in n
11.776 * [backup-simplify]: Simplify k into k
11.776 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
11.776 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.776 * [taylor]: Taking taylor expansion of 2.0 in n
11.776 * [backup-simplify]: Simplify 2.0 into 2.0
11.777 * [taylor]: Taking taylor expansion of (* n PI) in n
11.777 * [taylor]: Taking taylor expansion of n in n
11.777 * [backup-simplify]: Simplify 0 into 0
11.777 * [backup-simplify]: Simplify 1 into 1
11.777 * [taylor]: Taking taylor expansion of PI in n
11.777 * [backup-simplify]: Simplify PI into PI
11.777 * [backup-simplify]: Simplify (* 0 PI) into 0
11.778 * [backup-simplify]: Simplify (* 2.0 0) into 0
11.779 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.781 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
11.782 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
11.782 * [backup-simplify]: Simplify (- k) into (- k)
11.782 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
11.782 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
11.784 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
11.785 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
11.786 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
11.786 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
11.786 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
11.786 * [taylor]: Taking taylor expansion of 1.0 in n
11.786 * [backup-simplify]: Simplify 1.0 into 1.0
11.787 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
11.787 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
11.787 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
11.787 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.787 * [taylor]: Taking taylor expansion of k in n
11.787 * [backup-simplify]: Simplify k into k
11.788 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.788 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
11.788 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.788 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
11.788 * [taylor]: Taking taylor expansion of (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k))) in n
11.788 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in n
11.788 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
11.788 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
11.788 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
11.788 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
11.788 * [taylor]: Taking taylor expansion of 0.5 in n
11.788 * [backup-simplify]: Simplify 0.5 into 0.5
11.788 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
11.788 * [taylor]: Taking taylor expansion of 1.0 in n
11.788 * [backup-simplify]: Simplify 1.0 into 1.0
11.788 * [taylor]: Taking taylor expansion of k in n
11.788 * [backup-simplify]: Simplify k into k
11.788 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
11.788 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
11.788 * [taylor]: Taking taylor expansion of 2.0 in n
11.788 * [backup-simplify]: Simplify 2.0 into 2.0
11.788 * [taylor]: Taking taylor expansion of (* n PI) in n
11.788 * [taylor]: Taking taylor expansion of n in n
11.788 * [backup-simplify]: Simplify 0 into 0
11.789 * [backup-simplify]: Simplify 1 into 1
11.789 * [taylor]: Taking taylor expansion of PI in n
11.789 * [backup-simplify]: Simplify PI into PI
11.789 * [backup-simplify]: Simplify (* 0 PI) into 0
11.790 * [backup-simplify]: Simplify (* 2.0 0) into 0
11.791 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
11.793 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
11.794 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
11.794 * [backup-simplify]: Simplify (- k) into (- k)
11.794 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
11.794 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
11.795 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
11.797 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
11.798 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
11.798 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
11.798 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
11.798 * [taylor]: Taking taylor expansion of 1.0 in n
11.798 * [backup-simplify]: Simplify 1.0 into 1.0
11.798 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
11.799 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
11.799 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
11.799 * [taylor]: Taking taylor expansion of (/ 1 k) in n
11.799 * [taylor]: Taking taylor expansion of k in n
11.799 * [backup-simplify]: Simplify k into k
11.799 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
11.800 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
11.800 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
11.800 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
11.801 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
11.803 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))
11.805 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) (sqrt (/ 1 k))) into (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) (sqrt (/ 1 k)))
11.805 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) (sqrt (/ 1 k))) in k
11.806 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) in k
11.806 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
11.806 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
11.806 * [taylor]: Taking taylor expansion of 1.0 in k
11.806 * [backup-simplify]: Simplify 1.0 into 1.0
11.806 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
11.807 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
11.807 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
11.807 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
11.807 * [taylor]: Taking taylor expansion of 0.5 in k
11.807 * [backup-simplify]: Simplify 0.5 into 0.5
11.807 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
11.807 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
11.807 * [taylor]: Taking taylor expansion of 1.0 in k
11.807 * [backup-simplify]: Simplify 1.0 into 1.0
11.807 * [taylor]: Taking taylor expansion of k in k
11.807 * [backup-simplify]: Simplify 0 into 0
11.807 * [backup-simplify]: Simplify 1 into 1
11.807 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
11.807 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
11.807 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
11.807 * [taylor]: Taking taylor expansion of 2.0 in k
11.807 * [backup-simplify]: Simplify 2.0 into 2.0
11.807 * [taylor]: Taking taylor expansion of PI in k
11.807 * [backup-simplify]: Simplify PI into PI
11.808 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
11.809 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
11.809 * [taylor]: Taking taylor expansion of (log n) in k
11.809 * [taylor]: Taking taylor expansion of n in k
11.809 * [backup-simplify]: Simplify n into n
11.809 * [backup-simplify]: Simplify (log n) into (log n)
11.809 * [backup-simplify]: Simplify (- 0) into 0
11.810 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
11.811 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
11.812 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
11.813 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
11.814 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
11.814 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
11.814 * [taylor]: Taking taylor expansion of (/ 1 k) in k
11.814 * [taylor]: Taking taylor expansion of k in k
11.814 * [backup-simplify]: Simplify 0 into 0
11.814 * [backup-simplify]: Simplify 1 into 1
11.815 * [backup-simplify]: Simplify (/ 1 1) into 1
11.815 * [backup-simplify]: Simplify (sqrt 0) into 0
11.816 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
11.817 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
11.820 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))
11.822 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) 0) into 0
11.822 * [backup-simplify]: Simplify 0 into 0
11.823 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
11.824 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
11.825 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
11.827 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
11.828 * [backup-simplify]: Simplify (- 0) into 0
11.828 * [backup-simplify]: Simplify (+ 0 0) into 0
11.829 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
11.830 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
11.831 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
11.833 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
11.835 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (pow (sqrt 1.0) 2))) into 0
11.837 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
11.837 * [taylor]: Taking taylor expansion of 0 in k
11.837 * [backup-simplify]: Simplify 0 into 0
11.838 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
11.840 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
11.841 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
11.841 * [backup-simplify]: Simplify (+ 0 0) into 0
11.842 * [backup-simplify]: Simplify (- 1) into -1
11.842 * [backup-simplify]: Simplify (+ 0 -1) into -1
11.843 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
11.846 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
11.849 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
11.850 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
11.855 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.5 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.5 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))
11.863 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) +nan.0) (* (- (+ (* 0.5 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.5 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))) 0)) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))
11.865 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))
11.865 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.866 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
11.867 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
11.868 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
11.869 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
11.870 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
11.874 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
11.874 * [backup-simplify]: Simplify (- 0) into 0
11.875 * [backup-simplify]: Simplify (+ 0 0) into 0
11.876 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
11.877 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
11.879 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
11.882 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
11.884 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (pow (sqrt 1.0) 2)))) into 0
11.887 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
11.887 * [taylor]: Taking taylor expansion of 0 in k
11.887 * [backup-simplify]: Simplify 0 into 0
11.887 * [backup-simplify]: Simplify 0 into 0
11.888 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
11.891 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
11.895 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
11.899 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
11.901 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
11.901 * [backup-simplify]: Simplify (+ 0 0) into 0
11.902 * [backup-simplify]: Simplify (- 0) into 0
11.902 * [backup-simplify]: Simplify (+ 0 0) into 0
11.904 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
11.907 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
11.911 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
11.912 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
11.913 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
11.919 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))) (+ (* 0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) into (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.125 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))
11.931 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* (- (+ (* 0.5 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.5 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))) +nan.0) (* (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.125 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))))) 0))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
11.936 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
11.937 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
11.937 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
11.938 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
11.939 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
11.939 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
11.940 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
11.946 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
11.947 * [backup-simplify]: Simplify (- 0) into 0
11.947 * [backup-simplify]: Simplify (+ 0 0) into 0
11.948 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
11.950 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
11.952 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
11.955 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
11.957 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (sqrt 1.0) 2))))) into 0
11.959 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
11.959 * [taylor]: Taking taylor expansion of 0 in k
11.959 * [backup-simplify]: Simplify 0 into 0
11.959 * [backup-simplify]: Simplify 0 into 0
11.959 * [backup-simplify]: Simplify 0 into 0
11.959 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
11.962 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
11.963 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
11.966 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
11.968 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
11.968 * [backup-simplify]: Simplify (+ 0 0) into 0
11.968 * [backup-simplify]: Simplify (- 0) into 0
11.968 * [backup-simplify]: Simplify (+ 0 0) into 0
11.970 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
11.972 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))))) into 0
11.976 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
11.977 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
11.977 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
11.992 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))) (+ (* 0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.020833333333333332 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 3)))) (+ (* 0.0625 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))) (* 0.020833333333333332 (* (pow (log (* 2.0 PI)) 3) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
12.022 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* (- (+ (* 0.5 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.5 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))) +nan.0) (+ (* (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.125 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))))) +nan.0) (* (- (+ (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.020833333333333332 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 3)))) (+ (* 0.0625 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))) (* 0.020833333333333332 (* (pow (log (* 2.0 PI)) 3) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) 0)))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))))))))))))))
12.034 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))))))))))))))
12.067 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) (* k 1)) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k)))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))))))))))))))))))))))
12.070 * [backup-simplify]: Simplify (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) (sqrt (/ 1 k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) (sqrt (/ 1 k))))) into (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k))
12.070 * [approximate]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in (n k) around 0
12.070 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in k
12.070 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
12.070 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
12.070 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
12.070 * [taylor]: Taking taylor expansion of 1.0 in k
12.070 * [backup-simplify]: Simplify 1.0 into 1.0
12.070 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.071 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.071 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
12.071 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
12.071 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
12.071 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
12.071 * [taylor]: Taking taylor expansion of 0.5 in k
12.071 * [backup-simplify]: Simplify 0.5 into 0.5
12.071 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
12.071 * [taylor]: Taking taylor expansion of 1.0 in k
12.071 * [backup-simplify]: Simplify 1.0 into 1.0
12.071 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.071 * [taylor]: Taking taylor expansion of k in k
12.071 * [backup-simplify]: Simplify 0 into 0
12.072 * [backup-simplify]: Simplify 1 into 1
12.072 * [backup-simplify]: Simplify (/ 1 1) into 1
12.072 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
12.072 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
12.072 * [taylor]: Taking taylor expansion of 2.0 in k
12.072 * [backup-simplify]: Simplify 2.0 into 2.0
12.072 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.072 * [taylor]: Taking taylor expansion of PI in k
12.072 * [backup-simplify]: Simplify PI into PI
12.072 * [taylor]: Taking taylor expansion of n in k
12.072 * [backup-simplify]: Simplify n into n
12.072 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.072 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
12.072 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
12.073 * [backup-simplify]: Simplify (- 1) into -1
12.073 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.074 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
12.074 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
12.074 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
12.074 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.074 * [taylor]: Taking taylor expansion of k in k
12.074 * [backup-simplify]: Simplify 0 into 0
12.074 * [backup-simplify]: Simplify 1 into 1
12.075 * [backup-simplify]: Simplify (sqrt 0) into 0
12.076 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.076 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in n
12.076 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
12.076 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
12.076 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
12.076 * [taylor]: Taking taylor expansion of 1.0 in n
12.076 * [backup-simplify]: Simplify 1.0 into 1.0
12.077 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.077 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.077 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
12.077 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
12.077 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
12.077 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
12.077 * [taylor]: Taking taylor expansion of 0.5 in n
12.077 * [backup-simplify]: Simplify 0.5 into 0.5
12.078 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
12.078 * [taylor]: Taking taylor expansion of 1.0 in n
12.078 * [backup-simplify]: Simplify 1.0 into 1.0
12.078 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.078 * [taylor]: Taking taylor expansion of k in n
12.078 * [backup-simplify]: Simplify k into k
12.078 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.078 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
12.078 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
12.078 * [taylor]: Taking taylor expansion of 2.0 in n
12.078 * [backup-simplify]: Simplify 2.0 into 2.0
12.078 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.078 * [taylor]: Taking taylor expansion of PI in n
12.078 * [backup-simplify]: Simplify PI into PI
12.078 * [taylor]: Taking taylor expansion of n in n
12.078 * [backup-simplify]: Simplify 0 into 0
12.078 * [backup-simplify]: Simplify 1 into 1
12.078 * [backup-simplify]: Simplify (/ PI 1) into PI
12.079 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.080 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.080 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.080 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
12.080 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
12.082 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.083 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
12.084 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
12.085 * [taylor]: Taking taylor expansion of (sqrt k) in n
12.085 * [taylor]: Taking taylor expansion of k in n
12.085 * [backup-simplify]: Simplify k into k
12.085 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
12.085 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
12.085 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in n
12.085 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
12.085 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
12.085 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
12.085 * [taylor]: Taking taylor expansion of 1.0 in n
12.085 * [backup-simplify]: Simplify 1.0 into 1.0
12.085 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.086 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.086 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
12.086 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
12.086 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
12.086 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
12.086 * [taylor]: Taking taylor expansion of 0.5 in n
12.086 * [backup-simplify]: Simplify 0.5 into 0.5
12.086 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
12.086 * [taylor]: Taking taylor expansion of 1.0 in n
12.086 * [backup-simplify]: Simplify 1.0 into 1.0
12.086 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.086 * [taylor]: Taking taylor expansion of k in n
12.087 * [backup-simplify]: Simplify k into k
12.087 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.087 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
12.087 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
12.087 * [taylor]: Taking taylor expansion of 2.0 in n
12.087 * [backup-simplify]: Simplify 2.0 into 2.0
12.087 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.087 * [taylor]: Taking taylor expansion of PI in n
12.087 * [backup-simplify]: Simplify PI into PI
12.087 * [taylor]: Taking taylor expansion of n in n
12.087 * [backup-simplify]: Simplify 0 into 0
12.087 * [backup-simplify]: Simplify 1 into 1
12.088 * [backup-simplify]: Simplify (/ PI 1) into PI
12.088 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.089 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.089 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.089 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
12.089 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
12.091 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.092 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
12.093 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
12.093 * [taylor]: Taking taylor expansion of (sqrt k) in n
12.093 * [taylor]: Taking taylor expansion of k in n
12.093 * [backup-simplify]: Simplify k into k
12.093 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
12.093 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
12.095 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
12.097 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))
12.099 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) (sqrt k)) into (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) (sqrt k))
12.099 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) (sqrt k)) in k
12.099 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) in k
12.099 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
12.099 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
12.099 * [taylor]: Taking taylor expansion of 1.0 in k
12.099 * [backup-simplify]: Simplify 1.0 into 1.0
12.100 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.100 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.100 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
12.100 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
12.100 * [taylor]: Taking taylor expansion of 0.5 in k
12.101 * [backup-simplify]: Simplify 0.5 into 0.5
12.101 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
12.101 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
12.101 * [taylor]: Taking taylor expansion of 1.0 in k
12.101 * [backup-simplify]: Simplify 1.0 into 1.0
12.101 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.101 * [taylor]: Taking taylor expansion of k in k
12.101 * [backup-simplify]: Simplify 0 into 0
12.101 * [backup-simplify]: Simplify 1 into 1
12.101 * [backup-simplify]: Simplify (/ 1 1) into 1
12.101 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
12.101 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
12.101 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
12.101 * [taylor]: Taking taylor expansion of 2.0 in k
12.101 * [backup-simplify]: Simplify 2.0 into 2.0
12.101 * [taylor]: Taking taylor expansion of PI in k
12.101 * [backup-simplify]: Simplify PI into PI
12.102 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.103 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.103 * [taylor]: Taking taylor expansion of (log n) in k
12.103 * [taylor]: Taking taylor expansion of n in k
12.103 * [backup-simplify]: Simplify n into n
12.103 * [backup-simplify]: Simplify (log n) into (log n)
12.103 * [backup-simplify]: Simplify (- 1) into -1
12.104 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.104 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.105 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
12.106 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
12.107 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
12.108 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
12.108 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.108 * [taylor]: Taking taylor expansion of k in k
12.108 * [backup-simplify]: Simplify 0 into 0
12.108 * [backup-simplify]: Simplify 1 into 1
12.109 * [backup-simplify]: Simplify (sqrt 0) into 0
12.110 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.111 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
12.113 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))
12.115 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 0) into 0
12.116 * [backup-simplify]: Simplify 0 into 0
12.116 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.117 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
12.119 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
12.119 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.120 * [backup-simplify]: Simplify (- 0) into 0
12.120 * [backup-simplify]: Simplify (+ 0 0) into 0
12.120 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
12.122 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.126 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
12.128 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.129 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
12.131 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0
12.133 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 0) (* 0 (sqrt k))) into 0
12.133 * [taylor]: Taking taylor expansion of 0 in k
12.133 * [backup-simplify]: Simplify 0 into 0
12.133 * [backup-simplify]: Simplify 0 into 0
12.135 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
12.137 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0
12.139 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
12.142 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
12.143 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
12.144 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.145 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.148 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
12.148 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.149 * [backup-simplify]: Simplify (- 0) into 0
12.149 * [backup-simplify]: Simplify (+ 0 0) into 0
12.150 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
12.152 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.154 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
12.156 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.158 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
12.159 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
12.161 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into 0
12.164 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
12.164 * [taylor]: Taking taylor expansion of 0 in k
12.164 * [backup-simplify]: Simplify 0 into 0
12.164 * [backup-simplify]: Simplify 0 into 0
12.164 * [backup-simplify]: Simplify 0 into 0
12.167 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.169 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
12.170 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
12.172 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into 0
12.175 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
12.178 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
12.179 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
12.180 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.181 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.187 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
12.188 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.188 * [backup-simplify]: Simplify (- 0) into 0
12.188 * [backup-simplify]: Simplify (+ 0 0) into 0
12.190 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
12.191 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.193 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
12.196 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
12.198 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
12.199 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
12.201 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))) into 0
12.203 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
12.203 * [taylor]: Taking taylor expansion of 0 in k
12.203 * [backup-simplify]: Simplify 0 into 0
12.203 * [backup-simplify]: Simplify 0 into 0
12.203 * [backup-simplify]: Simplify 0 into 0
12.204 * [backup-simplify]: Simplify 0 into 0
12.206 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.207 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
12.207 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
12.209 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))) into 0
12.211 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
12.213 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
12.217 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n))))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n))))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n))))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) k)) (- (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) (pow k 2))))))))
12.218 * [backup-simplify]: Simplify (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) (sqrt (/ 1 (- k))))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) (sqrt (/ 1 (- k)))))) into (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
12.219 * [approximate]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in (n k) around 0
12.219 * [taylor]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in k
12.219 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in k
12.219 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
12.219 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
12.219 * [taylor]: Taking taylor expansion of 1.0 in k
12.219 * [backup-simplify]: Simplify 1.0 into 1.0
12.219 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.219 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.219 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
12.219 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
12.219 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
12.219 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
12.219 * [taylor]: Taking taylor expansion of 0.5 in k
12.219 * [backup-simplify]: Simplify 0.5 into 0.5
12.219 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
12.220 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.220 * [taylor]: Taking taylor expansion of k in k
12.220 * [backup-simplify]: Simplify 0 into 0
12.220 * [backup-simplify]: Simplify 1 into 1
12.220 * [backup-simplify]: Simplify (/ 1 1) into 1
12.220 * [taylor]: Taking taylor expansion of 1.0 in k
12.220 * [backup-simplify]: Simplify 1.0 into 1.0
12.220 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
12.220 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
12.220 * [taylor]: Taking taylor expansion of -2.0 in k
12.220 * [backup-simplify]: Simplify -2.0 into -2.0
12.220 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.220 * [taylor]: Taking taylor expansion of PI in k
12.220 * [backup-simplify]: Simplify PI into PI
12.220 * [taylor]: Taking taylor expansion of n in k
12.220 * [backup-simplify]: Simplify n into n
12.220 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.220 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
12.220 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
12.220 * [backup-simplify]: Simplify (+ 1 0) into 1
12.221 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
12.221 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
12.221 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
12.221 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.221 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.221 * [taylor]: Taking taylor expansion of -1 in k
12.221 * [backup-simplify]: Simplify -1 into -1
12.221 * [taylor]: Taking taylor expansion of k in k
12.221 * [backup-simplify]: Simplify 0 into 0
12.221 * [backup-simplify]: Simplify 1 into 1
12.221 * [backup-simplify]: Simplify (/ -1 1) into -1
12.222 * [backup-simplify]: Simplify (sqrt 0) into 0
12.222 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.223 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
12.224 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
12.225 * [backup-simplify]: Simplify (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) +nan.0) into (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))
12.225 * [taylor]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in n
12.225 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in n
12.225 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
12.225 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
12.225 * [taylor]: Taking taylor expansion of 1.0 in n
12.225 * [backup-simplify]: Simplify 1.0 into 1.0
12.225 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.225 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.225 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
12.225 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
12.225 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
12.225 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
12.226 * [taylor]: Taking taylor expansion of 0.5 in n
12.226 * [backup-simplify]: Simplify 0.5 into 0.5
12.226 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
12.226 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.226 * [taylor]: Taking taylor expansion of k in n
12.226 * [backup-simplify]: Simplify k into k
12.226 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.226 * [taylor]: Taking taylor expansion of 1.0 in n
12.226 * [backup-simplify]: Simplify 1.0 into 1.0
12.226 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
12.226 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
12.226 * [taylor]: Taking taylor expansion of -2.0 in n
12.226 * [backup-simplify]: Simplify -2.0 into -2.0
12.226 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.226 * [taylor]: Taking taylor expansion of PI in n
12.226 * [backup-simplify]: Simplify PI into PI
12.226 * [taylor]: Taking taylor expansion of n in n
12.226 * [backup-simplify]: Simplify 0 into 0
12.226 * [backup-simplify]: Simplify 1 into 1
12.226 * [backup-simplify]: Simplify (/ PI 1) into PI
12.226 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.227 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
12.227 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
12.227 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
12.228 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.229 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
12.230 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
12.230 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
12.230 * [taylor]: Taking taylor expansion of (/ -1 k) in n
12.230 * [taylor]: Taking taylor expansion of -1 in n
12.230 * [backup-simplify]: Simplify -1 into -1
12.230 * [taylor]: Taking taylor expansion of k in n
12.230 * [backup-simplify]: Simplify k into k
12.230 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
12.230 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
12.230 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
12.230 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
12.231 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
12.232 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
12.234 * [backup-simplify]: Simplify (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) into (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k)))
12.234 * [taylor]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in n
12.235 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in n
12.235 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
12.235 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
12.235 * [taylor]: Taking taylor expansion of 1.0 in n
12.235 * [backup-simplify]: Simplify 1.0 into 1.0
12.235 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.236 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.236 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
12.236 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
12.236 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
12.236 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
12.236 * [taylor]: Taking taylor expansion of 0.5 in n
12.236 * [backup-simplify]: Simplify 0.5 into 0.5
12.236 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
12.236 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.236 * [taylor]: Taking taylor expansion of k in n
12.236 * [backup-simplify]: Simplify k into k
12.236 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.236 * [taylor]: Taking taylor expansion of 1.0 in n
12.236 * [backup-simplify]: Simplify 1.0 into 1.0
12.236 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
12.236 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
12.236 * [taylor]: Taking taylor expansion of -2.0 in n
12.236 * [backup-simplify]: Simplify -2.0 into -2.0
12.236 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.236 * [taylor]: Taking taylor expansion of PI in n
12.236 * [backup-simplify]: Simplify PI into PI
12.236 * [taylor]: Taking taylor expansion of n in n
12.236 * [backup-simplify]: Simplify 0 into 0
12.236 * [backup-simplify]: Simplify 1 into 1
12.237 * [backup-simplify]: Simplify (/ PI 1) into PI
12.237 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.238 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
12.238 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
12.239 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
12.240 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.241 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
12.242 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
12.242 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
12.242 * [taylor]: Taking taylor expansion of (/ -1 k) in n
12.243 * [taylor]: Taking taylor expansion of -1 in n
12.243 * [backup-simplify]: Simplify -1 into -1
12.243 * [taylor]: Taking taylor expansion of k in n
12.243 * [backup-simplify]: Simplify k into k
12.243 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
12.243 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
12.243 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
12.243 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
12.244 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
12.246 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
12.248 * [backup-simplify]: Simplify (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) into (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k)))
12.249 * [taylor]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) in k
12.249 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) in k
12.249 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
12.249 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
12.249 * [taylor]: Taking taylor expansion of 1.0 in k
12.249 * [backup-simplify]: Simplify 1.0 into 1.0
12.249 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
12.250 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
12.250 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
12.250 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
12.250 * [taylor]: Taking taylor expansion of 0.5 in k
12.250 * [backup-simplify]: Simplify 0.5 into 0.5
12.250 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
12.250 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
12.250 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
12.250 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
12.250 * [taylor]: Taking taylor expansion of -2.0 in k
12.250 * [backup-simplify]: Simplify -2.0 into -2.0
12.250 * [taylor]: Taking taylor expansion of PI in k
12.250 * [backup-simplify]: Simplify PI into PI
12.251 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.255 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
12.255 * [taylor]: Taking taylor expansion of (log n) in k
12.255 * [taylor]: Taking taylor expansion of n in k
12.255 * [backup-simplify]: Simplify n into n
12.255 * [backup-simplify]: Simplify (log n) into (log n)
12.255 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
12.255 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.255 * [taylor]: Taking taylor expansion of k in k
12.255 * [backup-simplify]: Simplify 0 into 0
12.255 * [backup-simplify]: Simplify 1 into 1
12.255 * [backup-simplify]: Simplify (/ 1 1) into 1
12.255 * [taylor]: Taking taylor expansion of 1.0 in k
12.256 * [backup-simplify]: Simplify 1.0 into 1.0
12.256 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.257 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
12.257 * [backup-simplify]: Simplify (+ 1 0) into 1
12.258 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
12.259 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
12.260 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
12.260 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.260 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.260 * [taylor]: Taking taylor expansion of -1 in k
12.261 * [backup-simplify]: Simplify -1 into -1
12.261 * [taylor]: Taking taylor expansion of k in k
12.261 * [backup-simplify]: Simplify 0 into 0
12.261 * [backup-simplify]: Simplify 1 into 1
12.261 * [backup-simplify]: Simplify (/ -1 1) into -1
12.261 * [backup-simplify]: Simplify (sqrt 0) into 0
12.263 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.264 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
12.266 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
12.268 * [backup-simplify]: Simplify (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) +nan.0) into (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
12.270 * [backup-simplify]: Simplify (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
12.271 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.272 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
12.274 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
12.274 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.275 * [backup-simplify]: Simplify (+ 0 0) into 0
12.275 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
12.277 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.278 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
12.280 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
12.281 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
12.283 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0
12.285 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
12.285 * [taylor]: Taking taylor expansion of 0 in k
12.285 * [backup-simplify]: Simplify 0 into 0
12.285 * [backup-simplify]: Simplify 0 into 0
12.286 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
12.288 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0
12.289 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
12.292 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.296 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))
12.299 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))
12.300 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.301 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.306 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
12.307 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.307 * [backup-simplify]: Simplify (+ 0 0) into 0
12.308 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
12.310 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.311 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
12.314 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.315 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
12.316 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
12.319 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into 0
12.319 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.320 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
12.323 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
12.323 * [taylor]: Taking taylor expansion of 0 in k
12.323 * [backup-simplify]: Simplify 0 into 0
12.323 * [backup-simplify]: Simplify 0 into 0
12.323 * [backup-simplify]: Simplify 0 into 0
12.324 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
12.325 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
12.327 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into 0
12.328 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.333 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.339 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))
12.342 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))
12.350 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))))) into (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2)) k)) (- (+ (* +nan.0 (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2))) (- (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2)) (pow k 2))))))))
12.350 * * * * [progress]: [ 4 / 4 ] generating series at (2 2 1)
12.351 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))))
12.351 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (n k) around 0
12.351 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
12.351 * [taylor]: Taking taylor expansion of 1.0 in k
12.351 * [backup-simplify]: Simplify 1.0 into 1.0
12.351 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
12.351 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
12.351 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
12.351 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
12.351 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
12.351 * [taylor]: Taking taylor expansion of 0.5 in k
12.351 * [backup-simplify]: Simplify 0.5 into 0.5
12.351 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
12.351 * [taylor]: Taking taylor expansion of 1.0 in k
12.351 * [backup-simplify]: Simplify 1.0 into 1.0
12.351 * [taylor]: Taking taylor expansion of k in k
12.351 * [backup-simplify]: Simplify 0 into 0
12.351 * [backup-simplify]: Simplify 1 into 1
12.351 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
12.351 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
12.351 * [taylor]: Taking taylor expansion of 2.0 in k
12.351 * [backup-simplify]: Simplify 2.0 into 2.0
12.351 * [taylor]: Taking taylor expansion of (* n PI) in k
12.351 * [taylor]: Taking taylor expansion of n in k
12.351 * [backup-simplify]: Simplify n into n
12.351 * [taylor]: Taking taylor expansion of PI in k
12.351 * [backup-simplify]: Simplify PI into PI
12.351 * [backup-simplify]: Simplify (* n PI) into (* n PI)
12.351 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
12.352 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
12.352 * [backup-simplify]: Simplify (- 0) into 0
12.352 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
12.353 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
12.353 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
12.353 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
12.353 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.353 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.353 * [taylor]: Taking taylor expansion of k in k
12.353 * [backup-simplify]: Simplify 0 into 0
12.353 * [backup-simplify]: Simplify 1 into 1
12.354 * [backup-simplify]: Simplify (/ 1 1) into 1
12.354 * [backup-simplify]: Simplify (sqrt 0) into 0
12.355 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.355 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
12.355 * [taylor]: Taking taylor expansion of 1.0 in n
12.356 * [backup-simplify]: Simplify 1.0 into 1.0
12.356 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
12.356 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
12.356 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
12.356 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
12.356 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
12.356 * [taylor]: Taking taylor expansion of 0.5 in n
12.356 * [backup-simplify]: Simplify 0.5 into 0.5
12.356 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
12.356 * [taylor]: Taking taylor expansion of 1.0 in n
12.356 * [backup-simplify]: Simplify 1.0 into 1.0
12.356 * [taylor]: Taking taylor expansion of k in n
12.356 * [backup-simplify]: Simplify k into k
12.356 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
12.356 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
12.356 * [taylor]: Taking taylor expansion of 2.0 in n
12.356 * [backup-simplify]: Simplify 2.0 into 2.0
12.356 * [taylor]: Taking taylor expansion of (* n PI) in n
12.356 * [taylor]: Taking taylor expansion of n in n
12.356 * [backup-simplify]: Simplify 0 into 0
12.356 * [backup-simplify]: Simplify 1 into 1
12.356 * [taylor]: Taking taylor expansion of PI in n
12.356 * [backup-simplify]: Simplify PI into PI
12.357 * [backup-simplify]: Simplify (* 0 PI) into 0
12.357 * [backup-simplify]: Simplify (* 2.0 0) into 0
12.359 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.360 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
12.362 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.362 * [backup-simplify]: Simplify (- k) into (- k)
12.362 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
12.362 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
12.363 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.364 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
12.365 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
12.365 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
12.365 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.365 * [taylor]: Taking taylor expansion of k in n
12.365 * [backup-simplify]: Simplify k into k
12.365 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.365 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
12.365 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.365 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
12.365 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
12.365 * [taylor]: Taking taylor expansion of 1.0 in n
12.365 * [backup-simplify]: Simplify 1.0 into 1.0
12.365 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
12.365 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
12.365 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
12.366 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
12.366 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
12.366 * [taylor]: Taking taylor expansion of 0.5 in n
12.366 * [backup-simplify]: Simplify 0.5 into 0.5
12.366 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
12.366 * [taylor]: Taking taylor expansion of 1.0 in n
12.366 * [backup-simplify]: Simplify 1.0 into 1.0
12.366 * [taylor]: Taking taylor expansion of k in n
12.366 * [backup-simplify]: Simplify k into k
12.366 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
12.366 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
12.366 * [taylor]: Taking taylor expansion of 2.0 in n
12.366 * [backup-simplify]: Simplify 2.0 into 2.0
12.366 * [taylor]: Taking taylor expansion of (* n PI) in n
12.366 * [taylor]: Taking taylor expansion of n in n
12.366 * [backup-simplify]: Simplify 0 into 0
12.366 * [backup-simplify]: Simplify 1 into 1
12.366 * [taylor]: Taking taylor expansion of PI in n
12.366 * [backup-simplify]: Simplify PI into PI
12.366 * [backup-simplify]: Simplify (* 0 PI) into 0
12.367 * [backup-simplify]: Simplify (* 2.0 0) into 0
12.368 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
12.369 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
12.369 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.369 * [backup-simplify]: Simplify (- k) into (- k)
12.369 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
12.369 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
12.370 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.371 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
12.372 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
12.372 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
12.372 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.372 * [taylor]: Taking taylor expansion of k in n
12.372 * [backup-simplify]: Simplify k into k
12.372 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.372 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
12.372 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.372 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
12.373 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))
12.374 * [backup-simplify]: Simplify (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) into (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))
12.374 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) in k
12.374 * [taylor]: Taking taylor expansion of 1.0 in k
12.374 * [backup-simplify]: Simplify 1.0 into 1.0
12.374 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) in k
12.374 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
12.374 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
12.374 * [taylor]: Taking taylor expansion of 0.5 in k
12.374 * [backup-simplify]: Simplify 0.5 into 0.5
12.374 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
12.374 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
12.374 * [taylor]: Taking taylor expansion of 1.0 in k
12.374 * [backup-simplify]: Simplify 1.0 into 1.0
12.374 * [taylor]: Taking taylor expansion of k in k
12.374 * [backup-simplify]: Simplify 0 into 0
12.374 * [backup-simplify]: Simplify 1 into 1
12.374 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
12.374 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
12.374 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
12.374 * [taylor]: Taking taylor expansion of 2.0 in k
12.374 * [backup-simplify]: Simplify 2.0 into 2.0
12.374 * [taylor]: Taking taylor expansion of PI in k
12.374 * [backup-simplify]: Simplify PI into PI
12.374 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.375 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.375 * [taylor]: Taking taylor expansion of (log n) in k
12.375 * [taylor]: Taking taylor expansion of n in k
12.375 * [backup-simplify]: Simplify n into n
12.375 * [backup-simplify]: Simplify (log n) into (log n)
12.375 * [backup-simplify]: Simplify (- 0) into 0
12.376 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
12.376 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
12.377 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
12.378 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
12.378 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
12.378 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
12.378 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.378 * [taylor]: Taking taylor expansion of k in k
12.378 * [backup-simplify]: Simplify 0 into 0
12.378 * [backup-simplify]: Simplify 1 into 1
12.379 * [backup-simplify]: Simplify (/ 1 1) into 1
12.379 * [backup-simplify]: Simplify (sqrt 0) into 0
12.380 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.381 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0) into 0
12.381 * [backup-simplify]: Simplify (* 1.0 0) into 0
12.381 * [backup-simplify]: Simplify 0 into 0
12.382 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
12.383 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
12.385 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
12.386 * [backup-simplify]: Simplify (- 0) into 0
12.386 * [backup-simplify]: Simplify (+ 0 0) into 0
12.386 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
12.388 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.389 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
12.391 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.393 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
12.398 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))) into 0
12.398 * [taylor]: Taking taylor expansion of 0 in k
12.398 * [backup-simplify]: Simplify 0 into 0
12.399 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
12.401 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
12.401 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
12.402 * [backup-simplify]: Simplify (+ 0 0) into 0
12.402 * [backup-simplify]: Simplify (- 1) into -1
12.403 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.404 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
12.407 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
12.410 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
12.415 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
12.417 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
12.418 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
12.418 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.419 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
12.420 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
12.422 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
12.425 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
12.426 * [backup-simplify]: Simplify (- 0) into 0
12.426 * [backup-simplify]: Simplify (+ 0 0) into 0
12.427 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
12.428 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.430 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
12.432 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.434 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
12.436 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))))) into 0
12.436 * [taylor]: Taking taylor expansion of 0 in k
12.436 * [backup-simplify]: Simplify 0 into 0
12.436 * [backup-simplify]: Simplify 0 into 0
12.437 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
12.439 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.439 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.441 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
12.442 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
12.443 * [backup-simplify]: Simplify (+ 0 0) into 0
12.443 * [backup-simplify]: Simplify (- 0) into 0
12.443 * [backup-simplify]: Simplify (+ 0 0) into 0
12.444 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
12.446 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
12.448 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
12.454 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) +nan.0) (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 0))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
12.458 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
12.461 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
12.462 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.462 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
12.463 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
12.464 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
12.469 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
12.469 * [backup-simplify]: Simplify (- 0) into 0
12.470 * [backup-simplify]: Simplify (+ 0 0) into 0
12.471 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
12.472 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
12.474 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
12.478 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
12.480 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
12.482 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))))) into 0
12.482 * [taylor]: Taking taylor expansion of 0 in k
12.482 * [backup-simplify]: Simplify 0 into 0
12.482 * [backup-simplify]: Simplify 0 into 0
12.483 * [backup-simplify]: Simplify 0 into 0
12.483 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.488 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.489 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.495 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
12.498 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow n 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow n 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow n 1)))) 6) into 0
12.499 * [backup-simplify]: Simplify (+ 0 0) into 0
12.500 * [backup-simplify]: Simplify (- 0) into 0
12.500 * [backup-simplify]: Simplify (+ 0 0) into 0
12.503 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
12.506 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))))) into 0
12.513 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
12.535 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) +nan.0) (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) +nan.0) (* (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
12.556 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))) (+ (* 0 (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
12.569 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
12.591 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) (* k 1)) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))))))))))))))))))
12.592 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) (sqrt (/ 1 k))) into (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)))
12.592 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (n k) around 0
12.592 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k
12.592 * [taylor]: Taking taylor expansion of 1.0 in k
12.592 * [backup-simplify]: Simplify 1.0 into 1.0
12.592 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k
12.592 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
12.592 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
12.592 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
12.593 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
12.593 * [taylor]: Taking taylor expansion of 0.5 in k
12.593 * [backup-simplify]: Simplify 0.5 into 0.5
12.593 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
12.593 * [taylor]: Taking taylor expansion of 1.0 in k
12.593 * [backup-simplify]: Simplify 1.0 into 1.0
12.593 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.593 * [taylor]: Taking taylor expansion of k in k
12.593 * [backup-simplify]: Simplify 0 into 0
12.593 * [backup-simplify]: Simplify 1 into 1
12.593 * [backup-simplify]: Simplify (/ 1 1) into 1
12.593 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
12.593 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
12.593 * [taylor]: Taking taylor expansion of 2.0 in k
12.593 * [backup-simplify]: Simplify 2.0 into 2.0
12.593 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.593 * [taylor]: Taking taylor expansion of PI in k
12.593 * [backup-simplify]: Simplify PI into PI
12.593 * [taylor]: Taking taylor expansion of n in k
12.593 * [backup-simplify]: Simplify n into n
12.594 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.594 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
12.594 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
12.594 * [backup-simplify]: Simplify (- 1) into -1
12.595 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.595 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
12.595 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
12.596 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
12.596 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.596 * [taylor]: Taking taylor expansion of k in k
12.596 * [backup-simplify]: Simplify 0 into 0
12.596 * [backup-simplify]: Simplify 1 into 1
12.596 * [backup-simplify]: Simplify (sqrt 0) into 0
12.598 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.598 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
12.598 * [taylor]: Taking taylor expansion of 1.0 in n
12.598 * [backup-simplify]: Simplify 1.0 into 1.0
12.598 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
12.598 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
12.598 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
12.598 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
12.598 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
12.598 * [taylor]: Taking taylor expansion of 0.5 in n
12.598 * [backup-simplify]: Simplify 0.5 into 0.5
12.598 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
12.598 * [taylor]: Taking taylor expansion of 1.0 in n
12.598 * [backup-simplify]: Simplify 1.0 into 1.0
12.598 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.598 * [taylor]: Taking taylor expansion of k in n
12.598 * [backup-simplify]: Simplify k into k
12.598 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.598 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
12.599 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
12.599 * [taylor]: Taking taylor expansion of 2.0 in n
12.599 * [backup-simplify]: Simplify 2.0 into 2.0
12.599 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.599 * [taylor]: Taking taylor expansion of PI in n
12.599 * [backup-simplify]: Simplify PI into PI
12.599 * [taylor]: Taking taylor expansion of n in n
12.599 * [backup-simplify]: Simplify 0 into 0
12.599 * [backup-simplify]: Simplify 1 into 1
12.599 * [backup-simplify]: Simplify (/ PI 1) into PI
12.600 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.601 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.601 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.601 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
12.602 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
12.603 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.604 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
12.606 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
12.606 * [taylor]: Taking taylor expansion of (sqrt k) in n
12.606 * [taylor]: Taking taylor expansion of k in n
12.606 * [backup-simplify]: Simplify k into k
12.606 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
12.606 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
12.606 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
12.606 * [taylor]: Taking taylor expansion of 1.0 in n
12.606 * [backup-simplify]: Simplify 1.0 into 1.0
12.606 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
12.606 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
12.606 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
12.606 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
12.606 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
12.606 * [taylor]: Taking taylor expansion of 0.5 in n
12.606 * [backup-simplify]: Simplify 0.5 into 0.5
12.606 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
12.606 * [taylor]: Taking taylor expansion of 1.0 in n
12.606 * [backup-simplify]: Simplify 1.0 into 1.0
12.606 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.606 * [taylor]: Taking taylor expansion of k in n
12.606 * [backup-simplify]: Simplify k into k
12.606 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.606 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
12.607 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
12.607 * [taylor]: Taking taylor expansion of 2.0 in n
12.607 * [backup-simplify]: Simplify 2.0 into 2.0
12.607 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.607 * [taylor]: Taking taylor expansion of PI in n
12.607 * [backup-simplify]: Simplify PI into PI
12.607 * [taylor]: Taking taylor expansion of n in n
12.607 * [backup-simplify]: Simplify 0 into 0
12.607 * [backup-simplify]: Simplify 1 into 1
12.607 * [backup-simplify]: Simplify (/ PI 1) into PI
12.608 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.609 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.609 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
12.609 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
12.609 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
12.610 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.611 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
12.611 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
12.611 * [taylor]: Taking taylor expansion of (sqrt k) in n
12.611 * [taylor]: Taking taylor expansion of k in n
12.611 * [backup-simplify]: Simplify k into k
12.611 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
12.611 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
12.612 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) into (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))
12.613 * [backup-simplify]: Simplify (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) into (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))
12.613 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) in k
12.613 * [taylor]: Taking taylor expansion of 1.0 in k
12.613 * [backup-simplify]: Simplify 1.0 into 1.0
12.613 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) in k
12.613 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
12.613 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
12.613 * [taylor]: Taking taylor expansion of 0.5 in k
12.613 * [backup-simplify]: Simplify 0.5 into 0.5
12.613 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
12.613 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
12.613 * [taylor]: Taking taylor expansion of 1.0 in k
12.613 * [backup-simplify]: Simplify 1.0 into 1.0
12.613 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.613 * [taylor]: Taking taylor expansion of k in k
12.613 * [backup-simplify]: Simplify 0 into 0
12.613 * [backup-simplify]: Simplify 1 into 1
12.614 * [backup-simplify]: Simplify (/ 1 1) into 1
12.614 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
12.614 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
12.614 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
12.614 * [taylor]: Taking taylor expansion of 2.0 in k
12.614 * [backup-simplify]: Simplify 2.0 into 2.0
12.614 * [taylor]: Taking taylor expansion of PI in k
12.614 * [backup-simplify]: Simplify PI into PI
12.614 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
12.615 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
12.615 * [taylor]: Taking taylor expansion of (log n) in k
12.615 * [taylor]: Taking taylor expansion of n in k
12.615 * [backup-simplify]: Simplify n into n
12.615 * [backup-simplify]: Simplify (log n) into (log n)
12.615 * [backup-simplify]: Simplify (- 1) into -1
12.615 * [backup-simplify]: Simplify (+ 0 -1) into -1
12.615 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.616 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
12.617 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
12.617 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
12.618 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
12.618 * [taylor]: Taking taylor expansion of (sqrt k) in k
12.618 * [taylor]: Taking taylor expansion of k in k
12.618 * [backup-simplify]: Simplify 0 into 0
12.618 * [backup-simplify]: Simplify 1 into 1
12.618 * [backup-simplify]: Simplify (sqrt 0) into 0
12.619 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
12.620 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) into 0
12.620 * [backup-simplify]: Simplify (* 1.0 0) into 0
12.620 * [backup-simplify]: Simplify 0 into 0
12.621 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.621 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
12.622 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
12.622 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.623 * [backup-simplify]: Simplify (- 0) into 0
12.623 * [backup-simplify]: Simplify (+ 0 0) into 0
12.623 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
12.624 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.625 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
12.626 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
12.627 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
12.628 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))) into 0
12.628 * [taylor]: Taking taylor expansion of 0 in k
12.628 * [backup-simplify]: Simplify 0 into 0
12.628 * [backup-simplify]: Simplify 0 into 0
12.629 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
12.630 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
12.631 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
12.631 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
12.632 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.633 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.634 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
12.635 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.635 * [backup-simplify]: Simplify (- 0) into 0
12.635 * [backup-simplify]: Simplify (+ 0 0) into 0
12.636 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
12.637 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.638 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
12.639 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.640 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
12.641 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))))) into 0
12.641 * [taylor]: Taking taylor expansion of 0 in k
12.641 * [backup-simplify]: Simplify 0 into 0
12.641 * [backup-simplify]: Simplify 0 into 0
12.641 * [backup-simplify]: Simplify 0 into 0
12.643 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.647 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
12.649 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
12.650 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
12.651 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
12.651 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.652 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
12.657 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
12.657 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.658 * [backup-simplify]: Simplify (- 0) into 0
12.658 * [backup-simplify]: Simplify (+ 0 0) into 0
12.659 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
12.661 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
12.663 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
12.666 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
12.668 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
12.670 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))))) into 0
12.670 * [taylor]: Taking taylor expansion of 0 in k
12.670 * [backup-simplify]: Simplify 0 into 0
12.671 * [backup-simplify]: Simplify 0 into 0
12.671 * [backup-simplify]: Simplify 0 into 0
12.671 * [backup-simplify]: Simplify 0 into 0
12.675 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.677 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
12.681 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
12.682 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
12.685 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
12.686 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) (sqrt (/ 1 (- k)))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))))
12.686 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (n k) around 0
12.686 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
12.686 * [taylor]: Taking taylor expansion of 1.0 in k
12.686 * [backup-simplify]: Simplify 1.0 into 1.0
12.686 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
12.686 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
12.686 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
12.686 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
12.686 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
12.686 * [taylor]: Taking taylor expansion of 0.5 in k
12.686 * [backup-simplify]: Simplify 0.5 into 0.5
12.686 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
12.686 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.686 * [taylor]: Taking taylor expansion of k in k
12.686 * [backup-simplify]: Simplify 0 into 0
12.686 * [backup-simplify]: Simplify 1 into 1
12.686 * [backup-simplify]: Simplify (/ 1 1) into 1
12.686 * [taylor]: Taking taylor expansion of 1.0 in k
12.686 * [backup-simplify]: Simplify 1.0 into 1.0
12.686 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
12.686 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
12.686 * [taylor]: Taking taylor expansion of -2.0 in k
12.686 * [backup-simplify]: Simplify -2.0 into -2.0
12.686 * [taylor]: Taking taylor expansion of (/ PI n) in k
12.686 * [taylor]: Taking taylor expansion of PI in k
12.686 * [backup-simplify]: Simplify PI into PI
12.686 * [taylor]: Taking taylor expansion of n in k
12.686 * [backup-simplify]: Simplify n into n
12.686 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
12.686 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
12.687 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
12.687 * [backup-simplify]: Simplify (+ 1 0) into 1
12.687 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
12.687 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
12.687 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
12.687 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.687 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.687 * [taylor]: Taking taylor expansion of -1 in k
12.687 * [backup-simplify]: Simplify -1 into -1
12.687 * [taylor]: Taking taylor expansion of k in k
12.687 * [backup-simplify]: Simplify 0 into 0
12.687 * [backup-simplify]: Simplify 1 into 1
12.688 * [backup-simplify]: Simplify (/ -1 1) into -1
12.688 * [backup-simplify]: Simplify (sqrt 0) into 0
12.689 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.689 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
12.689 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
12.689 * [taylor]: Taking taylor expansion of 1.0 in n
12.689 * [backup-simplify]: Simplify 1.0 into 1.0
12.689 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
12.689 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
12.689 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
12.689 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
12.689 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
12.689 * [taylor]: Taking taylor expansion of 0.5 in n
12.689 * [backup-simplify]: Simplify 0.5 into 0.5
12.689 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
12.689 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.689 * [taylor]: Taking taylor expansion of k in n
12.689 * [backup-simplify]: Simplify k into k
12.689 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.689 * [taylor]: Taking taylor expansion of 1.0 in n
12.689 * [backup-simplify]: Simplify 1.0 into 1.0
12.689 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
12.689 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
12.690 * [taylor]: Taking taylor expansion of -2.0 in n
12.690 * [backup-simplify]: Simplify -2.0 into -2.0
12.690 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.690 * [taylor]: Taking taylor expansion of PI in n
12.690 * [backup-simplify]: Simplify PI into PI
12.690 * [taylor]: Taking taylor expansion of n in n
12.690 * [backup-simplify]: Simplify 0 into 0
12.690 * [backup-simplify]: Simplify 1 into 1
12.690 * [backup-simplify]: Simplify (/ PI 1) into PI
12.690 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.691 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
12.691 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
12.691 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
12.692 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.693 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
12.694 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
12.694 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
12.694 * [taylor]: Taking taylor expansion of (/ -1 k) in n
12.694 * [taylor]: Taking taylor expansion of -1 in n
12.694 * [backup-simplify]: Simplify -1 into -1
12.694 * [taylor]: Taking taylor expansion of k in n
12.694 * [backup-simplify]: Simplify k into k
12.694 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
12.694 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
12.694 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
12.694 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
12.695 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
12.695 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
12.695 * [taylor]: Taking taylor expansion of 1.0 in n
12.695 * [backup-simplify]: Simplify 1.0 into 1.0
12.695 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
12.695 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
12.695 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
12.695 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
12.695 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
12.695 * [taylor]: Taking taylor expansion of 0.5 in n
12.695 * [backup-simplify]: Simplify 0.5 into 0.5
12.695 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
12.695 * [taylor]: Taking taylor expansion of (/ 1 k) in n
12.695 * [taylor]: Taking taylor expansion of k in n
12.695 * [backup-simplify]: Simplify k into k
12.695 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
12.695 * [taylor]: Taking taylor expansion of 1.0 in n
12.695 * [backup-simplify]: Simplify 1.0 into 1.0
12.695 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
12.695 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
12.695 * [taylor]: Taking taylor expansion of -2.0 in n
12.695 * [backup-simplify]: Simplify -2.0 into -2.0
12.695 * [taylor]: Taking taylor expansion of (/ PI n) in n
12.695 * [taylor]: Taking taylor expansion of PI in n
12.695 * [backup-simplify]: Simplify PI into PI
12.695 * [taylor]: Taking taylor expansion of n in n
12.695 * [backup-simplify]: Simplify 0 into 0
12.695 * [backup-simplify]: Simplify 1 into 1
12.696 * [backup-simplify]: Simplify (/ PI 1) into PI
12.696 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.697 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
12.697 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
12.697 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
12.698 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.699 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
12.699 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
12.699 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
12.699 * [taylor]: Taking taylor expansion of (/ -1 k) in n
12.699 * [taylor]: Taking taylor expansion of -1 in n
12.699 * [backup-simplify]: Simplify -1 into -1
12.699 * [taylor]: Taking taylor expansion of k in n
12.699 * [backup-simplify]: Simplify k into k
12.699 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
12.700 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
12.700 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
12.700 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
12.700 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
12.701 * [backup-simplify]: Simplify (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) into (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))))
12.701 * [taylor]: Taking taylor expansion of (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) in k
12.701 * [taylor]: Taking taylor expansion of 1.0 in k
12.701 * [backup-simplify]: Simplify 1.0 into 1.0
12.701 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in k
12.702 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
12.702 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
12.702 * [taylor]: Taking taylor expansion of 0.5 in k
12.702 * [backup-simplify]: Simplify 0.5 into 0.5
12.702 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
12.702 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
12.702 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
12.702 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
12.702 * [taylor]: Taking taylor expansion of -2.0 in k
12.702 * [backup-simplify]: Simplify -2.0 into -2.0
12.702 * [taylor]: Taking taylor expansion of PI in k
12.702 * [backup-simplify]: Simplify PI into PI
12.702 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
12.703 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
12.703 * [taylor]: Taking taylor expansion of (log n) in k
12.703 * [taylor]: Taking taylor expansion of n in k
12.703 * [backup-simplify]: Simplify n into n
12.703 * [backup-simplify]: Simplify (log n) into (log n)
12.703 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
12.703 * [taylor]: Taking taylor expansion of (/ 1 k) in k
12.703 * [taylor]: Taking taylor expansion of k in k
12.703 * [backup-simplify]: Simplify 0 into 0
12.703 * [backup-simplify]: Simplify 1 into 1
12.703 * [backup-simplify]: Simplify (/ 1 1) into 1
12.703 * [taylor]: Taking taylor expansion of 1.0 in k
12.703 * [backup-simplify]: Simplify 1.0 into 1.0
12.703 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
12.704 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
12.704 * [backup-simplify]: Simplify (+ 1 0) into 1
12.705 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
12.706 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
12.706 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
12.706 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
12.706 * [taylor]: Taking taylor expansion of (/ -1 k) in k
12.706 * [taylor]: Taking taylor expansion of -1 in k
12.706 * [backup-simplify]: Simplify -1 into -1
12.707 * [taylor]: Taking taylor expansion of k in k
12.707 * [backup-simplify]: Simplify 0 into 0
12.707 * [backup-simplify]: Simplify 1 into 1
12.707 * [backup-simplify]: Simplify (/ -1 1) into -1
12.707 * [backup-simplify]: Simplify (sqrt 0) into 0
12.708 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
12.709 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
12.710 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
12.710 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
12.711 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
12.712 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
12.713 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
12.713 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
12.713 * [backup-simplify]: Simplify (+ 0 0) into 0
12.714 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
12.716 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.718 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
12.720 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
12.722 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
12.724 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))))) into 0
12.724 * [taylor]: Taking taylor expansion of 0 in k
12.724 * [backup-simplify]: Simplify 0 into 0
12.724 * [backup-simplify]: Simplify 0 into 0
12.725 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
12.727 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
12.730 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
12.732 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
12.734 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
12.735 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.736 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
12.740 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
12.740 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.741 * [backup-simplify]: Simplify (+ 0 0) into 0
12.742 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
12.743 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
12.745 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
12.748 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
12.748 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
12.749 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
12.750 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
12.753 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))))) into 0
12.753 * [taylor]: Taking taylor expansion of 0 in k
12.753 * [backup-simplify]: Simplify 0 into 0
12.753 * [backup-simplify]: Simplify 0 into 0
12.753 * [backup-simplify]: Simplify 0 into 0
12.754 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
12.757 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
12.762 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
12.767 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
12.768 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
12.773 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))))))))
12.773 * * * [progress]: simplifying candidates
12.782 * [simplify]: Simplifying:
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (expm1 (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (log1p (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (+ 1/2 1/2)
  (+ 1/2 (/ 1 2))
  (+ 1 1)
  (+ (/ 1 2) 1/2)
  (+ (/ 1 2) (/ 1 2))
  (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (+ 1 1)
  (+ (log (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (log (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (log (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (exp (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (cbrt (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))) (cbrt (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))))
  (cbrt (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))) (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (sqrt (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt (sqrt k)) (sqrt (sqrt k)))
  (* (* (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))) (* (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))))
  (* (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))) (sqrt (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))))
  (* (sqrt (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))) (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt 1))) (sqrt (/ 1.0 (sqrt 1))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 (sqrt (sqrt k)))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ 1.0 1)) (sqrt (/ 1.0 1)))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))))
  (* (sqrt 1) (sqrt 1))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (/ 1 (sqrt k))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* 1 1)
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* 2 1/2)
  (* 2 1)
  (* 2 (/ 1 2))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (* (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt 1))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) 1)
  (* (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
  (* (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (expm1 (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (log1p (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (- (+ (log 1.0) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k)))
  (- (log (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k)))
  (log (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (exp (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (/ (* (* (* 1.0 1.0) 1.0) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (/ (* (* (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (* (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (- (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- (sqrt k))
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 (sqrt 1))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 1)
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt 1))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1)
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k)))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) k)) (- (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2)) k)) (- (+ (* +nan.0 (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2))) (- (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2)) (pow k 2))))))))
  (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))))))))
12.788 * * [simplify]: iteration 0: 346 enodes
12.881 * * [simplify]: iteration 1: 954 enodes
13.293 * * [simplify]: iteration 2: 4819 enodes
14.583 * * [simplify]: iteration complete: 5000 enodes
14.583 * * [simplify]: Extracting #0: cost 70 inf + 0
14.584 * * [simplify]: Extracting #1: cost 580 inf + 3
14.591 * * [simplify]: Extracting #2: cost 1070 inf + 7209
14.609 * * [simplify]: Extracting #3: cost 1096 inf + 37539
14.633 * * [simplify]: Extracting #4: cost 1014 inf + 97538
14.703 * * [simplify]: Extracting #5: cost 592 inf + 348313
14.822 * * [simplify]: Extracting #6: cost 267 inf + 546077
15.006 * * [simplify]: Extracting #7: cost 115 inf + 644698
15.211 * * [simplify]: Extracting #8: cost 84 inf + 667601
15.460 * * [simplify]: Extracting #9: cost 38 inf + 691832
15.703 * * [simplify]: Extracting #10: cost 4 inf + 712341
15.903 * * [simplify]: Extracting #11: cost 0 inf + 714337
16.151 * * [simplify]: Extracting #12: cost 0 inf + 713937
16.380 * * [simplify]: Extracting #13: cost 0 inf + 713732
16.596 * * [simplify]: Extracting #14: cost 0 inf + 713707
16.838 * [simplify]: Simplified to:
  (expm1 (* 2.0 (* n PI)))
  (log1p (* 2.0 (* n PI)))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (log (* 2.0 (* n PI)))
  (log (* 2.0 (* n PI)))
  (log (* 2.0 (* n PI)))
  (exp (* 2.0 (* n PI)))
  (* (* 2.0 (* (* 2.0 PI) (* 2.0 PI))) (* PI (* (* n n) n)))
  (* (* 2.0 PI) (* (* (* 2.0 PI) (* 2.0 PI)) (* (* n n) n)))
  (* (cbrt (* 2.0 (* n PI))) (cbrt (* 2.0 (* n PI))))
  (cbrt (* 2.0 (* n PI)))
  (* (* (* 2.0 (* n PI)) (* 2.0 (* n PI))) (* 2.0 (* n PI)))
  (sqrt (* 2.0 (* n PI)))
  (sqrt (* 2.0 (* n PI)))
  (* (* (* 2.0 PI) (cbrt n)) (cbrt n))
  (* (sqrt n) (* 2.0 PI))
  (* 2.0 PI)
  (* n PI)
  (expm1 (* 2.0 (* n PI)))
  (log1p (* 2.0 (* n PI)))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (log (* 2.0 (* n PI)))
  (log (* 2.0 (* n PI)))
  (log (* 2.0 (* n PI)))
  (exp (* 2.0 (* n PI)))
  (* (* 2.0 (* (* 2.0 PI) (* 2.0 PI))) (* PI (* (* n n) n)))
  (* (* 2.0 PI) (* (* (* 2.0 PI) (* 2.0 PI)) (* (* n n) n)))
  (* (cbrt (* 2.0 (* n PI))) (cbrt (* 2.0 (* n PI))))
  (cbrt (* 2.0 (* n PI)))
  (* (* (* 2.0 (* n PI)) (* 2.0 (* n PI))) (* 2.0 (* n PI)))
  (sqrt (* 2.0 (* n PI)))
  (sqrt (* 2.0 (* n PI)))
  (* (* (* 2.0 PI) (cbrt n)) (cbrt n))
  (* (sqrt n) (* 2.0 PI))
  (* 2.0 PI)
  (* n PI)
  (expm1 (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (log1p (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  1
  1
  2
  1
  1
  (* (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))
  (* (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  2
  (- (fma (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))) (log 1.0)) (log (sqrt k)))
  (- (fma (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))) (log 1.0)) (log (sqrt k)))
  (exp (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (* (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (* (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (* (cbrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (cbrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (cbrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (* (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (* (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (* (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (sqrt k)
  (* (* (cbrt (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))) (cbrt (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))) (* (cbrt (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))) (cbrt (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))))
  (* (cbrt (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))) (cbrt (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (cbrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (cbrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (cbrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (fabs (cbrt k)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt k))
  1
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))
  (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (/ 1 (sqrt k))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  1
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  1
  2
  1
  (* (cbrt (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))) (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (cbrt (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))))
  (* (fabs (cbrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))) (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))))
  (* (sqrt (/ 1.0 (fabs (cbrt k)))) (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt 1.0) (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt 1.0) (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (cbrt (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (cbrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))) (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt k))))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt k))))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (/ 1 (sqrt k))))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))))
  (* (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (sqrt (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))))
  (expm1 (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (log1p (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (- (fma (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))) (log 1.0)) (log (sqrt k)))
  (- (fma (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))) (log 1.0)) (log (sqrt k)))
  (- (fma (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))) (log 1.0)) (log (sqrt k)))
  (- (fma (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))) (log 1.0)) (log (sqrt k)))
  (- (fma (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))) (log 1.0)) (log (sqrt k)))
  (- (fma (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))) (log 1.0)) (log (sqrt k)))
  (- (fma (/ (- 1.0 k) 2.0) (log (* 2.0 (* n PI))) (log 1.0)) (log (sqrt k)))
  (exp (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (/ (* (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))) (* (sqrt k) k))
  (/ (* (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))) (* (sqrt k) k))
  (* (cbrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))) (cbrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (cbrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (* (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (* (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)) (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0))))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (sqrt (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (/ (sqrt k) 1.0)))
  (* (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (- 1.0))
  (- (sqrt k))
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (fabs (cbrt k)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (/ 1.0 (cbrt (sqrt k))) (/ (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k))))
  (/ 1.0 (/ (fabs (cbrt k)) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (/ 1.0 (sqrt (sqrt k))) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* 1.0 (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (/ (sqrt k) (pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0)))
  (* (pow (* 2.0 (* n PI)) (/ k 2.0)) (sqrt k))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (- (* (* +nan.0 (* 1.0 (exp (* (log (* 2.0 (* n PI))) 0.5)))) (* k (log n))) (fma (* k (* 1.0 (exp (* (log (* 2.0 (* n PI))) 0.5)))) +nan.0 (- (fma (* (log (* 2.0 PI)) +nan.0) (* k (* 1.0 (exp (* (log (* 2.0 (* n PI))) 0.5)))) (fma (- (* (log (* 2.0 PI)) +nan.0)) (* (* 1.0 (* k k)) (exp (* (log (* 2.0 (* n PI))) 0.5))) (fma (* (* 1.0 (* k k)) (exp (* (log (* 2.0 (* n PI))) 0.5))) +nan.0 (- (fma (* (log (* 2.0 PI)) +nan.0) (* (* 1.0 (* (log n) (* k k))) (exp (* (log (* 2.0 (* n PI))) 0.5))) (+ (- (* (* (exp (* (log (* 2.0 (* n PI))) 0.5)) +nan.0) 1.0) (* +nan.0 (- (* (* (log (* 2.0 PI)) (log (* 2.0 PI))) (* (* 1.0 (* k k)) (exp (* (log (* 2.0 (* n PI))) 0.5)))) (* (* 1.0 (* (log n) (* k k))) (exp (* (log (* 2.0 (* n PI))) 0.5)))))) (- (* 1.0 (* (* (* k (log n)) (* k (log n))) (* (exp (* (log (* 2.0 (* n PI))) 0.5)) +nan.0))))))))))))))
  (- (+ (- (/ (* (/ (exp (* (* (log (* 2.0 (* n PI))) 0.5) (- 1.0 k))) (/ (* k k) 1.0)) +nan.0) k) (* (/ (exp (* (* (log (* 2.0 (* n PI))) 0.5) (- 1.0 k))) (/ k 1.0)) +nan.0)) (* (/ (exp (* (* (log (* 2.0 (* n PI))) 0.5) (- 1.0 k))) (/ (* k k) 1.0)) +nan.0)))
  (+ (* (/ (exp (* (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))) 0.5)) (/ k 1.0)) (- +nan.0)) (* +nan.0 (- (* 1.0 (exp (* (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))) 0.5))) (/ (* 1.0 (exp (* (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))) 0.5))) (* k k)))))
  (- (fma (* (log (* 2.0 PI)) +nan.0) (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* (log n) (* k k))) (+ (* (- +nan.0) (exp (* (log (* 2.0 (* n PI))) 0.5))) (fma (* (* (log (* 2.0 PI)) (log (* 2.0 PI))) +nan.0) (* k (* k (exp (* (log (* 2.0 (* n PI))) 0.5)))) (- (* (* (- +nan.0) (exp (* (log (* 2.0 (* n PI))) 0.5))) (* k k)) (- (* (* (- +nan.0) (exp (* (log (* 2.0 (* n PI))) 0.5))) (* (* k (log n)) (* k (log n)))) (+ (* (* (- +nan.0) (exp (* (log (* 2.0 (* n PI))) 0.5))) (* (log n) (* k k))) (+ (- (* (* (log (* 2.0 PI)) +nan.0) (* k (* k (exp (* (log (* 2.0 (* n PI))) 0.5))))) (* (* (exp (* (log (* 2.0 (* n PI))) 0.5)) (* k (log n))) +nan.0)) (* (* k (exp (* (log (* 2.0 (* n PI))) 0.5))) (- (* (log (* 2.0 PI)) +nan.0) +nan.0))))))))))
  (- (* (- +nan.0) (/ (exp (* (* (log (* 2.0 (* n PI))) 0.5) (- 1.0 k))) (* k k))) (fma (/ (exp (* (* (log (* 2.0 (* n PI))) 0.5) (- 1.0 k))) k) (- +nan.0) (* (/ +nan.0 k) (/ (exp (* (* (log (* 2.0 (* n PI))) 0.5) (- 1.0 k))) (* k k)))))
  (+ (* +nan.0 (- (/ (exp (* (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))) 0.5)) k) (/ (exp (* (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))) 0.5)) (* k k)))) (* (exp (* (* (- 1.0 k) (- (log (* PI -2.0)) (log (/ -1 n)))) 0.5)) (- +nan.0)))
16.870 * * * [progress]: adding candidates to table
17.999 * * [progress]: iteration 4 / 4
17.999 * * * [progress]: picking best candidate
18.071 * * * * [pick]: Picked  #<alt (λ (k n) (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))>
18.071 * * * [progress]: localizing error
18.156 * * * [progress]: generating rewritten candidates
18.156 * * * * [progress]: [ 1 / 4 ] rewriting at (2 2 1 1 1 2 1)
18.169 * * * * [progress]: [ 2 / 4 ] rewriting at (2 1 1 1 2 1)
18.183 * * * * [progress]: [ 3 / 4 ] rewriting at (2)
18.348 * * * * [progress]: [ 4 / 4 ] rewriting at (2 1 1)
18.397 * * * [progress]: generating series expansions
18.397 * * * * [progress]: [ 1 / 4 ] generating series at (2 2 1 1 1 2 1)
18.398 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
18.398 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
18.398 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
18.398 * [taylor]: Taking taylor expansion of 2.0 in n
18.398 * [backup-simplify]: Simplify 2.0 into 2.0
18.398 * [taylor]: Taking taylor expansion of (* n PI) in n
18.398 * [taylor]: Taking taylor expansion of n in n
18.398 * [backup-simplify]: Simplify 0 into 0
18.398 * [backup-simplify]: Simplify 1 into 1
18.398 * [taylor]: Taking taylor expansion of PI in n
18.398 * [backup-simplify]: Simplify PI into PI
18.398 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
18.398 * [taylor]: Taking taylor expansion of 2.0 in n
18.398 * [backup-simplify]: Simplify 2.0 into 2.0
18.398 * [taylor]: Taking taylor expansion of (* n PI) in n
18.398 * [taylor]: Taking taylor expansion of n in n
18.398 * [backup-simplify]: Simplify 0 into 0
18.398 * [backup-simplify]: Simplify 1 into 1
18.398 * [taylor]: Taking taylor expansion of PI in n
18.398 * [backup-simplify]: Simplify PI into PI
18.398 * [backup-simplify]: Simplify (* 0 PI) into 0
18.399 * [backup-simplify]: Simplify (* 2.0 0) into 0
18.399 * [backup-simplify]: Simplify 0 into 0
18.400 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
18.401 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
18.401 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
18.402 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
18.402 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
18.402 * [backup-simplify]: Simplify 0 into 0
18.403 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
18.403 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
18.404 * [backup-simplify]: Simplify 0 into 0
18.404 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
18.405 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
18.405 * [backup-simplify]: Simplify 0 into 0
18.406 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
18.411 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
18.411 * [backup-simplify]: Simplify 0 into 0
18.412 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
18.413 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
18.413 * [backup-simplify]: Simplify 0 into 0
18.414 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
18.415 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
18.415 * [backup-simplify]: Simplify 0 into 0
18.416 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
18.416 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
18.416 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
18.416 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
18.416 * [taylor]: Taking taylor expansion of 2.0 in n
18.416 * [backup-simplify]: Simplify 2.0 into 2.0
18.416 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.416 * [taylor]: Taking taylor expansion of PI in n
18.416 * [backup-simplify]: Simplify PI into PI
18.416 * [taylor]: Taking taylor expansion of n in n
18.416 * [backup-simplify]: Simplify 0 into 0
18.416 * [backup-simplify]: Simplify 1 into 1
18.417 * [backup-simplify]: Simplify (/ PI 1) into PI
18.417 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
18.417 * [taylor]: Taking taylor expansion of 2.0 in n
18.417 * [backup-simplify]: Simplify 2.0 into 2.0
18.417 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.417 * [taylor]: Taking taylor expansion of PI in n
18.417 * [backup-simplify]: Simplify PI into PI
18.417 * [taylor]: Taking taylor expansion of n in n
18.417 * [backup-simplify]: Simplify 0 into 0
18.417 * [backup-simplify]: Simplify 1 into 1
18.417 * [backup-simplify]: Simplify (/ PI 1) into PI
18.417 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
18.418 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
18.418 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
18.419 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
18.419 * [backup-simplify]: Simplify 0 into 0
18.419 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.420 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
18.420 * [backup-simplify]: Simplify 0 into 0
18.420 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.421 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
18.421 * [backup-simplify]: Simplify 0 into 0
18.422 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.422 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
18.422 * [backup-simplify]: Simplify 0 into 0
18.423 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.424 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
18.424 * [backup-simplify]: Simplify 0 into 0
18.425 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.426 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
18.426 * [backup-simplify]: Simplify 0 into 0
18.426 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
18.427 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
18.427 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
18.427 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
18.427 * [taylor]: Taking taylor expansion of -2.0 in n
18.427 * [backup-simplify]: Simplify -2.0 into -2.0
18.427 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.427 * [taylor]: Taking taylor expansion of PI in n
18.427 * [backup-simplify]: Simplify PI into PI
18.427 * [taylor]: Taking taylor expansion of n in n
18.427 * [backup-simplify]: Simplify 0 into 0
18.427 * [backup-simplify]: Simplify 1 into 1
18.427 * [backup-simplify]: Simplify (/ PI 1) into PI
18.427 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
18.427 * [taylor]: Taking taylor expansion of -2.0 in n
18.427 * [backup-simplify]: Simplify -2.0 into -2.0
18.427 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.427 * [taylor]: Taking taylor expansion of PI in n
18.427 * [backup-simplify]: Simplify PI into PI
18.427 * [taylor]: Taking taylor expansion of n in n
18.427 * [backup-simplify]: Simplify 0 into 0
18.427 * [backup-simplify]: Simplify 1 into 1
18.428 * [backup-simplify]: Simplify (/ PI 1) into PI
18.428 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
18.428 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
18.429 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
18.429 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
18.429 * [backup-simplify]: Simplify 0 into 0
18.430 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.430 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
18.430 * [backup-simplify]: Simplify 0 into 0
18.431 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.432 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
18.432 * [backup-simplify]: Simplify 0 into 0
18.432 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.433 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
18.433 * [backup-simplify]: Simplify 0 into 0
18.434 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.435 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
18.435 * [backup-simplify]: Simplify 0 into 0
18.435 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.436 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
18.436 * [backup-simplify]: Simplify 0 into 0
18.437 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
18.437 * * * * [progress]: [ 2 / 4 ] generating series at (2 1 1 1 2 1)
18.437 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
18.437 * [approximate]: Taking taylor expansion of (* 2.0 (* n PI)) in (n) around 0
18.437 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
18.437 * [taylor]: Taking taylor expansion of 2.0 in n
18.437 * [backup-simplify]: Simplify 2.0 into 2.0
18.437 * [taylor]: Taking taylor expansion of (* n PI) in n
18.437 * [taylor]: Taking taylor expansion of n in n
18.437 * [backup-simplify]: Simplify 0 into 0
18.437 * [backup-simplify]: Simplify 1 into 1
18.437 * [taylor]: Taking taylor expansion of PI in n
18.437 * [backup-simplify]: Simplify PI into PI
18.437 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
18.437 * [taylor]: Taking taylor expansion of 2.0 in n
18.437 * [backup-simplify]: Simplify 2.0 into 2.0
18.437 * [taylor]: Taking taylor expansion of (* n PI) in n
18.437 * [taylor]: Taking taylor expansion of n in n
18.437 * [backup-simplify]: Simplify 0 into 0
18.437 * [backup-simplify]: Simplify 1 into 1
18.437 * [taylor]: Taking taylor expansion of PI in n
18.437 * [backup-simplify]: Simplify PI into PI
18.438 * [backup-simplify]: Simplify (* 0 PI) into 0
18.438 * [backup-simplify]: Simplify (* 2.0 0) into 0
18.438 * [backup-simplify]: Simplify 0 into 0
18.439 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
18.440 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
18.440 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
18.441 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
18.442 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
18.442 * [backup-simplify]: Simplify 0 into 0
18.443 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
18.445 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
18.445 * [backup-simplify]: Simplify 0 into 0
18.446 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
18.447 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
18.447 * [backup-simplify]: Simplify 0 into 0
18.449 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
18.450 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))) into 0
18.451 * [backup-simplify]: Simplify 0 into 0
18.452 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
18.454 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))))) into 0
18.454 * [backup-simplify]: Simplify 0 into 0
18.456 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))))) into 0
18.458 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))))))) into 0
18.458 * [backup-simplify]: Simplify 0 into 0
18.459 * [backup-simplify]: Simplify (* (* 2.0 PI) n) into (* 2.0 (* n PI))
18.459 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 n)) into (* 2.0 (/ PI n))
18.459 * [approximate]: Taking taylor expansion of (* 2.0 (/ PI n)) in (n) around 0
18.460 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
18.460 * [taylor]: Taking taylor expansion of 2.0 in n
18.460 * [backup-simplify]: Simplify 2.0 into 2.0
18.460 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.460 * [taylor]: Taking taylor expansion of PI in n
18.460 * [backup-simplify]: Simplify PI into PI
18.460 * [taylor]: Taking taylor expansion of n in n
18.460 * [backup-simplify]: Simplify 0 into 0
18.460 * [backup-simplify]: Simplify 1 into 1
18.460 * [backup-simplify]: Simplify (/ PI 1) into PI
18.460 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
18.460 * [taylor]: Taking taylor expansion of 2.0 in n
18.460 * [backup-simplify]: Simplify 2.0 into 2.0
18.460 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.460 * [taylor]: Taking taylor expansion of PI in n
18.460 * [backup-simplify]: Simplify PI into PI
18.460 * [taylor]: Taking taylor expansion of n in n
18.460 * [backup-simplify]: Simplify 0 into 0
18.460 * [backup-simplify]: Simplify 1 into 1
18.461 * [backup-simplify]: Simplify (/ PI 1) into PI
18.462 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
18.462 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
18.463 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
18.464 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
18.464 * [backup-simplify]: Simplify 0 into 0
18.465 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.467 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
18.467 * [backup-simplify]: Simplify 0 into 0
18.468 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.469 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
18.469 * [backup-simplify]: Simplify 0 into 0
18.470 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.471 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
18.471 * [backup-simplify]: Simplify 0 into 0
18.473 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.474 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
18.474 * [backup-simplify]: Simplify 0 into 0
18.475 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.477 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
18.477 * [backup-simplify]: Simplify 0 into 0
18.478 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (/ 1 n))) into (* 2.0 (* n PI))
18.478 * [backup-simplify]: Simplify (* (* 2.0 PI) (/ 1 (- n))) into (* -2.0 (/ PI n))
18.478 * [approximate]: Taking taylor expansion of (* -2.0 (/ PI n)) in (n) around 0
18.479 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
18.479 * [taylor]: Taking taylor expansion of -2.0 in n
18.479 * [backup-simplify]: Simplify -2.0 into -2.0
18.479 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.479 * [taylor]: Taking taylor expansion of PI in n
18.479 * [backup-simplify]: Simplify PI into PI
18.479 * [taylor]: Taking taylor expansion of n in n
18.479 * [backup-simplify]: Simplify 0 into 0
18.479 * [backup-simplify]: Simplify 1 into 1
18.479 * [backup-simplify]: Simplify (/ PI 1) into PI
18.479 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
18.479 * [taylor]: Taking taylor expansion of -2.0 in n
18.479 * [backup-simplify]: Simplify -2.0 into -2.0
18.479 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.479 * [taylor]: Taking taylor expansion of PI in n
18.479 * [backup-simplify]: Simplify PI into PI
18.479 * [taylor]: Taking taylor expansion of n in n
18.480 * [backup-simplify]: Simplify 0 into 0
18.480 * [backup-simplify]: Simplify 1 into 1
18.480 * [backup-simplify]: Simplify (/ PI 1) into PI
18.481 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
18.481 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
18.482 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
18.483 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
18.483 * [backup-simplify]: Simplify 0 into 0
18.484 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.485 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
18.485 * [backup-simplify]: Simplify 0 into 0
18.486 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.487 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
18.487 * [backup-simplify]: Simplify 0 into 0
18.488 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.490 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
18.490 * [backup-simplify]: Simplify 0 into 0
18.491 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.492 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))))) into 0
18.492 * [backup-simplify]: Simplify 0 into 0
18.494 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.495 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))))) into 0
18.495 * [backup-simplify]: Simplify 0 into 0
18.496 * [backup-simplify]: Simplify (* (* -2.0 PI) (/ 1 (/ 1 (- n)))) into (* 2.0 (* n PI))
18.496 * * * * [progress]: [ 3 / 4 ] generating series at (2)
18.498 * [backup-simplify]: Simplify (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))) into (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k)))
18.498 * [approximate]: Taking taylor expansion of (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k))) in (n k) around 0
18.498 * [taylor]: Taking taylor expansion of (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k))) in k
18.498 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in k
18.498 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
18.498 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
18.498 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
18.498 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
18.498 * [taylor]: Taking taylor expansion of 0.5 in k
18.498 * [backup-simplify]: Simplify 0.5 into 0.5
18.498 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
18.498 * [taylor]: Taking taylor expansion of 1.0 in k
18.498 * [backup-simplify]: Simplify 1.0 into 1.0
18.498 * [taylor]: Taking taylor expansion of k in k
18.498 * [backup-simplify]: Simplify 0 into 0
18.498 * [backup-simplify]: Simplify 1 into 1
18.498 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
18.498 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
18.498 * [taylor]: Taking taylor expansion of 2.0 in k
18.498 * [backup-simplify]: Simplify 2.0 into 2.0
18.498 * [taylor]: Taking taylor expansion of (* n PI) in k
18.498 * [taylor]: Taking taylor expansion of n in k
18.498 * [backup-simplify]: Simplify n into n
18.498 * [taylor]: Taking taylor expansion of PI in k
18.498 * [backup-simplify]: Simplify PI into PI
18.498 * [backup-simplify]: Simplify (* n PI) into (* n PI)
18.499 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
18.499 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
18.499 * [backup-simplify]: Simplify (- 0) into 0
18.499 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
18.500 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
18.500 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
18.500 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
18.500 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
18.500 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
18.500 * [taylor]: Taking taylor expansion of 1.0 in k
18.500 * [backup-simplify]: Simplify 1.0 into 1.0
18.501 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
18.501 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
18.501 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
18.501 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.501 * [taylor]: Taking taylor expansion of k in k
18.502 * [backup-simplify]: Simplify 0 into 0
18.502 * [backup-simplify]: Simplify 1 into 1
18.502 * [backup-simplify]: Simplify (/ 1 1) into 1
18.502 * [backup-simplify]: Simplify (sqrt 0) into 0
18.504 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
18.504 * [taylor]: Taking taylor expansion of (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k))) in n
18.504 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in n
18.504 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
18.504 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
18.504 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
18.504 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
18.504 * [taylor]: Taking taylor expansion of 0.5 in n
18.504 * [backup-simplify]: Simplify 0.5 into 0.5
18.504 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
18.504 * [taylor]: Taking taylor expansion of 1.0 in n
18.504 * [backup-simplify]: Simplify 1.0 into 1.0
18.504 * [taylor]: Taking taylor expansion of k in n
18.504 * [backup-simplify]: Simplify k into k
18.504 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
18.504 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
18.504 * [taylor]: Taking taylor expansion of 2.0 in n
18.504 * [backup-simplify]: Simplify 2.0 into 2.0
18.504 * [taylor]: Taking taylor expansion of (* n PI) in n
18.504 * [taylor]: Taking taylor expansion of n in n
18.504 * [backup-simplify]: Simplify 0 into 0
18.504 * [backup-simplify]: Simplify 1 into 1
18.504 * [taylor]: Taking taylor expansion of PI in n
18.504 * [backup-simplify]: Simplify PI into PI
18.505 * [backup-simplify]: Simplify (* 0 PI) into 0
18.505 * [backup-simplify]: Simplify (* 2.0 0) into 0
18.507 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
18.508 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
18.510 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
18.510 * [backup-simplify]: Simplify (- k) into (- k)
18.510 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
18.510 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
18.511 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
18.512 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
18.514 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
18.514 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
18.514 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
18.514 * [taylor]: Taking taylor expansion of 1.0 in n
18.514 * [backup-simplify]: Simplify 1.0 into 1.0
18.514 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
18.515 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
18.515 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
18.515 * [taylor]: Taking taylor expansion of (/ 1 k) in n
18.515 * [taylor]: Taking taylor expansion of k in n
18.515 * [backup-simplify]: Simplify k into k
18.515 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
18.515 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
18.515 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
18.515 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
18.515 * [taylor]: Taking taylor expansion of (* (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) (sqrt (/ 1 k))) in n
18.515 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (pow (sqrt 1.0) 2)) in n
18.516 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
18.516 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
18.516 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
18.516 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
18.516 * [taylor]: Taking taylor expansion of 0.5 in n
18.516 * [backup-simplify]: Simplify 0.5 into 0.5
18.516 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
18.516 * [taylor]: Taking taylor expansion of 1.0 in n
18.516 * [backup-simplify]: Simplify 1.0 into 1.0
18.516 * [taylor]: Taking taylor expansion of k in n
18.516 * [backup-simplify]: Simplify k into k
18.516 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
18.516 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
18.516 * [taylor]: Taking taylor expansion of 2.0 in n
18.516 * [backup-simplify]: Simplify 2.0 into 2.0
18.516 * [taylor]: Taking taylor expansion of (* n PI) in n
18.516 * [taylor]: Taking taylor expansion of n in n
18.516 * [backup-simplify]: Simplify 0 into 0
18.516 * [backup-simplify]: Simplify 1 into 1
18.516 * [taylor]: Taking taylor expansion of PI in n
18.516 * [backup-simplify]: Simplify PI into PI
18.517 * [backup-simplify]: Simplify (* 0 PI) into 0
18.517 * [backup-simplify]: Simplify (* 2.0 0) into 0
18.519 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
18.520 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
18.521 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
18.521 * [backup-simplify]: Simplify (- k) into (- k)
18.521 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
18.522 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
18.523 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
18.524 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
18.525 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
18.525 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
18.525 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
18.525 * [taylor]: Taking taylor expansion of 1.0 in n
18.525 * [backup-simplify]: Simplify 1.0 into 1.0
18.526 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
18.526 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
18.527 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
18.527 * [taylor]: Taking taylor expansion of (/ 1 k) in n
18.527 * [taylor]: Taking taylor expansion of k in n
18.527 * [backup-simplify]: Simplify k into k
18.527 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
18.527 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
18.527 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
18.527 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
18.528 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
18.530 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (pow (sqrt 1.0) 2)) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))))
18.533 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) (sqrt (/ 1 k))) into (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) (sqrt (/ 1 k)))
18.533 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) (sqrt (/ 1 k))) in k
18.533 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) in k
18.533 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
18.533 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
18.533 * [taylor]: Taking taylor expansion of 1.0 in k
18.533 * [backup-simplify]: Simplify 1.0 into 1.0
18.533 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
18.534 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
18.534 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
18.534 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
18.534 * [taylor]: Taking taylor expansion of 0.5 in k
18.534 * [backup-simplify]: Simplify 0.5 into 0.5
18.534 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
18.534 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
18.534 * [taylor]: Taking taylor expansion of 1.0 in k
18.534 * [backup-simplify]: Simplify 1.0 into 1.0
18.534 * [taylor]: Taking taylor expansion of k in k
18.534 * [backup-simplify]: Simplify 0 into 0
18.534 * [backup-simplify]: Simplify 1 into 1
18.534 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
18.535 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
18.535 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
18.535 * [taylor]: Taking taylor expansion of 2.0 in k
18.535 * [backup-simplify]: Simplify 2.0 into 2.0
18.535 * [taylor]: Taking taylor expansion of PI in k
18.535 * [backup-simplify]: Simplify PI into PI
18.535 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
18.536 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
18.536 * [taylor]: Taking taylor expansion of (log n) in k
18.536 * [taylor]: Taking taylor expansion of n in k
18.536 * [backup-simplify]: Simplify n into n
18.536 * [backup-simplify]: Simplify (log n) into (log n)
18.537 * [backup-simplify]: Simplify (- 0) into 0
18.537 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
18.538 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
18.539 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
18.546 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
18.548 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
18.548 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
18.548 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.548 * [taylor]: Taking taylor expansion of k in k
18.548 * [backup-simplify]: Simplify 0 into 0
18.548 * [backup-simplify]: Simplify 1 into 1
18.548 * [backup-simplify]: Simplify (/ 1 1) into 1
18.548 * [backup-simplify]: Simplify (sqrt 0) into 0
18.550 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
18.551 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
18.553 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))
18.555 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) 0) into 0
18.555 * [backup-simplify]: Simplify 0 into 0
18.556 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
18.557 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
18.558 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
18.560 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
18.561 * [backup-simplify]: Simplify (- 0) into 0
18.561 * [backup-simplify]: Simplify (+ 0 0) into 0
18.561 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
18.563 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
18.564 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
18.566 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
18.568 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (pow (sqrt 1.0) 2))) into 0
18.570 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
18.571 * [taylor]: Taking taylor expansion of 0 in k
18.571 * [backup-simplify]: Simplify 0 into 0
18.571 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
18.573 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
18.574 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
18.575 * [backup-simplify]: Simplify (+ 0 0) into 0
18.575 * [backup-simplify]: Simplify (- 1) into -1
18.575 * [backup-simplify]: Simplify (+ 0 -1) into -1
18.577 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
18.579 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
18.583 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
18.584 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
18.589 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (+ (* 0.5 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.5 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))
18.597 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) +nan.0) (* (- (+ (* 0.5 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.5 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))) 0)) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))
18.600 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))
18.600 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
18.601 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
18.602 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
18.603 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
18.604 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
18.605 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
18.609 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
18.609 * [backup-simplify]: Simplify (- 0) into 0
18.610 * [backup-simplify]: Simplify (+ 0 0) into 0
18.611 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
18.612 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
18.614 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
18.616 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
18.618 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (pow (sqrt 1.0) 2)))) into 0
18.621 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
18.621 * [taylor]: Taking taylor expansion of 0 in k
18.621 * [backup-simplify]: Simplify 0 into 0
18.621 * [backup-simplify]: Simplify 0 into 0
18.622 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
18.625 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
18.627 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
18.630 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
18.632 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
18.632 * [backup-simplify]: Simplify (+ 0 0) into 0
18.633 * [backup-simplify]: Simplify (- 0) into 0
18.633 * [backup-simplify]: Simplify (+ 0 0) into 0
18.635 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
18.638 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
18.643 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
18.644 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
18.645 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
18.653 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))) (+ (* 0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) into (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.125 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))
18.664 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* (- (+ (* 0.5 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.5 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))) +nan.0) (* (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.125 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))))) 0))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
18.670 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
18.670 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
18.670 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
18.671 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
18.672 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
18.673 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
18.679 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
18.684 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
18.685 * [backup-simplify]: Simplify (- 0) into 0
18.685 * [backup-simplify]: Simplify (+ 0 0) into 0
18.686 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
18.688 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
18.690 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
18.693 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
18.694 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (pow (sqrt 1.0) 2))))) into 0
18.696 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
18.696 * [taylor]: Taking taylor expansion of 0 in k
18.696 * [backup-simplify]: Simplify 0 into 0
18.697 * [backup-simplify]: Simplify 0 into 0
18.697 * [backup-simplify]: Simplify 0 into 0
18.697 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.699 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
18.700 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
18.703 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
18.705 * [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
18.705 * [backup-simplify]: Simplify (+ 0 0) into 0
18.705 * [backup-simplify]: Simplify (- 0) into 0
18.706 * [backup-simplify]: Simplify (+ 0 0) into 0
18.707 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
18.709 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))))) into 0
18.713 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
18.714 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
18.714 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
18.725 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (+ (* 0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))) (+ (* 0 (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.020833333333333332 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 3)))) (+ (* 0.0625 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))) (* 0.020833333333333332 (* (pow (log (* 2.0 PI)) 3) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
18.746 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* (- (+ (* 0.5 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (* 0.5 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))) +nan.0) (+ (* (+ (* 0.25 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.125 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0.125 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))))) +nan.0) (* (- (+ (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (+ (* 0.020833333333333332 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 3)))) (+ (* 0.0625 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))) (* 0.020833333333333332 (* (pow (log (* 2.0 PI)) 3) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) 0)))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))))))))))))))
18.758 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2)))))))))))))))
18.782 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) (* k 1)) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))) into (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k)))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))))))))))))))))))))))
18.783 * [backup-simplify]: Simplify (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) (sqrt (/ 1 k)))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) (sqrt (sqrt (/ 1 k)))) (sqrt (sqrt (/ 1 k)))))) into (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k))
18.783 * [approximate]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in (n k) around 0
18.784 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in k
18.784 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in k
18.784 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
18.784 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
18.784 * [taylor]: Taking taylor expansion of 1.0 in k
18.784 * [backup-simplify]: Simplify 1.0 into 1.0
18.784 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
18.784 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
18.784 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
18.784 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
18.784 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
18.784 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
18.784 * [taylor]: Taking taylor expansion of 0.5 in k
18.784 * [backup-simplify]: Simplify 0.5 into 0.5
18.784 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
18.784 * [taylor]: Taking taylor expansion of 1.0 in k
18.784 * [backup-simplify]: Simplify 1.0 into 1.0
18.784 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.785 * [taylor]: Taking taylor expansion of k in k
18.785 * [backup-simplify]: Simplify 0 into 0
18.785 * [backup-simplify]: Simplify 1 into 1
18.785 * [backup-simplify]: Simplify (/ 1 1) into 1
18.785 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
18.785 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
18.785 * [taylor]: Taking taylor expansion of 2.0 in k
18.785 * [backup-simplify]: Simplify 2.0 into 2.0
18.785 * [taylor]: Taking taylor expansion of (/ PI n) in k
18.785 * [taylor]: Taking taylor expansion of PI in k
18.785 * [backup-simplify]: Simplify PI into PI
18.785 * [taylor]: Taking taylor expansion of n in k
18.785 * [backup-simplify]: Simplify n into n
18.785 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
18.785 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
18.785 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
18.785 * [backup-simplify]: Simplify (- 1) into -1
18.786 * [backup-simplify]: Simplify (+ 0 -1) into -1
18.786 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
18.786 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
18.786 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
18.786 * [taylor]: Taking taylor expansion of (sqrt k) in k
18.786 * [taylor]: Taking taylor expansion of k in k
18.786 * [backup-simplify]: Simplify 0 into 0
18.786 * [backup-simplify]: Simplify 1 into 1
18.786 * [backup-simplify]: Simplify (sqrt 0) into 0
18.788 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
18.788 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in n
18.788 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
18.788 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
18.788 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
18.788 * [taylor]: Taking taylor expansion of 1.0 in n
18.788 * [backup-simplify]: Simplify 1.0 into 1.0
18.788 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
18.788 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
18.788 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
18.788 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
18.788 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
18.788 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
18.788 * [taylor]: Taking taylor expansion of 0.5 in n
18.788 * [backup-simplify]: Simplify 0.5 into 0.5
18.788 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
18.788 * [taylor]: Taking taylor expansion of 1.0 in n
18.788 * [backup-simplify]: Simplify 1.0 into 1.0
18.789 * [taylor]: Taking taylor expansion of (/ 1 k) in n
18.789 * [taylor]: Taking taylor expansion of k in n
18.789 * [backup-simplify]: Simplify k into k
18.789 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
18.789 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
18.789 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
18.789 * [taylor]: Taking taylor expansion of 2.0 in n
18.789 * [backup-simplify]: Simplify 2.0 into 2.0
18.789 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.789 * [taylor]: Taking taylor expansion of PI in n
18.789 * [backup-simplify]: Simplify PI into PI
18.789 * [taylor]: Taking taylor expansion of n in n
18.789 * [backup-simplify]: Simplify 0 into 0
18.789 * [backup-simplify]: Simplify 1 into 1
18.789 * [backup-simplify]: Simplify (/ PI 1) into PI
18.789 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
18.790 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
18.790 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
18.790 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
18.790 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
18.791 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
18.792 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
18.793 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
18.793 * [taylor]: Taking taylor expansion of (sqrt k) in n
18.793 * [taylor]: Taking taylor expansion of k in n
18.793 * [backup-simplify]: Simplify k into k
18.793 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
18.793 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
18.793 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) (sqrt k)) in n
18.793 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k))))) in n
18.793 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
18.793 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
18.793 * [taylor]: Taking taylor expansion of 1.0 in n
18.793 * [backup-simplify]: Simplify 1.0 into 1.0
18.793 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
18.793 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
18.793 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
18.794 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
18.794 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
18.794 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
18.794 * [taylor]: Taking taylor expansion of 0.5 in n
18.794 * [backup-simplify]: Simplify 0.5 into 0.5
18.794 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
18.794 * [taylor]: Taking taylor expansion of 1.0 in n
18.794 * [backup-simplify]: Simplify 1.0 into 1.0
18.794 * [taylor]: Taking taylor expansion of (/ 1 k) in n
18.794 * [taylor]: Taking taylor expansion of k in n
18.794 * [backup-simplify]: Simplify k into k
18.794 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
18.794 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
18.794 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
18.794 * [taylor]: Taking taylor expansion of 2.0 in n
18.794 * [backup-simplify]: Simplify 2.0 into 2.0
18.794 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.794 * [taylor]: Taking taylor expansion of PI in n
18.794 * [backup-simplify]: Simplify PI into PI
18.794 * [taylor]: Taking taylor expansion of n in n
18.794 * [backup-simplify]: Simplify 0 into 0
18.794 * [backup-simplify]: Simplify 1 into 1
18.794 * [backup-simplify]: Simplify (/ PI 1) into PI
18.795 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
18.795 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
18.795 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
18.795 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
18.795 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
18.796 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
18.797 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
18.798 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
18.798 * [taylor]: Taking taylor expansion of (sqrt k) in n
18.798 * [taylor]: Taking taylor expansion of k in n
18.798 * [backup-simplify]: Simplify k into k
18.798 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
18.798 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
18.799 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
18.800 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))
18.801 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) (sqrt k)) into (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) (sqrt k))
18.801 * [taylor]: Taking taylor expansion of (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) (sqrt k)) in k
18.801 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) in k
18.801 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
18.801 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
18.801 * [taylor]: Taking taylor expansion of 1.0 in k
18.801 * [backup-simplify]: Simplify 1.0 into 1.0
18.802 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
18.802 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
18.802 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
18.802 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
18.802 * [taylor]: Taking taylor expansion of 0.5 in k
18.802 * [backup-simplify]: Simplify 0.5 into 0.5
18.802 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
18.802 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
18.802 * [taylor]: Taking taylor expansion of 1.0 in k
18.802 * [backup-simplify]: Simplify 1.0 into 1.0
18.802 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.802 * [taylor]: Taking taylor expansion of k in k
18.802 * [backup-simplify]: Simplify 0 into 0
18.802 * [backup-simplify]: Simplify 1 into 1
18.803 * [backup-simplify]: Simplify (/ 1 1) into 1
18.803 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
18.803 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
18.803 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
18.803 * [taylor]: Taking taylor expansion of 2.0 in k
18.803 * [backup-simplify]: Simplify 2.0 into 2.0
18.803 * [taylor]: Taking taylor expansion of PI in k
18.803 * [backup-simplify]: Simplify PI into PI
18.803 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
18.804 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
18.804 * [taylor]: Taking taylor expansion of (log n) in k
18.804 * [taylor]: Taking taylor expansion of n in k
18.804 * [backup-simplify]: Simplify n into n
18.804 * [backup-simplify]: Simplify (log n) into (log n)
18.804 * [backup-simplify]: Simplify (- 1) into -1
18.804 * [backup-simplify]: Simplify (+ 0 -1) into -1
18.804 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
18.805 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
18.806 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
18.808 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
18.809 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
18.809 * [taylor]: Taking taylor expansion of (sqrt k) in k
18.809 * [taylor]: Taking taylor expansion of k in k
18.809 * [backup-simplify]: Simplify 0 into 0
18.809 * [backup-simplify]: Simplify 1 into 1
18.810 * [backup-simplify]: Simplify (sqrt 0) into 0
18.811 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
18.812 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
18.814 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))
18.817 * [backup-simplify]: Simplify (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 0) into 0
18.817 * [backup-simplify]: Simplify 0 into 0
18.818 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
18.818 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
18.820 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
18.820 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
18.821 * [backup-simplify]: Simplify (- 0) into 0
18.821 * [backup-simplify]: Simplify (+ 0 0) into 0
18.822 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
18.823 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
18.824 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
18.826 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
18.827 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
18.829 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0
18.832 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 0) (* 0 (sqrt k))) into 0
18.832 * [taylor]: Taking taylor expansion of 0 in k
18.832 * [backup-simplify]: Simplify 0 into 0
18.832 * [backup-simplify]: Simplify 0 into 0
18.832 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
18.834 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into 0
18.837 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) +nan.0) (* 0 0)) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
18.840 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
18.840 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
18.842 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.843 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
18.846 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
18.846 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
18.847 * [backup-simplify]: Simplify (- 0) into 0
18.847 * [backup-simplify]: Simplify (+ 0 0) into 0
18.848 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
18.849 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
18.851 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
18.854 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
18.855 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
18.856 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
18.858 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into 0
18.861 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
18.861 * [taylor]: Taking taylor expansion of 0 in k
18.861 * [backup-simplify]: Simplify 0 into 0
18.861 * [backup-simplify]: Simplify 0 into 0
18.861 * [backup-simplify]: Simplify 0 into 0
18.864 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
18.865 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
18.866 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
18.868 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into 0
18.871 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
18.873 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
18.874 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
18.875 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.877 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
18.882 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
18.883 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
18.883 * [backup-simplify]: Simplify (- 0) into 0
18.883 * [backup-simplify]: Simplify (+ 0 0) into 0
18.885 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
18.886 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
18.894 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
18.897 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
18.898 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
18.899 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
18.901 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))) into 0
18.903 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
18.903 * [taylor]: Taking taylor expansion of 0 in k
18.904 * [backup-simplify]: Simplify 0 into 0
18.904 * [backup-simplify]: Simplify 0 into 0
18.904 * [backup-simplify]: Simplify 0 into 0
18.904 * [backup-simplify]: Simplify 0 into 0
18.906 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
18.907 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt 1.0))) into 0
18.908 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt 1.0))))) into 0
18.909 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))) into 0
18.911 * [backup-simplify]: Simplify (+ (* (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
18.913 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))))
18.918 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n))))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n))))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n))))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) k)) (- (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) (pow k 2))))))))
18.919 * [backup-simplify]: Simplify (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) (sqrt (/ 1 (- k))))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) (sqrt (sqrt (/ 1 (- k))))) (sqrt (sqrt (/ 1 (- k))))))) into (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
18.919 * [approximate]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in (n k) around 0
18.919 * [taylor]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in k
18.919 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in k
18.919 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
18.919 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
18.919 * [taylor]: Taking taylor expansion of 1.0 in k
18.919 * [backup-simplify]: Simplify 1.0 into 1.0
18.920 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
18.920 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
18.920 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
18.920 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
18.920 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
18.920 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
18.920 * [taylor]: Taking taylor expansion of 0.5 in k
18.920 * [backup-simplify]: Simplify 0.5 into 0.5
18.920 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
18.920 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.920 * [taylor]: Taking taylor expansion of k in k
18.920 * [backup-simplify]: Simplify 0 into 0
18.920 * [backup-simplify]: Simplify 1 into 1
18.920 * [backup-simplify]: Simplify (/ 1 1) into 1
18.920 * [taylor]: Taking taylor expansion of 1.0 in k
18.921 * [backup-simplify]: Simplify 1.0 into 1.0
18.921 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
18.921 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
18.921 * [taylor]: Taking taylor expansion of -2.0 in k
18.921 * [backup-simplify]: Simplify -2.0 into -2.0
18.921 * [taylor]: Taking taylor expansion of (/ PI n) in k
18.921 * [taylor]: Taking taylor expansion of PI in k
18.921 * [backup-simplify]: Simplify PI into PI
18.921 * [taylor]: Taking taylor expansion of n in k
18.921 * [backup-simplify]: Simplify n into n
18.921 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
18.921 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
18.921 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
18.921 * [backup-simplify]: Simplify (+ 1 0) into 1
18.921 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
18.922 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
18.922 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
18.922 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
18.922 * [taylor]: Taking taylor expansion of (/ -1 k) in k
18.922 * [taylor]: Taking taylor expansion of -1 in k
18.922 * [backup-simplify]: Simplify -1 into -1
18.922 * [taylor]: Taking taylor expansion of k in k
18.922 * [backup-simplify]: Simplify 0 into 0
18.922 * [backup-simplify]: Simplify 1 into 1
18.922 * [backup-simplify]: Simplify (/ -1 1) into -1
18.922 * [backup-simplify]: Simplify (sqrt 0) into 0
18.923 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
18.924 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
18.925 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
18.926 * [backup-simplify]: Simplify (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))) +nan.0) into (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))))
18.926 * [taylor]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in n
18.926 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in n
18.926 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
18.926 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
18.926 * [taylor]: Taking taylor expansion of 1.0 in n
18.926 * [backup-simplify]: Simplify 1.0 into 1.0
18.927 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
18.927 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
18.927 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
18.928 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
18.928 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
18.928 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
18.928 * [taylor]: Taking taylor expansion of 0.5 in n
18.928 * [backup-simplify]: Simplify 0.5 into 0.5
18.928 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
18.928 * [taylor]: Taking taylor expansion of (/ 1 k) in n
18.928 * [taylor]: Taking taylor expansion of k in n
18.928 * [backup-simplify]: Simplify k into k
18.928 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
18.928 * [taylor]: Taking taylor expansion of 1.0 in n
18.928 * [backup-simplify]: Simplify 1.0 into 1.0
18.928 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
18.928 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
18.928 * [taylor]: Taking taylor expansion of -2.0 in n
18.928 * [backup-simplify]: Simplify -2.0 into -2.0
18.928 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.928 * [taylor]: Taking taylor expansion of PI in n
18.928 * [backup-simplify]: Simplify PI into PI
18.928 * [taylor]: Taking taylor expansion of n in n
18.928 * [backup-simplify]: Simplify 0 into 0
18.928 * [backup-simplify]: Simplify 1 into 1
18.928 * [backup-simplify]: Simplify (/ PI 1) into PI
18.929 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
18.929 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
18.930 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
18.930 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
18.931 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
18.931 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
18.932 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
18.932 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
18.932 * [taylor]: Taking taylor expansion of (/ -1 k) in n
18.932 * [taylor]: Taking taylor expansion of -1 in n
18.932 * [backup-simplify]: Simplify -1 into -1
18.932 * [taylor]: Taking taylor expansion of k in n
18.932 * [backup-simplify]: Simplify k into k
18.932 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
18.932 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
18.933 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
18.933 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
18.933 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
18.935 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
18.936 * [backup-simplify]: Simplify (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) into (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k)))
18.936 * [taylor]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in n
18.936 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0)))) in n
18.936 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in n
18.936 * [taylor]: Taking taylor expansion of (sqrt 1.0) in n
18.936 * [taylor]: Taking taylor expansion of 1.0 in n
18.936 * [backup-simplify]: Simplify 1.0 into 1.0
18.936 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
18.937 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
18.937 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
18.937 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
18.937 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
18.937 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
18.937 * [taylor]: Taking taylor expansion of 0.5 in n
18.937 * [backup-simplify]: Simplify 0.5 into 0.5
18.937 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
18.937 * [taylor]: Taking taylor expansion of (/ 1 k) in n
18.937 * [taylor]: Taking taylor expansion of k in n
18.937 * [backup-simplify]: Simplify k into k
18.937 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
18.937 * [taylor]: Taking taylor expansion of 1.0 in n
18.937 * [backup-simplify]: Simplify 1.0 into 1.0
18.937 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
18.937 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
18.937 * [taylor]: Taking taylor expansion of -2.0 in n
18.937 * [backup-simplify]: Simplify -2.0 into -2.0
18.937 * [taylor]: Taking taylor expansion of (/ PI n) in n
18.937 * [taylor]: Taking taylor expansion of PI in n
18.937 * [backup-simplify]: Simplify PI into PI
18.937 * [taylor]: Taking taylor expansion of n in n
18.937 * [backup-simplify]: Simplify 0 into 0
18.937 * [backup-simplify]: Simplify 1 into 1
18.938 * [backup-simplify]: Simplify (/ PI 1) into PI
18.938 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
18.939 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
18.939 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
18.939 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
18.940 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
18.940 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
18.941 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
18.941 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
18.941 * [taylor]: Taking taylor expansion of (/ -1 k) in n
18.941 * [taylor]: Taking taylor expansion of -1 in n
18.941 * [backup-simplify]: Simplify -1 into -1
18.941 * [taylor]: Taking taylor expansion of k in n
18.941 * [backup-simplify]: Simplify k into k
18.941 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
18.941 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
18.941 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
18.941 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
18.942 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
18.943 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
18.945 * [backup-simplify]: Simplify (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) into (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k)))
18.945 * [taylor]: Taking taylor expansion of (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) in k
18.945 * [taylor]: Taking taylor expansion of (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) in k
18.945 * [taylor]: Taking taylor expansion of (pow (sqrt 1.0) 2) in k
18.945 * [taylor]: Taking taylor expansion of (sqrt 1.0) in k
18.945 * [taylor]: Taking taylor expansion of 1.0 in k
18.945 * [backup-simplify]: Simplify 1.0 into 1.0
18.945 * [backup-simplify]: Simplify (sqrt 1.0) into (sqrt 1.0)
18.946 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt 1.0))) into 0
18.946 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
18.946 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
18.946 * [taylor]: Taking taylor expansion of 0.5 in k
18.946 * [backup-simplify]: Simplify 0.5 into 0.5
18.946 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
18.946 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
18.946 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
18.946 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
18.946 * [taylor]: Taking taylor expansion of -2.0 in k
18.946 * [backup-simplify]: Simplify -2.0 into -2.0
18.946 * [taylor]: Taking taylor expansion of PI in k
18.946 * [backup-simplify]: Simplify PI into PI
18.946 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
18.947 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
18.947 * [taylor]: Taking taylor expansion of (log n) in k
18.947 * [taylor]: Taking taylor expansion of n in k
18.947 * [backup-simplify]: Simplify n into n
18.947 * [backup-simplify]: Simplify (log n) into (log n)
18.947 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
18.947 * [taylor]: Taking taylor expansion of (/ 1 k) in k
18.947 * [taylor]: Taking taylor expansion of k in k
18.947 * [backup-simplify]: Simplify 0 into 0
18.947 * [backup-simplify]: Simplify 1 into 1
18.947 * [backup-simplify]: Simplify (/ 1 1) into 1
18.947 * [taylor]: Taking taylor expansion of 1.0 in k
18.947 * [backup-simplify]: Simplify 1.0 into 1.0
18.947 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
18.948 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
18.948 * [backup-simplify]: Simplify (+ 1 0) into 1
18.949 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
18.950 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
18.951 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
18.951 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
18.951 * [taylor]: Taking taylor expansion of (/ -1 k) in k
18.951 * [taylor]: Taking taylor expansion of -1 in k
18.951 * [backup-simplify]: Simplify -1 into -1
18.951 * [taylor]: Taking taylor expansion of k in k
18.951 * [backup-simplify]: Simplify 0 into 0
18.951 * [backup-simplify]: Simplify 1 into 1
18.951 * [backup-simplify]: Simplify (/ -1 1) into -1
18.951 * [backup-simplify]: Simplify (sqrt 0) into 0
18.952 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
18.953 * [backup-simplify]: Simplify (* (sqrt 1.0) (sqrt 1.0)) into (pow (sqrt 1.0) 2)
18.954 * [backup-simplify]: Simplify (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
18.956 * [backup-simplify]: Simplify (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) +nan.0) into (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
18.957 * [backup-simplify]: Simplify (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
18.958 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
18.958 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
18.959 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
18.959 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
18.959 * [backup-simplify]: Simplify (+ 0 0) into 0
18.960 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
18.961 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
18.961 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
18.962 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
18.963 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
18.964 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0
18.966 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
18.966 * [taylor]: Taking taylor expansion of 0 in k
18.966 * [backup-simplify]: Simplify 0 into 0
18.966 * [backup-simplify]: Simplify 0 into 0
18.966 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (* 0 (sqrt 1.0))) into 0
18.967 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into 0
18.968 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
18.970 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
18.974 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))
18.976 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))
18.977 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
18.978 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
18.982 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
18.982 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
18.982 * [backup-simplify]: Simplify (+ 0 0) into 0
18.983 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
18.985 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
18.986 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
18.989 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
18.990 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
18.991 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
18.994 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into 0
18.994 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
18.995 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
19.003 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
19.003 * [taylor]: Taking taylor expansion of 0 in k
19.003 * [backup-simplify]: Simplify 0 into 0
19.003 * [backup-simplify]: Simplify 0 into 0
19.003 * [backup-simplify]: Simplify 0 into 0
19.005 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt 1.0))) into 0
19.006 * [backup-simplify]: Simplify (+ (* (sqrt 1.0) 0) (+ (* 0 0) (* 0 (sqrt 1.0)))) into 0
19.008 * [backup-simplify]: Simplify (+ (* (pow (sqrt 1.0) 2) 0) (+ (* 0 0) (* 0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into 0
19.009 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.014 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
19.020 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))
19.022 * [backup-simplify]: Simplify (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))
19.030 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) (* (/ 1 (- k)) 1)) (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))))) into (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2)) k)) (- (+ (* +nan.0 (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2))) (- (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2)) (pow k 2))))))))
19.031 * * * * [progress]: [ 4 / 4 ] generating series at (2 1 1)
19.031 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) into (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))))
19.031 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in (n k) around 0
19.031 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in k
19.031 * [taylor]: Taking taylor expansion of 1.0 in k
19.032 * [backup-simplify]: Simplify 1.0 into 1.0
19.032 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in k
19.032 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in k
19.032 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in k
19.032 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in k
19.032 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in k
19.032 * [taylor]: Taking taylor expansion of 0.5 in k
19.032 * [backup-simplify]: Simplify 0.5 into 0.5
19.032 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
19.032 * [taylor]: Taking taylor expansion of 1.0 in k
19.032 * [backup-simplify]: Simplify 1.0 into 1.0
19.032 * [taylor]: Taking taylor expansion of k in k
19.032 * [backup-simplify]: Simplify 0 into 0
19.032 * [backup-simplify]: Simplify 1 into 1
19.032 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in k
19.032 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in k
19.032 * [taylor]: Taking taylor expansion of 2.0 in k
19.032 * [backup-simplify]: Simplify 2.0 into 2.0
19.032 * [taylor]: Taking taylor expansion of (* n PI) in k
19.032 * [taylor]: Taking taylor expansion of n in k
19.032 * [backup-simplify]: Simplify n into n
19.032 * [taylor]: Taking taylor expansion of PI in k
19.032 * [backup-simplify]: Simplify PI into PI
19.032 * [backup-simplify]: Simplify (* n PI) into (* n PI)
19.032 * [backup-simplify]: Simplify (* 2.0 (* n PI)) into (* 2.0 (* n PI))
19.032 * [backup-simplify]: Simplify (log (* 2.0 (* n PI))) into (log (* 2.0 (* n PI)))
19.033 * [backup-simplify]: Simplify (- 0) into 0
19.033 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
19.034 * [backup-simplify]: Simplify (* 0.5 1.0) into 0.5
19.034 * [backup-simplify]: Simplify (* 0.5 (log (* 2.0 (* n PI)))) into (* 0.5 (log (* 2.0 (* n PI))))
19.034 * [backup-simplify]: Simplify (exp (* 0.5 (log (* 2.0 (* n PI))))) into (pow (* 2.0 (* n PI)) 0.5)
19.034 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
19.034 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.034 * [taylor]: Taking taylor expansion of k in k
19.034 * [backup-simplify]: Simplify 0 into 0
19.034 * [backup-simplify]: Simplify 1 into 1
19.035 * [backup-simplify]: Simplify (/ 1 1) into 1
19.035 * [backup-simplify]: Simplify (sqrt 0) into 0
19.036 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
19.036 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
19.036 * [taylor]: Taking taylor expansion of 1.0 in n
19.036 * [backup-simplify]: Simplify 1.0 into 1.0
19.036 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
19.036 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
19.036 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
19.037 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
19.037 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
19.037 * [taylor]: Taking taylor expansion of 0.5 in n
19.037 * [backup-simplify]: Simplify 0.5 into 0.5
19.037 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
19.037 * [taylor]: Taking taylor expansion of 1.0 in n
19.037 * [backup-simplify]: Simplify 1.0 into 1.0
19.037 * [taylor]: Taking taylor expansion of k in n
19.037 * [backup-simplify]: Simplify k into k
19.037 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
19.037 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
19.037 * [taylor]: Taking taylor expansion of 2.0 in n
19.037 * [backup-simplify]: Simplify 2.0 into 2.0
19.037 * [taylor]: Taking taylor expansion of (* n PI) in n
19.037 * [taylor]: Taking taylor expansion of n in n
19.037 * [backup-simplify]: Simplify 0 into 0
19.037 * [backup-simplify]: Simplify 1 into 1
19.037 * [taylor]: Taking taylor expansion of PI in n
19.037 * [backup-simplify]: Simplify PI into PI
19.038 * [backup-simplify]: Simplify (* 0 PI) into 0
19.038 * [backup-simplify]: Simplify (* 2.0 0) into 0
19.040 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.041 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
19.042 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.042 * [backup-simplify]: Simplify (- k) into (- k)
19.042 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
19.043 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
19.044 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
19.045 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
19.046 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
19.046 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
19.046 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.046 * [taylor]: Taking taylor expansion of k in n
19.046 * [backup-simplify]: Simplify k into k
19.046 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.047 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
19.047 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
19.047 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
19.047 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k)))) in n
19.047 * [taylor]: Taking taylor expansion of 1.0 in n
19.047 * [backup-simplify]: Simplify 1.0 into 1.0
19.047 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) (sqrt (/ 1 k))) in n
19.047 * [taylor]: Taking taylor expansion of (pow (* 2.0 (* n PI)) (* 0.5 (- 1.0 k))) in n
19.047 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI))))) in n
19.047 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 k)) (log (* 2.0 (* n PI)))) in n
19.047 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 k)) in n
19.047 * [taylor]: Taking taylor expansion of 0.5 in n
19.047 * [backup-simplify]: Simplify 0.5 into 0.5
19.047 * [taylor]: Taking taylor expansion of (- 1.0 k) in n
19.047 * [taylor]: Taking taylor expansion of 1.0 in n
19.047 * [backup-simplify]: Simplify 1.0 into 1.0
19.047 * [taylor]: Taking taylor expansion of k in n
19.047 * [backup-simplify]: Simplify k into k
19.047 * [taylor]: Taking taylor expansion of (log (* 2.0 (* n PI))) in n
19.047 * [taylor]: Taking taylor expansion of (* 2.0 (* n PI)) in n
19.047 * [taylor]: Taking taylor expansion of 2.0 in n
19.047 * [backup-simplify]: Simplify 2.0 into 2.0
19.047 * [taylor]: Taking taylor expansion of (* n PI) in n
19.047 * [taylor]: Taking taylor expansion of n in n
19.047 * [backup-simplify]: Simplify 0 into 0
19.047 * [backup-simplify]: Simplify 1 into 1
19.047 * [taylor]: Taking taylor expansion of PI in n
19.047 * [backup-simplify]: Simplify PI into PI
19.048 * [backup-simplify]: Simplify (* 0 PI) into 0
19.048 * [backup-simplify]: Simplify (* 2.0 0) into 0
19.050 * [backup-simplify]: Simplify (+ (* 0 0) (* 1 PI)) into PI
19.052 * [backup-simplify]: Simplify (+ (* 2.0 PI) (* 0 0)) into (* 2.0 PI)
19.053 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.053 * [backup-simplify]: Simplify (- k) into (- k)
19.053 * [backup-simplify]: Simplify (+ 1.0 (- k)) into (- 1.0 k)
19.053 * [backup-simplify]: Simplify (* 0.5 (- 1.0 k)) into (* 0.5 (- 1.0 k))
19.054 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
19.055 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 k)) (+ (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))
19.056 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))))
19.057 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in n
19.057 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.057 * [taylor]: Taking taylor expansion of k in n
19.057 * [backup-simplify]: Simplify k into k
19.057 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.057 * [backup-simplify]: Simplify (sqrt (/ 1 k)) into (sqrt (/ 1 k))
19.057 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
19.057 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ 1 k)))) into 0
19.058 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) into (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))
19.060 * [backup-simplify]: Simplify (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) into (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))
19.060 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))) in k
19.060 * [taylor]: Taking taylor expansion of 1.0 in k
19.060 * [backup-simplify]: Simplify 1.0 into 1.0
19.060 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))) in k
19.060 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) in k
19.060 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n)))) in k
19.060 * [taylor]: Taking taylor expansion of 0.5 in k
19.060 * [backup-simplify]: Simplify 0.5 into 0.5
19.060 * [taylor]: Taking taylor expansion of (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))) in k
19.061 * [taylor]: Taking taylor expansion of (- 1.0 k) in k
19.061 * [taylor]: Taking taylor expansion of 1.0 in k
19.061 * [backup-simplify]: Simplify 1.0 into 1.0
19.061 * [taylor]: Taking taylor expansion of k in k
19.061 * [backup-simplify]: Simplify 0 into 0
19.061 * [backup-simplify]: Simplify 1 into 1
19.061 * [taylor]: Taking taylor expansion of (+ (log (* 2.0 PI)) (log n)) in k
19.061 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
19.061 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
19.061 * [taylor]: Taking taylor expansion of 2.0 in k
19.061 * [backup-simplify]: Simplify 2.0 into 2.0
19.061 * [taylor]: Taking taylor expansion of PI in k
19.061 * [backup-simplify]: Simplify PI into PI
19.061 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
19.063 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.063 * [taylor]: Taking taylor expansion of (log n) in k
19.063 * [taylor]: Taking taylor expansion of n in k
19.063 * [backup-simplify]: Simplify n into n
19.063 * [backup-simplify]: Simplify (log n) into (log n)
19.063 * [backup-simplify]: Simplify (- 0) into 0
19.064 * [backup-simplify]: Simplify (+ 1.0 0) into 1.0
19.065 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (log n)) into (+ (log (* 2.0 PI)) (log n))
19.066 * [backup-simplify]: Simplify (* 1.0 (+ (log (* 2.0 PI)) (log n))) into (* 1.0 (+ (log (* 2.0 PI)) (log n)))
19.068 * [backup-simplify]: Simplify (* 0.5 (* 1.0 (+ (log (* 2.0 PI)) (log n)))) into (* 0.5 (+ (log (* 2.0 PI)) (log n)))
19.069 * [backup-simplify]: Simplify (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) into (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))
19.069 * [taylor]: Taking taylor expansion of (sqrt (/ 1 k)) in k
19.069 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.069 * [taylor]: Taking taylor expansion of k in k
19.069 * [backup-simplify]: Simplify 0 into 0
19.069 * [backup-simplify]: Simplify 1 into 1
19.070 * [backup-simplify]: Simplify (/ 1 1) into 1
19.070 * [backup-simplify]: Simplify (sqrt 0) into 0
19.072 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
19.073 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) 0) into 0
19.074 * [backup-simplify]: Simplify (* 1.0 0) into 0
19.074 * [backup-simplify]: Simplify 0 into 0
19.075 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (* 0 PI))) into 0
19.076 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 PI) (* 0 0))) into 0
19.078 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
19.079 * [backup-simplify]: Simplify (- 0) into 0
19.079 * [backup-simplify]: Simplify (+ 0 0) into 0
19.080 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 k))) into 0
19.081 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
19.082 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (* 0 (+ (log (* 2.0 PI)) (log n)))) into 0
19.085 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
19.086 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt (/ 1 k)))) into 0
19.088 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))) into 0
19.088 * [taylor]: Taking taylor expansion of 0 in k
19.088 * [backup-simplify]: Simplify 0 into 0
19.089 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
19.092 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
19.093 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow n 1)))) 1) into 0
19.094 * [backup-simplify]: Simplify (+ 0 0) into 0
19.094 * [backup-simplify]: Simplify (- 1) into -1
19.095 * [backup-simplify]: Simplify (+ 0 -1) into -1
19.096 * [backup-simplify]: Simplify (+ (* 1.0 0) (* -1 (+ (log (* 2.0 PI)) (log n)))) into (- (+ (log (* 2.0 PI)) (log n)))
19.099 * [backup-simplify]: Simplify (+ (* 0.5 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))) into (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))))
19.103 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1)))) into (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
19.107 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
19.109 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
19.110 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) into (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
19.111 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.111 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ 1 k)))) into 0
19.113 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (* 0 PI)))) into 0
19.113 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0)))) into 0
19.115 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
19.115 * [backup-simplify]: Simplify (- 0) into 0
19.116 * [backup-simplify]: Simplify (+ 0 0) into 0
19.116 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 k)))) into 0
19.117 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
19.118 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
19.119 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
19.120 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k))))) into 0
19.122 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k)))))) into 0
19.122 * [taylor]: Taking taylor expansion of 0 in k
19.122 * [backup-simplify]: Simplify 0 into 0
19.122 * [backup-simplify]: Simplify 0 into 0
19.122 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)))) into 0
19.124 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
19.125 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
19.127 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
19.128 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow n 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow n 1)))) 2) into 0
19.128 * [backup-simplify]: Simplify (+ 0 0) into 0
19.128 * [backup-simplify]: Simplify (- 0) into 0
19.129 * [backup-simplify]: Simplify (+ 0 0) into 0
19.130 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (* 0 (+ (log (* 2.0 PI)) (log n))))) into 0
19.131 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n)))))) into 0
19.134 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 2) 2)) (* (/ (pow 0 1) 1)))) into (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n))))))
19.144 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) +nan.0) (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) 0))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
19.151 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
19.156 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))
19.156 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.157 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt (/ 1 k)))) into 0
19.159 * [backup-simplify]: Simplify (+ (* 0 0) (+ (* 1 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI))))) into 0
19.160 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (+ (* 0 PI) (* 0 0))))) into 0
19.167 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
19.167 * [backup-simplify]: Simplify (- 0) into 0
19.168 * [backup-simplify]: Simplify (+ 0 0) into 0
19.169 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 k))))) into 0
19.170 * [backup-simplify]: Simplify (+ (* (- -1) (log n)) (log (* 2.0 PI))) into (+ (log (* 2.0 PI)) (log n))
19.172 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 k)) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
19.175 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
19.177 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt (/ 1 k)))))) into 0
19.180 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 k) (+ (log (* 2.0 PI)) (log n))))) (sqrt (/ 1 k))))))) into 0
19.180 * [taylor]: Taking taylor expansion of 0 in k
19.180 * [backup-simplify]: Simplify 0 into 0
19.180 * [backup-simplify]: Simplify 0 into 0
19.180 * [backup-simplify]: Simplify 0 into 0
19.181 * [backup-simplify]: Simplify (- (+ (* 1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.185 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
19.187 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
19.193 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
19.196 * [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
19.196 * [backup-simplify]: Simplify (+ 0 0) into 0
19.197 * [backup-simplify]: Simplify (- 0) into 0
19.197 * [backup-simplify]: Simplify (+ 0 0) into 0
19.199 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* -1 0) (+ (* 0 0) (* 0 (+ (log (* 2.0 PI)) (log n)))))) into 0
19.202 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 (- (+ (log (* 2.0 PI)) (log n)))) (* 0 (* 1.0 (+ (log (* 2.0 PI)) (log n))))))) into 0
19.210 * [backup-simplify]: Simplify (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 3) 6)) (* (/ (pow (- (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n)))) 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))
19.230 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) +nan.0) (+ (* (* -1 (* (+ (* 0.5 (log (* 2.0 PI))) (* 0.5 (log n))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) +nan.0) (+ (* (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (+ (* 0.125 (pow (log n) 2)) (+ (* 0.125 (pow (log (* 2.0 PI)) 2)) (* 0.25 (* (log (* 2.0 PI)) (log n)))))) +nan.0) (* (* -1 (* (+ (* 0.0625 (* (log (* 2.0 PI)) (pow (log n) 2))) (+ (* 0.020833333333333332 (pow (log (* 2.0 PI)) 3)) (+ (* 0.020833333333333332 (pow (log n) 3)) (* 0.0625 (* (pow (log (* 2.0 PI)) 2) (log n)))))) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) 0)))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
19.251 * [backup-simplify]: Simplify (+ (* 1.0 (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))) (+ (* 0 (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))) (* 0 0)))) into (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
19.265 * [backup-simplify]: Simplify (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))))))))))))
19.296 * [backup-simplify]: Simplify (+ (* (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow (log n) 2))) (- (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))))))))) (pow (* k 1) 2)) (+ (* (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (log n))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (* +nan.0 (* (log (* 2.0 PI)) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))))))))) (* k 1)) (- (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))))) into (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))))))))))))))))))
19.297 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 n)) (/ (- 1.0 (/ 1 k)) 2.0))) (sqrt (/ 1 k))) into (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)))
19.297 * [approximate]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in (n k) around 0
19.298 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in k
19.298 * [taylor]: Taking taylor expansion of 1.0 in k
19.298 * [backup-simplify]: Simplify 1.0 into 1.0
19.298 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in k
19.298 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in k
19.298 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in k
19.298 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in k
19.298 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in k
19.298 * [taylor]: Taking taylor expansion of 0.5 in k
19.298 * [backup-simplify]: Simplify 0.5 into 0.5
19.298 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
19.298 * [taylor]: Taking taylor expansion of 1.0 in k
19.298 * [backup-simplify]: Simplify 1.0 into 1.0
19.298 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.298 * [taylor]: Taking taylor expansion of k in k
19.298 * [backup-simplify]: Simplify 0 into 0
19.298 * [backup-simplify]: Simplify 1 into 1
19.298 * [backup-simplify]: Simplify (/ 1 1) into 1
19.298 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in k
19.298 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in k
19.298 * [taylor]: Taking taylor expansion of 2.0 in k
19.299 * [backup-simplify]: Simplify 2.0 into 2.0
19.299 * [taylor]: Taking taylor expansion of (/ PI n) in k
19.299 * [taylor]: Taking taylor expansion of PI in k
19.299 * [backup-simplify]: Simplify PI into PI
19.299 * [taylor]: Taking taylor expansion of n in k
19.299 * [backup-simplify]: Simplify n into n
19.299 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
19.299 * [backup-simplify]: Simplify (* 2.0 (/ PI n)) into (* 2.0 (/ PI n))
19.299 * [backup-simplify]: Simplify (log (* 2.0 (/ PI n))) into (log (* 2.0 (/ PI n)))
19.299 * [backup-simplify]: Simplify (- 1) into -1
19.300 * [backup-simplify]: Simplify (+ 0 -1) into -1
19.300 * [backup-simplify]: Simplify (* 0.5 -1) into -0.5
19.300 * [backup-simplify]: Simplify (* -0.5 (log (* 2.0 (/ PI n)))) into (* -0.5 (log (* 2.0 (/ PI n))))
19.301 * [backup-simplify]: Simplify (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (log (* 2.0 (/ PI n))))))
19.301 * [taylor]: Taking taylor expansion of (sqrt k) in k
19.301 * [taylor]: Taking taylor expansion of k in k
19.301 * [backup-simplify]: Simplify 0 into 0
19.301 * [backup-simplify]: Simplify 1 into 1
19.301 * [backup-simplify]: Simplify (sqrt 0) into 0
19.303 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
19.303 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
19.303 * [taylor]: Taking taylor expansion of 1.0 in n
19.303 * [backup-simplify]: Simplify 1.0 into 1.0
19.303 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
19.303 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
19.303 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
19.303 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
19.303 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
19.303 * [taylor]: Taking taylor expansion of 0.5 in n
19.303 * [backup-simplify]: Simplify 0.5 into 0.5
19.303 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
19.303 * [taylor]: Taking taylor expansion of 1.0 in n
19.303 * [backup-simplify]: Simplify 1.0 into 1.0
19.303 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.303 * [taylor]: Taking taylor expansion of k in n
19.303 * [backup-simplify]: Simplify k into k
19.303 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.303 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
19.303 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
19.303 * [taylor]: Taking taylor expansion of 2.0 in n
19.303 * [backup-simplify]: Simplify 2.0 into 2.0
19.303 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.303 * [taylor]: Taking taylor expansion of PI in n
19.303 * [backup-simplify]: Simplify PI into PI
19.303 * [taylor]: Taking taylor expansion of n in n
19.303 * [backup-simplify]: Simplify 0 into 0
19.303 * [backup-simplify]: Simplify 1 into 1
19.304 * [backup-simplify]: Simplify (/ PI 1) into PI
19.304 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
19.305 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.306 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
19.306 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
19.306 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
19.307 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
19.308 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
19.310 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
19.310 * [taylor]: Taking taylor expansion of (sqrt k) in n
19.310 * [taylor]: Taking taylor expansion of k in n
19.310 * [backup-simplify]: Simplify k into k
19.310 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
19.310 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
19.310 * [taylor]: Taking taylor expansion of (* 1.0 (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k))) in n
19.310 * [taylor]: Taking taylor expansion of 1.0 in n
19.310 * [backup-simplify]: Simplify 1.0 into 1.0
19.310 * [taylor]: Taking taylor expansion of (* (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) (sqrt k)) in n
19.310 * [taylor]: Taking taylor expansion of (pow (* 2.0 (/ PI n)) (* 0.5 (- 1.0 (/ 1 k)))) in n
19.310 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n))))) in n
19.310 * [taylor]: Taking taylor expansion of (* (* 0.5 (- 1.0 (/ 1 k))) (log (* 2.0 (/ PI n)))) in n
19.310 * [taylor]: Taking taylor expansion of (* 0.5 (- 1.0 (/ 1 k))) in n
19.310 * [taylor]: Taking taylor expansion of 0.5 in n
19.310 * [backup-simplify]: Simplify 0.5 into 0.5
19.310 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in n
19.310 * [taylor]: Taking taylor expansion of 1.0 in n
19.310 * [backup-simplify]: Simplify 1.0 into 1.0
19.310 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.310 * [taylor]: Taking taylor expansion of k in n
19.311 * [backup-simplify]: Simplify k into k
19.311 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.311 * [taylor]: Taking taylor expansion of (log (* 2.0 (/ PI n))) in n
19.311 * [taylor]: Taking taylor expansion of (* 2.0 (/ PI n)) in n
19.311 * [taylor]: Taking taylor expansion of 2.0 in n
19.311 * [backup-simplify]: Simplify 2.0 into 2.0
19.311 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.311 * [taylor]: Taking taylor expansion of PI in n
19.311 * [backup-simplify]: Simplify PI into PI
19.311 * [taylor]: Taking taylor expansion of n in n
19.311 * [backup-simplify]: Simplify 0 into 0
19.311 * [backup-simplify]: Simplify 1 into 1
19.311 * [backup-simplify]: Simplify (/ PI 1) into PI
19.312 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
19.313 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.313 * [backup-simplify]: Simplify (- (/ 1 k)) into (- (/ 1 k))
19.313 * [backup-simplify]: Simplify (+ 1.0 (- (/ 1 k))) into (- 1.0 (/ 1 k))
19.313 * [backup-simplify]: Simplify (* 0.5 (- 1.0 (/ 1 k))) into (* 0.5 (- 1.0 (/ 1 k)))
19.315 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
19.316 * [backup-simplify]: Simplify (* (* 0.5 (- 1.0 (/ 1 k))) (- (log (* 2.0 PI)) (log n))) into (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))
19.317 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
19.317 * [taylor]: Taking taylor expansion of (sqrt k) in n
19.317 * [taylor]: Taking taylor expansion of k in n
19.317 * [backup-simplify]: Simplify k into k
19.318 * [backup-simplify]: Simplify (sqrt k) into (sqrt k)
19.318 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt k))) into 0
19.319 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) into (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))
19.321 * [backup-simplify]: Simplify (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) into (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))
19.321 * [taylor]: Taking taylor expansion of (* 1.0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))) in k
19.321 * [taylor]: Taking taylor expansion of 1.0 in k
19.321 * [backup-simplify]: Simplify 1.0 into 1.0
19.321 * [taylor]: Taking taylor expansion of (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)) in k
19.321 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) in k
19.321 * [taylor]: Taking taylor expansion of (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))) in k
19.321 * [taylor]: Taking taylor expansion of 0.5 in k
19.321 * [backup-simplify]: Simplify 0.5 into 0.5
19.321 * [taylor]: Taking taylor expansion of (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))) in k
19.321 * [taylor]: Taking taylor expansion of (- 1.0 (/ 1 k)) in k
19.321 * [taylor]: Taking taylor expansion of 1.0 in k
19.321 * [backup-simplify]: Simplify 1.0 into 1.0
19.321 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.321 * [taylor]: Taking taylor expansion of k in k
19.321 * [backup-simplify]: Simplify 0 into 0
19.321 * [backup-simplify]: Simplify 1 into 1
19.322 * [backup-simplify]: Simplify (/ 1 1) into 1
19.322 * [taylor]: Taking taylor expansion of (- (log (* 2.0 PI)) (log n)) in k
19.322 * [taylor]: Taking taylor expansion of (log (* 2.0 PI)) in k
19.322 * [taylor]: Taking taylor expansion of (* 2.0 PI) in k
19.322 * [taylor]: Taking taylor expansion of 2.0 in k
19.322 * [backup-simplify]: Simplify 2.0 into 2.0
19.322 * [taylor]: Taking taylor expansion of PI in k
19.322 * [backup-simplify]: Simplify PI into PI
19.322 * [backup-simplify]: Simplify (* 2.0 PI) into (* 2.0 PI)
19.323 * [backup-simplify]: Simplify (log (* 2.0 PI)) into (log (* 2.0 PI))
19.323 * [taylor]: Taking taylor expansion of (log n) in k
19.323 * [taylor]: Taking taylor expansion of n in k
19.323 * [backup-simplify]: Simplify n into n
19.323 * [backup-simplify]: Simplify (log n) into (log n)
19.324 * [backup-simplify]: Simplify (- 1) into -1
19.324 * [backup-simplify]: Simplify (+ 0 -1) into -1
19.324 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
19.325 * [backup-simplify]: Simplify (+ (log (* 2.0 PI)) (- (log n))) into (- (log (* 2.0 PI)) (log n))
19.327 * [backup-simplify]: Simplify (* -1 (- (log (* 2.0 PI)) (log n))) into (* -1 (- (log (* 2.0 PI)) (log n)))
19.328 * [backup-simplify]: Simplify (* 0.5 (* -1 (- (log (* 2.0 PI)) (log n)))) into (* -0.5 (- (log (* 2.0 PI)) (log n)))
19.329 * [backup-simplify]: Simplify (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) into (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))
19.329 * [taylor]: Taking taylor expansion of (sqrt k) in k
19.329 * [taylor]: Taking taylor expansion of k in k
19.329 * [backup-simplify]: Simplify 0 into 0
19.329 * [backup-simplify]: Simplify 1 into 1
19.329 * [backup-simplify]: Simplify (sqrt 0) into 0
19.331 * [backup-simplify]: Simplify (/ 1 (* 2 (sqrt 0))) into +nan.0
19.332 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) into 0
19.333 * [backup-simplify]: Simplify (* 1.0 0) into 0
19.333 * [backup-simplify]: Simplify 0 into 0
19.334 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
19.334 * [backup-simplify]: Simplify (+ (* 2.0 0) (* 0 PI)) into 0
19.336 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* 2.0 PI) 1)))) 1) into 0
19.336 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
19.337 * [backup-simplify]: Simplify (- 0) into 0
19.337 * [backup-simplify]: Simplify (+ 0 0) into 0
19.338 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (- 1.0 (/ 1 k)))) into 0
19.339 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
19.340 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (* 0 (- (log (* 2.0 PI)) (log n)))) into 0
19.342 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 1) 1)))) into 0
19.344 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (* 0 (sqrt k))) into 0
19.345 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))) into 0
19.345 * [taylor]: Taking taylor expansion of 0 in k
19.345 * [backup-simplify]: Simplify 0 into 0
19.345 * [backup-simplify]: Simplify 0 into 0
19.347 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
19.349 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0)) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
19.350 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
19.351 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt k))) into 0
19.352 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.353 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (* 0 PI))) into 0
19.357 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* 2.0 PI) 1)))) 2) into 0
19.357 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.357 * [backup-simplify]: Simplify (- 0) into 0
19.358 * [backup-simplify]: Simplify (+ 0 0) into 0
19.359 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k))))) into 0
19.360 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
19.362 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n))))) into 0
19.364 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
19.366 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (* 0 (sqrt k)))) into 0
19.368 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k))))) into 0
19.368 * [taylor]: Taking taylor expansion of 0 in k
19.368 * [backup-simplify]: Simplify 0 into 0
19.368 * [backup-simplify]: Simplify 0 into 0
19.368 * [backup-simplify]: Simplify 0 into 0
19.372 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
19.374 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
19.377 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
19.378 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
19.379 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* 0 0)))) (* 2 (sqrt k))) into 0
19.380 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.381 * [backup-simplify]: Simplify (+ (* 2.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 PI)))) into 0
19.388 * [backup-simplify]: Simplify (/ (+ (* 2 (/ (* (pow (* 1 0) 3)) (pow (* 2.0 PI) 3))) (* -3 (/ (* (pow (* 1 0) 1) (pow (* 2 0) 1)) (pow (* 2.0 PI) 2))) (* 1 (/ (* 1 1 (pow (* 6 0) 1)) (pow (* 2.0 PI) 1)))) 6) into 0
19.388 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.389 * [backup-simplify]: Simplify (- 0) into 0
19.389 * [backup-simplify]: Simplify (+ 0 0) into 0
19.390 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- 1.0 (/ 1 k)))))) into 0
19.392 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* 2.0 PI))) into (- (log (* 2.0 PI)) (log n))
19.394 * [backup-simplify]: Simplify (+ (* (* 0.5 (- 1.0 (/ 1 k))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (- (log (* 2.0 PI)) (log n)))))) into 0
19.397 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (+ (* (/ (pow 0 3) 6)) (* (/ (pow 0 1) 1) (/ (pow 0 1) 1)) (* (/ (pow 0 1) 1)))) into 0
19.399 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) 0) (+ (* 0 0) (+ (* 0 0) (* 0 (sqrt k))))) into 0
19.401 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (+ (* 0 0) (* 0 (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) (sqrt k)))))) into 0
19.402 * [taylor]: Taking taylor expansion of 0 in k
19.402 * [backup-simplify]: Simplify 0 into 0
19.402 * [backup-simplify]: Simplify 0 into 0
19.402 * [backup-simplify]: Simplify 0 into 0
19.402 * [backup-simplify]: Simplify 0 into 0
19.406 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
19.408 * [backup-simplify]: Simplify (+ (* (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))) +nan.0) (+ (* 0 +nan.0) (+ (* 0 +nan.0) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
19.413 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))) (* 0 0)))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
19.414 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n))))))) into (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 k)) (- (log (* 2.0 PI)) (log n)))))))
19.419 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 3)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (pow (* (/ 1 k) 1) 2)) (* (- (* +nan.0 (exp (* 0.5 (* (- 1.0 (/ 1 (/ 1 k))) (- (log (* 2.0 PI)) (log (/ 1 n)))))))) (* (/ 1 k) 1)))) into (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
19.420 * [backup-simplify]: Simplify (/ (* 1.0 (pow (* (* 2.0 PI) (/ 1 (- n))) (/ (- 1.0 (/ 1 (- k))) 2.0))) (sqrt (/ 1 (- k)))) into (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))))
19.420 * [approximate]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in (n k) around 0
19.420 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in k
19.420 * [taylor]: Taking taylor expansion of 1.0 in k
19.420 * [backup-simplify]: Simplify 1.0 into 1.0
19.420 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in k
19.420 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in k
19.420 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in k
19.420 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in k
19.420 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in k
19.420 * [taylor]: Taking taylor expansion of 0.5 in k
19.420 * [backup-simplify]: Simplify 0.5 into 0.5
19.420 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
19.420 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.420 * [taylor]: Taking taylor expansion of k in k
19.420 * [backup-simplify]: Simplify 0 into 0
19.420 * [backup-simplify]: Simplify 1 into 1
19.421 * [backup-simplify]: Simplify (/ 1 1) into 1
19.421 * [taylor]: Taking taylor expansion of 1.0 in k
19.421 * [backup-simplify]: Simplify 1.0 into 1.0
19.421 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in k
19.421 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in k
19.421 * [taylor]: Taking taylor expansion of -2.0 in k
19.421 * [backup-simplify]: Simplify -2.0 into -2.0
19.421 * [taylor]: Taking taylor expansion of (/ PI n) in k
19.421 * [taylor]: Taking taylor expansion of PI in k
19.421 * [backup-simplify]: Simplify PI into PI
19.421 * [taylor]: Taking taylor expansion of n in k
19.421 * [backup-simplify]: Simplify n into n
19.421 * [backup-simplify]: Simplify (/ PI n) into (/ PI n)
19.422 * [backup-simplify]: Simplify (* -2.0 (/ PI n)) into (* -2.0 (/ PI n))
19.422 * [backup-simplify]: Simplify (log (* -2.0 (/ PI n))) into (log (* -2.0 (/ PI n)))
19.422 * [backup-simplify]: Simplify (+ 1 0) into 1
19.423 * [backup-simplify]: Simplify (* 0.5 1) into 0.5
19.423 * [backup-simplify]: Simplify (* 0.5 (log (* -2.0 (/ PI n)))) into (* 0.5 (log (* -2.0 (/ PI n))))
19.423 * [backup-simplify]: Simplify (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) into (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0))))
19.423 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
19.423 * [taylor]: Taking taylor expansion of (/ -1 k) in k
19.423 * [taylor]: Taking taylor expansion of -1 in k
19.423 * [backup-simplify]: Simplify -1 into -1
19.423 * [taylor]: Taking taylor expansion of k in k
19.423 * [backup-simplify]: Simplify 0 into 0
19.423 * [backup-simplify]: Simplify 1 into 1
19.424 * [backup-simplify]: Simplify (/ -1 1) into -1
19.424 * [backup-simplify]: Simplify (sqrt 0) into 0
19.426 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
19.426 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (log (* -2.0 (/ PI n))) (+ (/ 1 k) 1.0)))))
19.426 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
19.426 * [taylor]: Taking taylor expansion of 1.0 in n
19.426 * [backup-simplify]: Simplify 1.0 into 1.0
19.426 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
19.426 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
19.426 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
19.426 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
19.426 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
19.426 * [taylor]: Taking taylor expansion of 0.5 in n
19.426 * [backup-simplify]: Simplify 0.5 into 0.5
19.426 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
19.426 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.426 * [taylor]: Taking taylor expansion of k in n
19.426 * [backup-simplify]: Simplify k into k
19.426 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.426 * [taylor]: Taking taylor expansion of 1.0 in n
19.427 * [backup-simplify]: Simplify 1.0 into 1.0
19.427 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
19.427 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
19.427 * [taylor]: Taking taylor expansion of -2.0 in n
19.427 * [backup-simplify]: Simplify -2.0 into -2.0
19.427 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.427 * [taylor]: Taking taylor expansion of PI in n
19.427 * [backup-simplify]: Simplify PI into PI
19.427 * [taylor]: Taking taylor expansion of n in n
19.427 * [backup-simplify]: Simplify 0 into 0
19.427 * [backup-simplify]: Simplify 1 into 1
19.427 * [backup-simplify]: Simplify (/ PI 1) into PI
19.428 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
19.429 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
19.429 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
19.429 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
19.431 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
19.432 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
19.433 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
19.433 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
19.433 * [taylor]: Taking taylor expansion of (/ -1 k) in n
19.433 * [taylor]: Taking taylor expansion of -1 in n
19.433 * [backup-simplify]: Simplify -1 into -1
19.433 * [taylor]: Taking taylor expansion of k in n
19.433 * [backup-simplify]: Simplify k into k
19.433 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
19.434 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
19.434 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
19.434 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
19.435 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
19.436 * [taylor]: Taking taylor expansion of (* 1.0 (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k)))) in n
19.436 * [taylor]: Taking taylor expansion of 1.0 in n
19.436 * [backup-simplify]: Simplify 1.0 into 1.0
19.436 * [taylor]: Taking taylor expansion of (/ (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) (sqrt (/ -1 k))) in n
19.436 * [taylor]: Taking taylor expansion of (pow (* -2.0 (/ PI n)) (* 0.5 (+ (/ 1 k) 1.0))) in n
19.436 * [taylor]: Taking taylor expansion of (exp (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n))))) in n
19.436 * [taylor]: Taking taylor expansion of (* (* 0.5 (+ (/ 1 k) 1.0)) (log (* -2.0 (/ PI n)))) in n
19.436 * [taylor]: Taking taylor expansion of (* 0.5 (+ (/ 1 k) 1.0)) in n
19.436 * [taylor]: Taking taylor expansion of 0.5 in n
19.436 * [backup-simplify]: Simplify 0.5 into 0.5
19.436 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in n
19.436 * [taylor]: Taking taylor expansion of (/ 1 k) in n
19.436 * [taylor]: Taking taylor expansion of k in n
19.436 * [backup-simplify]: Simplify k into k
19.436 * [backup-simplify]: Simplify (/ 1 k) into (/ 1 k)
19.436 * [taylor]: Taking taylor expansion of 1.0 in n
19.436 * [backup-simplify]: Simplify 1.0 into 1.0
19.436 * [taylor]: Taking taylor expansion of (log (* -2.0 (/ PI n))) in n
19.436 * [taylor]: Taking taylor expansion of (* -2.0 (/ PI n)) in n
19.436 * [taylor]: Taking taylor expansion of -2.0 in n
19.436 * [backup-simplify]: Simplify -2.0 into -2.0
19.436 * [taylor]: Taking taylor expansion of (/ PI n) in n
19.436 * [taylor]: Taking taylor expansion of PI in n
19.436 * [backup-simplify]: Simplify PI into PI
19.436 * [taylor]: Taking taylor expansion of n in n
19.436 * [backup-simplify]: Simplify 0 into 0
19.436 * [backup-simplify]: Simplify 1 into 1
19.437 * [backup-simplify]: Simplify (/ PI 1) into PI
19.438 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
19.439 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
19.439 * [backup-simplify]: Simplify (+ (/ 1 k) 1.0) into (+ (/ 1 k) 1.0)
19.439 * [backup-simplify]: Simplify (* 0.5 (+ (/ 1 k) 1.0)) into (* 0.5 (+ (/ 1 k) 1.0))
19.441 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
19.442 * [backup-simplify]: Simplify (* (* 0.5 (+ (/ 1 k) 1.0)) (- (log (* -2.0 PI)) (log n))) into (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))
19.449 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
19.449 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in n
19.449 * [taylor]: Taking taylor expansion of (/ -1 k) in n
19.449 * [taylor]: Taking taylor expansion of -1 in n
19.450 * [backup-simplify]: Simplify -1 into -1
19.450 * [taylor]: Taking taylor expansion of k in n
19.450 * [backup-simplify]: Simplify k into k
19.450 * [backup-simplify]: Simplify (/ -1 k) into (/ -1 k)
19.450 * [backup-simplify]: Simplify (sqrt (/ -1 k)) into (sqrt (/ -1 k))
19.450 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)))) into 0
19.450 * [backup-simplify]: Simplify (/ 0 (* 2 (sqrt (/ -1 k)))) into 0
19.451 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) into (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))
19.453 * [backup-simplify]: Simplify (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) into (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))))
19.453 * [taylor]: Taking taylor expansion of (* 1.0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))) in k
19.453 * [taylor]: Taking taylor expansion of 1.0 in k
19.453 * [backup-simplify]: Simplify 1.0 into 1.0
19.453 * [taylor]: Taking taylor expansion of (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) in k
19.453 * [taylor]: Taking taylor expansion of (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) in k
19.453 * [taylor]: Taking taylor expansion of (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))) in k
19.453 * [taylor]: Taking taylor expansion of 0.5 in k
19.453 * [backup-simplify]: Simplify 0.5 into 0.5
19.453 * [taylor]: Taking taylor expansion of (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)) in k
19.453 * [taylor]: Taking taylor expansion of (- (log (* -2.0 PI)) (log n)) in k
19.453 * [taylor]: Taking taylor expansion of (log (* -2.0 PI)) in k
19.453 * [taylor]: Taking taylor expansion of (* -2.0 PI) in k
19.453 * [taylor]: Taking taylor expansion of -2.0 in k
19.453 * [backup-simplify]: Simplify -2.0 into -2.0
19.453 * [taylor]: Taking taylor expansion of PI in k
19.453 * [backup-simplify]: Simplify PI into PI
19.454 * [backup-simplify]: Simplify (* -2.0 PI) into (* -2.0 PI)
19.455 * [backup-simplify]: Simplify (log (* -2.0 PI)) into (log (* -2.0 PI))
19.455 * [taylor]: Taking taylor expansion of (log n) in k
19.455 * [taylor]: Taking taylor expansion of n in k
19.455 * [backup-simplify]: Simplify n into n
19.455 * [backup-simplify]: Simplify (log n) into (log n)
19.455 * [taylor]: Taking taylor expansion of (+ (/ 1 k) 1.0) in k
19.455 * [taylor]: Taking taylor expansion of (/ 1 k) in k
19.455 * [taylor]: Taking taylor expansion of k in k
19.455 * [backup-simplify]: Simplify 0 into 0
19.455 * [backup-simplify]: Simplify 1 into 1
19.455 * [backup-simplify]: Simplify (/ 1 1) into 1
19.455 * [taylor]: Taking taylor expansion of 1.0 in k
19.455 * [backup-simplify]: Simplify 1.0 into 1.0
19.455 * [backup-simplify]: Simplify (- (log n)) into (- (log n))
19.456 * [backup-simplify]: Simplify (+ (log (* -2.0 PI)) (- (log n))) into (- (log (* -2.0 PI)) (log n))
19.457 * [backup-simplify]: Simplify (+ 1 0) into 1
19.458 * [backup-simplify]: Simplify (* (- (log (* -2.0 PI)) (log n)) 1) into (- (log (* -2.0 PI)) (log n))
19.459 * [backup-simplify]: Simplify (* 0.5 (- (log (* -2.0 PI)) (log n))) into (* 0.5 (- (log (* -2.0 PI)) (log n)))
19.460 * [backup-simplify]: Simplify (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) into (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))
19.460 * [taylor]: Taking taylor expansion of (sqrt (/ -1 k)) in k
19.460 * [taylor]: Taking taylor expansion of (/ -1 k) in k
19.460 * [taylor]: Taking taylor expansion of -1 in k
19.460 * [backup-simplify]: Simplify -1 into -1
19.460 * [taylor]: Taking taylor expansion of k in k
19.460 * [backup-simplify]: Simplify 0 into 0
19.460 * [backup-simplify]: Simplify 1 into 1
19.461 * [backup-simplify]: Simplify (/ -1 1) into -1
19.461 * [backup-simplify]: Simplify (sqrt 0) into 0
19.462 * [backup-simplify]: Simplify (/ -1 (* 2 (sqrt 0))) into +nan.0
19.464 * [backup-simplify]: Simplify (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) +nan.0) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
19.465 * [backup-simplify]: Simplify (* 1.0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
19.466 * [backup-simplify]: Simplify (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) into (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))
19.467 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)))) into 0
19.468 * [backup-simplify]: Simplify (+ (* -2.0 0) (* 0 PI)) into 0
19.469 * [backup-simplify]: Simplify (/ (+ (* 1 (/ (* (pow (* 1 0) 1)) (pow (* -2.0 PI) 1)))) 1) into 0
19.470 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)))) into 0
19.470 * [backup-simplify]: Simplify (+ 0 0) into 0
19.471 * [backup-simplify]: Simplify (+ (* 0.5 0) (* 0 (+ (/ 1 k) 1.0))) into 0
19.472 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
19.474 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (* 0 (- (log (* -2.0 PI)) (log n)))) into 0
19.476 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 1) 1)))) into 0
19.477 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))))) into 0
19.479 * [backup-simplify]: Simplify (+ (* 1.0 0) (* 0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))))) into 0
19.479 * [taylor]: Taking taylor expansion of 0 in k
19.479 * [backup-simplify]: Simplify 0 into 0
19.479 * [backup-simplify]: Simplify 0 into 0
19.480 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)))) into 0
19.484 * [backup-simplify]: Simplify (/ (- 0 (pow +nan.0 2) (+)) (* 2 0)) into +nan.0
19.486 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
19.489 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
19.490 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
19.492 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* PI (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.493 * [backup-simplify]: Simplify (+ (* -2.0 0) (+ (* 0 0) (* 0 PI))) into 0
19.495 * [backup-simplify]: Simplify (/ (+ (* -1 (/ (* (pow (* 1 0) 2)) (pow (* -2.0 PI) 2))) (* 1 (/ (* 1 (pow (* 2 0) 1)) (pow (* -2.0 PI) 1)))) 2) into 0
19.495 * [backup-simplify]: Simplify (- (+ (* (/ 1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.495 * [backup-simplify]: Simplify (+ 0 0) into 0
19.496 * [backup-simplify]: Simplify (+ (* 0.5 0) (+ (* 0 0) (* 0 (+ (/ 1 k) 1.0)))) into 0
19.497 * [backup-simplify]: Simplify (+ (* (- 1) (log n)) (log (* -2.0 PI))) into (- (log (* -2.0 PI)) (log n))
19.498 * [backup-simplify]: Simplify (+ (* (* 0.5 (+ (/ 1 k) 1.0)) 0) (+ (* 0 0) (* 0 (- (log (* -2.0 PI)) (log n))))) into 0
19.499 * [backup-simplify]: Simplify (* (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (+ (* (/ (pow 0 2) 2)) (* (/ (pow 0 1) 1)))) into 0
19.499 * [backup-simplify]: Simplify (- (/ 0 k) (+ (* (/ -1 k) (/ 0 k)) (* 0 (/ 0 k)))) into 0
19.500 * [backup-simplify]: Simplify (/ (- 0 (pow 0 2) (+)) (* 2 (sqrt (/ -1 k)))) into 0
19.501 * [backup-simplify]: Simplify (- (/ 0 (sqrt (/ -1 k))) (+ (* (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k))) (/ 0 (sqrt (/ -1 k)))) (* 0 (/ 0 (sqrt (/ -1 k)))))) into 0
19.502 * [backup-simplify]: Simplify (+ (* 1.0 0) (+ (* 0 0) (* 0 (/ (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))) (sqrt (/ -1 k)))))) into 0
19.502 * [taylor]: Taking taylor expansion of 0 in k
19.502 * [backup-simplify]: Simplify 0 into 0
19.502 * [backup-simplify]: Simplify 0 into 0
19.502 * [backup-simplify]: Simplify 0 into 0
19.503 * [backup-simplify]: Simplify (- (/ 0 1) (+ (* -1 (/ 0 1)) (* 0 (/ 0 1)))) into 0
19.505 * [backup-simplify]: Simplify (/ (- 0 (+ (* 2 (* +nan.0 +nan.0)))) (* 2 0)) into +nan.0
19.507 * [backup-simplify]: Simplify (- (/ 0 +nan.0) (+ (* (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))) (/ +nan.0 +nan.0)) (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) (/ +nan.0 +nan.0)))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
19.510 * [backup-simplify]: Simplify (+ (* 1.0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (+ (* 0 (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))) (* 0 (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
19.511 * [backup-simplify]: Simplify (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0)))))) into (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log n)) (+ (/ 1 k) 1.0))))))
19.513 * [backup-simplify]: Simplify (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (pow (* (/ 1 (- k)) 1) 2)) (+ (* (- (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0)))))) (* (/ 1 (- k)) 1)) (* +nan.0 (exp (* 0.5 (* (- (log (* -2.0 PI)) (log (/ 1 (- n)))) (+ (/ 1 (/ 1 (- k))) 1.0))))))) into (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))))))))
19.513 * * * [progress]: simplifying candidates
19.518 * [simplify]: Simplifying:
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (+ (log 2.0) (log PI)) (log n))
  (+ (log (* 2.0 PI)) (log n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* (* 2.0 2.0) 2.0) (* (* PI PI) PI)) (* (* n n) n))
  (* (* (* (* 2.0 PI) (* 2.0 PI)) (* 2.0 PI)) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (* 2.0 PI) (* (cbrt n) (cbrt n)))
  (* (* 2.0 PI) (sqrt n))
  (* (* 2.0 PI) 1)
  (* PI n)
  (expm1 (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (log1p (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
  (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))
  (+ (log (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (log (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (log (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (exp (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (* (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (* (* (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (* (cbrt (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))) (cbrt (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))))
  (cbrt (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (* (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))) (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))) (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))
  (sqrt (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (sqrt (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (* (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))))
  (* (sqrt (sqrt k)) (sqrt (sqrt (sqrt k))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (* (cbrt (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))) (cbrt (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (* (cbrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))) (cbrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))))) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k))))) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (* (cbrt k) (cbrt k))))) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt 1))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt 1))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt 1))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt 1))) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt 1))) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt 1))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt 1))) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt 1)) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt 1)) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt 1)) (sqrt (sqrt (* (cbrt k) (cbrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt 1)) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt 1)) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt 1)) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt 1)) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt 1)) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt 1)) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 1) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 1) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 1) (sqrt (sqrt (* (cbrt k) (cbrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 1) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 1) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 1) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 1) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 1) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ 1.0 1) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1 (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1 (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt (* (cbrt k) (cbrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1 (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (* (cbrt (sqrt k)) (cbrt (sqrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt (* (cbrt k) (cbrt k)))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt 1)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt 1))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1)))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt 1))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) 1)
  (* (cbrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
  (* (sqrt (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
  (* (sqrt (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))))
  (* (sqrt (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
  (expm1 (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (log1p (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (- (+ (log 1.0) (* (+ (+ (log 2.0) (log PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (+ (log (* 2.0 PI)) (log n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (* (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0))) (log (sqrt k)))
  (- (+ (log 1.0) (log (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k)))
  (- (log (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (log (sqrt k)))
  (log (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (exp (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (/ (* (* (* 1.0 1.0) 1.0) (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (/ (* (* (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
  (* (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))))
  (cbrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (* (* (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k)))
  (- (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (- (sqrt k))
  (/ 1.0 (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (sqrt (* (cbrt k) (cbrt k))))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 (sqrt 1))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  (/ 1.0 1)
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (* (cbrt (sqrt k)) (cbrt (sqrt k))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (* (cbrt k) (cbrt k))))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt 1))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))
  (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) 1)
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (* 2.0 (* n PI))
  (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k)))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2))))) (- (+ (* +nan.0 (* (pow (sqrt 1.0) 2) (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))))) (- (* +nan.0 (* (pow (sqrt 1.0) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))))))))))))))))))))))
  (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) (pow k 3))) (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) k)) (- (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow (sqrt 1.0) 2)) (pow k 2))))))))
  (- (+ (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2)) k)) (- (+ (* +nan.0 (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2))) (- (* +nan.0 (/ (* (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow (sqrt 1.0) 2)) (pow k 2))))))))
  (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2))))) (- (+ (* +nan.0 (exp (* 0.5 (+ (log (* 2.0 PI)) (log n))))) (- (+ (* +nan.0 (* (pow (log (* 2.0 PI)) 2) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (pow (log n) 2) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) (pow k 2)))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (pow k 2)))) (- (+ (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) (* (log n) k))) (- (+ (* +nan.0 (* (log (* 2.0 PI)) (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k))) (- (* +nan.0 (* (exp (* 0.5 (+ (log (* 2.0 PI)) (log n)))) k)))))))))))))))))))))
  (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 2))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* 2.0 PI)) (log (/ 1 n)))))) (pow k 3))))))))
  (- (+ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n))))))) (- (+ (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) k)) (- (* +nan.0 (/ (exp (* 0.5 (* (- 1.0 k) (- (log (* -2.0 PI)) (log (/ -1 n)))))) (pow k 2))))))))
19.526 * * [simplify]: iteration 0: 566 enodes
19.784 * * [simplify]: iteration 1: 1366 enodes
20.114 * * [simplify]: iteration complete: 5000 enodes
20.114 * * [simplify]: Extracting #0: cost 106 inf + 0
20.117 * * [simplify]: Extracting #1: cost 761 inf + 1
20.125 * * [simplify]: Extracting #2: cost 1277 inf + 5358
20.139 * * [simplify]: Extracting #3: cost 1363 inf + 39690
20.153 * * [simplify]: Extracting #4: cost 1385 inf + 70419
20.189 * * [simplify]: Extracting #5: cost 1091 inf + 205519
20.275 * * [simplify]: Extracting #6: cost 643 inf + 436819
20.446 * * [simplify]: Extracting #7: cost 264 inf + 692543
20.677 * * [simplify]: Extracting #8: cost 93 inf + 816930
20.927 * * [simplify]: Extracting #9: cost 81 inf + 819987
21.148 * * [simplify]: Extracting #10: cost 32 inf + 850015
21.363 * * [simplify]: Extracting #11: cost 0 inf + 869897
21.602 * * [simplify]: Extracting #12: cost 0 inf + 863812
21.849 * [simplify]: Simplified to:
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* n n) n) (* (* 2.0 (* (* 2.0 PI) (* 2.0 PI))) PI))
  (* (* (* 2.0 PI) (* (* 2.0 PI) (* 2.0 PI))) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (cbrt n) (* (cbrt n) (* 2.0 PI)))
  (* 2.0 (* PI (sqrt n)))
  (* 2.0 PI)
  (* n PI)
  (expm1 (* (* 2.0 PI) n))
  (log1p (* (* 2.0 PI) n))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (log (* (* 2.0 PI) n))
  (exp (* (* 2.0 PI) n))
  (* (* (* n n) n) (* (* 2.0 (* (* 2.0 PI) (* 2.0 PI))) PI))
  (* (* (* 2.0 PI) (* (* 2.0 PI) (* 2.0 PI))) (* (* n n) n))
  (* (cbrt (* (* 2.0 PI) n)) (cbrt (* (* 2.0 PI) n)))
  (cbrt (* (* 2.0 PI) n))
  (* (* (* (* 2.0 PI) n) (* (* 2.0 PI) n)) (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (sqrt (* (* 2.0 PI) n))
  (* (cbrt n) (* (cbrt n) (* 2.0 PI)))
  (* 2.0 (* PI (sqrt n)))
  (* 2.0 PI)
  (* n PI)
  (expm1 (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (log1p (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))
  (* (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (- (fma (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0) (log 1.0)) (log (sqrt k)))
  (- (fma (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0) (log 1.0)) (log (sqrt k)))
  (exp (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (* (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (cbrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (cbrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (cbrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (* (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0)))
  (* (sqrt (sqrt (sqrt k))) (sqrt (sqrt k)))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (/ (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (/ (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (/ (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (/ (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (/ (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (/ (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (/ (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (/ (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (/ (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (/ (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (/ (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (/ (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (* (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (* (cbrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (cbrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (fabs (cbrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (fabs (/ (cbrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (* (cbrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (fabs (cbrt (sqrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (cbrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (/ (sqrt (fabs (cbrt k))) (cbrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))))))
  (* (sqrt (/ (* (cbrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (sqrt (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (fabs (cbrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))))
  (* (sqrt (/ (* (cbrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (sqrt (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (fabs (cbrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))))
  (* (sqrt (/ (* (cbrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (sqrt (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (fabs (cbrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))))
  (* (sqrt (/ (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (fabs (cbrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (fabs (cbrt k))))))
  (* (sqrt (/ (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ 1.0 (* (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (* (fabs (cbrt (sqrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (* (sqrt (fabs (cbrt k))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k))))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))))
  (* (sqrt (/ (/ (/ 1.0 (fabs (cbrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k)))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (fabs (cbrt (sqrt k)))) (sqrt (fabs (cbrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (fabs (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ 1.0 (fabs (cbrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (fabs (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ 1.0 (fabs (cbrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (fabs (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ 1.0 (fabs (cbrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (fabs (cbrt k)))) (* (cbrt (sqrt (sqrt k))) (cbrt (sqrt (sqrt k)))))))
  (* (sqrt (/ 1.0 (* (fabs (cbrt (sqrt k))) (sqrt (fabs (cbrt k)))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ 1.0 (fabs (cbrt k)))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (fabs (cbrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (fabs (cbrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (fabs (cbrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (fabs (cbrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (sqrt (fabs (cbrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (fabs (cbrt k))))))
  (* (sqrt (/ (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (/ 1.0 (fabs (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (fabs (cbrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))))
  (* (sqrt (/ 1.0 (fabs (cbrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (fabs (cbrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k))))))
  (* (sqrt 1.0) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k))))))
  (* (sqrt 1.0) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k))))))
  (* (sqrt 1.0) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (/ 1.0 (fabs (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (fabs (cbrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))))
  (* (sqrt (/ 1.0 (fabs (cbrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (fabs (cbrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k))))))
  (* (sqrt 1.0) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k))))))
  (* (sqrt 1.0) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k))))))
  (* (sqrt 1.0) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (/ (/ 1.0 (sqrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (/ 1.0 (fabs (cbrt (sqrt k)))) (sqrt (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (sqrt (fabs (cbrt k)))) (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt k)))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (/ 1.0 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))))
  (* (sqrt (/ 1.0 (fabs (cbrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (fabs (cbrt k))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k))))))
  (* (sqrt 1.0) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k))))))
  (* (sqrt 1.0) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (sqrt (sqrt (sqrt k))))))
  (* (sqrt 1.0) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (/ 1 (cbrt (sqrt (sqrt k)))) (cbrt (sqrt (sqrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1 (fabs (cbrt (sqrt k))))))
  (* (sqrt (/ 1 (sqrt (fabs (cbrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt (sqrt k))))))
  (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt (sqrt k))))))
  (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1 (sqrt (sqrt (sqrt k))))))
  (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (sqrt (* (/ 1.0 (cbrt (sqrt (sqrt k)))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt (sqrt k)))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ 1.0 (/ (fabs (cbrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt (fabs (cbrt k))))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (/ (sqrt (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (* (sqrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0)) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (/ (sqrt (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (* (sqrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0)) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (/ (sqrt (sqrt (sqrt k))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (* (sqrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0)) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (cbrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (cbrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))))
  (* (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))))
  (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))
  (* (sqrt (/ 1 (sqrt k))) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))))
  (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))
  (* (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (sqrt (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))))
  (* (sqrt (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0)) (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (expm1 (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (log1p (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (- (fma (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0) (log 1.0)) (log (sqrt k)))
  (- (fma (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0) (log 1.0)) (log (sqrt k)))
  (- (fma (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0) (log 1.0)) (log (sqrt k)))
  (- (fma (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0) (log 1.0)) (log (sqrt k)))
  (- (fma (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0) (log 1.0)) (log (sqrt k)))
  (- (fma (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0) (log 1.0)) (log (sqrt k)))
  (- (fma (log (* (* 2.0 PI) n)) (/ (- 1.0 k) 2.0) (log 1.0)) (log (sqrt k)))
  (exp (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (/ (* (* 1.0 1.0) 1.0) (sqrt k)) (/ (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) k))
  (* (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (/ (* (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0)) k))
  (* (cbrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))) (cbrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (cbrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (* (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)) (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
  (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (sqrt (/ (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k)))
  (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (- 1.0))
  (- (sqrt k))
  (/ (/ 1.0 (cbrt (sqrt k))) (cbrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k)))
  (/ 1.0 (fabs (cbrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k)))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1.0 (sqrt (sqrt k)))
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
  1.0
  (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
  (/ 1 (sqrt k))
  (/ (sqrt k) (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0))
  (* (/ 1.0 (cbrt (sqrt k))) (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (cbrt (sqrt k))))
  (/ 1.0 (/ (fabs (cbrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0)
  (/ 1.0 (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
  (* (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) 1.0)
  (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
  (* (pow (* (* 2.0 PI) n) (/ k 2.0)) (sqrt k))
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (* (* 2.0 PI) n)
  (+ (* (* (* 1.0 (* (log n) k)) (exp (* 0.5 (log (* (* 2.0 PI) n))))) (- +nan.0)) (fma +nan.0 (* (* 1.0 (exp (* 0.5 (log (* (* 2.0 PI) n))))) k) (+ (* (* +nan.0 (log (* 2.0 PI))) (- (* (* 1.0 (exp (* 0.5 (log (* (* 2.0 PI) n))))) k))) (fma (* +nan.0 (log (* 2.0 PI))) (* (* 1.0 (exp (* 0.5 (log (* (* 2.0 PI) n))))) (* k k)) (- (fma (* (* 1.0 (exp (* 0.5 (log (* (* 2.0 PI) n))))) (* k k)) +nan.0 (- (fma (* +nan.0 (log (* 2.0 PI))) (* (* (exp (* 0.5 (log (* (* 2.0 PI) n)))) (* (log n) (* k k))) 1.0) (+ (+ (* (- (* (* +nan.0 (log (* 2.0 PI))) (log (* 2.0 PI)))) (* (* 1.0 (exp (* 0.5 (log (* (* 2.0 PI) n))))) (* k k))) (+ (* (* +nan.0 (* 1.0 (exp (* 0.5 (log (* (* 2.0 PI) n)))))) (* (log n) (* k k))) (* +nan.0 (* 1.0 (exp (* 0.5 (log (* (* 2.0 PI) n)))))))) (- (* (* +nan.0 (* 1.0 (exp (* 0.5 (log (* (* 2.0 PI) n)))))) (* (* k (log n)) (* k (log n))))))))))))))
  (+ (* (/ (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))) (/ (* (* k k) k) 1.0)) (- +nan.0)) (- (/ (* (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))) +nan.0) (/ k 1.0)) (/ (* (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))) +nan.0) (/ (* k k) 1.0))))
  (+ (- (* (* +nan.0 (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5)))) 1.0) (* (/ (* +nan.0 (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5)))) k) (/ 1.0 k))) (/ (* (* +nan.0 (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5)))) (- 1.0)) k))
  (+ (- (* (exp (* 0.5 (log (* (* 2.0 PI) n)))) +nan.0) (fma +nan.0 (* (* (exp (* 0.5 (log (* (* 2.0 PI) n)))) (* (* k k) (log (* 2.0 PI)))) (log (* 2.0 PI))) (- (+ (- (* (* (exp (* 0.5 (log (* (* 2.0 PI) n)))) +nan.0) (* k k)) (* (* (* (exp (* 0.5 (log (* (* 2.0 PI) n)))) +nan.0) (* k k)) (* (log n) (log n)))) (fma (* (exp (* 0.5 (log (* (* 2.0 PI) n)))) (* (log n) (* k k))) +nan.0 (+ (* (- +nan.0) (* (exp (* 0.5 (log (* (* 2.0 PI) n)))) (* (* k k) (log (* 2.0 PI))))) (- (* (exp (* 0.5 (log (* (* 2.0 PI) n)))) (* (* (log n) k) +nan.0)) (fma (- +nan.0) (* (exp (* 0.5 (log (* (* 2.0 PI) n)))) k) (* (* (* (exp (* 0.5 (log (* (* 2.0 PI) n)))) k) (log (* 2.0 PI))) +nan.0))))))))) (* (* +nan.0 (log (* 2.0 PI))) (- (* (exp (* 0.5 (log (* (* 2.0 PI) n)))) (* (log n) (* k k))))))
  (- (- (/ (* +nan.0 (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n)))))) (* k k)) (* +nan.0 (- (/ (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))) k) (/ (exp (* 0.5 (* (- 1.0 k) (log (* (* 2.0 PI) n))))) (* (* k k) k))))))
  (- (- (* +nan.0 (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5)))) (- (/ (* +nan.0 (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5)))) k) (/ (* +nan.0 (exp (* (- (log (* PI -2.0)) (log (/ -1 n))) (* (- 1.0 k) 0.5)))) (* k k)))))
21.894 * * * [progress]: adding candidates to table
23.486 * [progress]: [Phase 3 of 3] Extracting.
23.486 * * [regime]: Finding splitpoints for: (#<alt (λ (k n) (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ (* 1.0 (pow (pow (* (* n 2.0) PI) (+ (sqrt k) (sqrt 1.0))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k)))> #<alt (λ (k n) (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) 1))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt k))))))> #<alt (λ (k n) (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))> #<alt (λ (k n) (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))))))> #<alt (λ (k n) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))>)
23.490 * * * [regime-changes]: Trying 3 branch expressions: ((* (* 2.0 PI) n) n k)
23.490 * * * * [regimes]: Trying to branch on (* (* 2.0 PI) n) from (#<alt (λ (k n) (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ (* 1.0 (pow (pow (* (* n 2.0) PI) (+ (sqrt k) (sqrt 1.0))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k)))> #<alt (λ (k n) (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) 1))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt k))))))> #<alt (λ (k n) (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))> #<alt (λ (k n) (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))))))> #<alt (λ (k n) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))>)
23.559 * * * * [regimes]: Trying to branch on n from (#<alt (λ (k n) (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ (* 1.0 (pow (pow (* (* n 2.0) PI) (+ (sqrt k) (sqrt 1.0))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k)))> #<alt (λ (k n) (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) 1))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt k))))))> #<alt (λ (k n) (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))> #<alt (λ (k n) (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))))))> #<alt (λ (k n) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))>)
23.651 * * * * [regimes]: Trying to branch on k from (#<alt (λ (k n) (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k))))))> #<alt (λ (k n) (/ (* 1.0 (pow (pow (* (* n 2.0) PI) (+ (sqrt k) (sqrt 1.0))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k)))> #<alt (λ (k n) (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) 1))) (sqrt (/ (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k)))) (sqrt (sqrt k))))))> #<alt (λ (k n) (* (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))))> #<alt (λ (k n) (* (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ 1.0 (sqrt (* (cbrt k) (cbrt k)))))) (sqrt (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (cbrt k))))))> #<alt (λ (k n) (* (* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k)))) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))> #<alt (λ (k n) (/ (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (pow (* (* 2.0 PI) n) (/ k 2.0))))>)
23.770 * * * [regime]: Found split indices: #<option (#s(si 0 255))>
23.770 * [simplify]: Simplifying:
  (* (sqrt (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))) (sqrt (/ (/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt (sqrt k))) (sqrt (sqrt k)))))
23.771 * * [simplify]: iteration 0: 19 enodes
23.773 * * [simplify]: iteration 1: 23 enodes
23.775 * * [simplify]: iteration complete: 23 enodes
23.775 * * [simplify]: Extracting #0: cost 1 inf + 0
23.775 * * [simplify]: Extracting #1: cost 3 inf + 0
23.775 * * [simplify]: Extracting #2: cost 5 inf + 0
23.775 * * [simplify]: Extracting #3: cost 9 inf + 0
23.775 * * [simplify]: Extracting #4: cost 12 inf + 0
23.776 * * [simplify]: Extracting #5: cost 10 inf + 124
23.776 * * [simplify]: Extracting #6: cost 14 inf + 124
23.776 * * [simplify]: Extracting #7: cost 12 inf + 168
23.776 * * [simplify]: Extracting #8: cost 7 inf + 752
23.776 * * [simplify]: Extracting #9: cost 3 inf + 2732
23.777 * * [simplify]: Extracting #10: cost 2 inf + 3307
23.778 * * [simplify]: Extracting #11: cost 0 inf + 4657
23.779 * [simplify]: Simplified to:
  (* (sqrt (/ (/ (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt (sqrt k))) (sqrt (sqrt k)))) (sqrt (/ (* (pow (* (* PI 2.0) n) (/ (- 1.0 k) 2.0)) 1.0) (sqrt k))))
30.935 * [regime-testing]: Baseline error score: 0.42650952365267747
30.946 * [regime-testing]: Oracle error score: 0.06474869514984445
30.966 * [regime-testing]: End program error score: 0.42650952365267747